- Kari kolehmainen Samaa tarkoittava suhdelaskenta

These pages are for

Strength of Materials
Studying products
Visual Geometry

Nämä sivut ovat:

Näkemisen geometriaa
Tuotteiden tarkastelua

Visitors - Kävijät

Käyntejä kotisivuilla:396515 kpl

Visual Geometryfinnish_translation.jpg

Näkemisen geometria


  1.     Introduction to Visual Geometry.

  2.     Diameter of the Moon

  3.     Iron After Big Bang

  4.     Cheops Pyramid - Location

  5.     Cheops Pyramid - Speed of Light

  6.     Time Dilation in Pascal's Triangle

  7.     Plato, the Cave Metaphor

  8.     Space Filling.

  9.     Calculation is Divided Into Two Way Study the Phenomena

10.      Pythagorean Pentagon

11.     Number Five to EP-Calculation.


20.     Mother and Child Example.

21.     Euclid's Geometry

22.     EPC and Visual Geometry

23.     Nature Modular Structure.

24.     Right Angle Dimensionality

25.     Point

26.     Pi 3.14 the Length of Rivers

27.     Circle Description

27.1   Circle and Ellipse

27.2   The Fear of Physics

27.3   Describing a Circle of Steel

28.     Circle and Square Areas

29.     Golden Ratio 1.618 in the Circle

30.     Equilateral Triangle

31.     Speed of Light as Geometry

32.     Angles of a Pentagon


39.      Pentagon in Oranges.

40.      Pentagon in Apples.

41.      Pentagon in the Hand

42.      Surface Areas of the Pentagon

43.      Johannes Kepler; Ellipses Description of Planetary Orbits

44.       Ellipse

44.1     Ellipse with the Rope and Two Pins

44.2     Ellipse with Two Circles

44.3     Ellipse Inside the circle

45.       The world's Picture, Areas of the Circles

46.       Friction coefficient 1.03.

47.       Universal Friction 1.03.

48.       Stopping Distance Visual Geometry

49.       Volum of a Pyramid

50.       The Volume of a Ball

50.1     The volume of a Ball; By Formula

50.2    Volume of a Ball; Equivalent Proportional Calculation

50.3    Volume of a Ball; The Golden Section and Gravity

50.4    Volume of a ball; Lifetime to Machine Elements

50.5    Volume of a Ball; Area of the Circle / (π / 1,034)


60.      Pascal's Triangle - Phi 1.618

61.      Pascal's Triangle & Pi (3.14)

61.1    The Nature Factor 1.1

62.      Fibonacci Numbers

           - The Golden Ratio

63.      Golden Ratio in the Products

64.     The Specific Gravity of Steel

65.      Steel Strength as Visual Geometry

65.1    Steel Hardness Golden Ratio

66.      Strength Such as Visual Geometry

66.1    The Golden Triangle

66.2    Bending Shadow

67.      Products, such as Visual Geometry

67.1    Lifting Lugs from 500 to 40,000 kg

68.      Visual Geometry as Physiology

68.1    Short Run Events in Pascal's Triangle.

1.   Introduction to Visual Geometry

One day we do have a wide view of point to calculate things. Even now it may desire to think;

The red perimeter of the circle per the green diagonal line = 3.14

There is no need to know any lengths or diameters. All other same kind of figures have the ratio 3.14. Colours and figures are a visual way to understand them.


Units are human made. By this way thinking, all circles can have their diameter of 1. One millimeter,inch, foott, mail, light year etc. of their diametters. Size of the circle, does not specify a unit to plural form. We calculate e.g. phenomena on products, so the interior area of circle includes in the value of the specific gravity of steel (0,785).

A = pi x r2

A = 3.14 x 0.52

A = 0.785

We stop to this for a moment to find out, letters also having the information of phenomena. All phenomena have originally derived from the formula.

E = m x c2

Energy (E) and the speed of light (c) are not recognized by the mass. This is the mean principle as we think of them.

Letter Codes

In three-dimensional world the first three letter codes of the formula E = m x c2 are known. Pressure can consists of material or from almost tangible media. The mass on the area forms the two-dimensional pressure between the area and materia on it. When an air-bottle, the mass is minimal, but the three-dimensional pressure can be high.

L = length            A = area            V = volume          P = pressure


1.   There is a phenomenon having the shape of a circle (d1)

      The circle is symmetric, so that its width is the same as its height.

      Interior area of circle;          A = Pi x r x r                      (Pi = 3.14)

                                                  A = 3,14 x 0,5 x 0,5

                                                  A = 0.785


2.   There is a phenomenon having the shape of a square

      The square is symmetric, so that its width is the same as its height.

                                            A = 4 x 0,5 x 0,5

                                            A = 1

      It will be appreciated 3.14 / 4 = 0.785

(We calculate e.g. phenomena on products, so the interior area of circle includes in the value of the specific gravity of steel (0,785))

3.   There is a phenomenon having the shape of a ellipse 1.6 x 1 (r = 0,8  ;  s = 0.5)

                                           A = pi x r x s

                                           A = 3.14 x 0.8 x 0.5

                                           A = 1.25

We say to the phenomena to be mutually exclusive, because the phenomena are different. Is this the case, it will look for a while. You know, the mentioned three geometric shape, so they are not presented in detail. I think, you hardly know the geometric form of the phenomenon, so I'll tell them to behave, such as calculatings show the geometrical figures. The surface area is two-dimensional, in which case the two-dimensional (phenomenon) having double values, is four times the mean phenomenon. This is known, but also increases in the value of 0.785 is 4 x 0.785 = Pi (3.14). The main dimensions of the ellipse 1 and 1.6 (18) are the ratio of the all in nature. (880)

1 + 0.618 = 1.618

1 / 1,618 = 0.618

2.   Diameter of the moon


Celestial body need to measure the devicewhich structure is described below. In past time designers used an aperture plate when drawing circles on the drawingsIn addition to this is needed, one meter long piece of a cordParts are cheapThese are enough to determine the diameter of the Moon.

Set 10 mm = 1 centimeter hole of the aperture plate, 111 cm off the eye. Any 10 mm hole is suitable for this. The moon locates exactly in the holeCalculate the diameter of the moon on the basis of the informationThe moon is an average of 384 400 km away from the earthMoon's diameter as literature it say, 3470 km. Measuring error 0.2 %The example provides an idea of a straight linear proportionality.

      1 cm    =           x                => x = 3463 km    

    111 cm        384 400 km

                 1 - 1,12 - 1,25 - 1,6

3.   Iron After Big Bang

No need to go further than the Big Bang, when the number five appears, and later by an understandable way determines the golden ratio in Pascal's triangle, known as a pattern. The pattern known, but not understood to phenomenas.

Strength needs to calculate the material iron, the most common element on Earth. Iron, named steel is the material for this purpose. EP-Calculation five steps is the proportionality limit in values ​​and iron is on this step, the temperature of 4000 Kelvin. The heavier material than iron needs for formation the nuclear fusion. We stay in steel grades (S235 and S355), ie. to the temperature of 4,000 Kelvin, as the table shows. The lighter elements than steel make up 99.99997 % of the composition of stars. Heavier elements than iron are a small minority, but they are two-thirds of the elements.

The formation of metal

Nuclear reaction                                  Temperature 106 K     Pascal's triangle

0. Hydrogen => helium                                 10 - 40                                1

1. Helium => carbon, oxygen                       100 -200                       1           1

2. Carbon => neon, sodium, magnesium         800                     1           2          1

3. Neon => magnesium, silicon                      1 700                1        3            3       1

4. Oxygen => silicon, sulphur                         2 100          1         4          6          4        1

5. Silicon => titanium, Zinc, nickel, Iron          4 000      1       6          1           1         6       1


viisikulmiot.jpgPascal's triangle, the lowest row is the fifth row from the output value of 0. Row five finds the golden ratio 1.618, even the value of 1.611 is slightly different.

The fifth element describes the pentagon where the golden ratio occurs in many. This is described in visual geometry and strength calculation. (985)

4.   Cheops Pyramid Location

The Great Pyramid 2560–2540 BC (the Pyramid of Khufu, or Cheops in Greek) in the Giza, Egypt, demonstrates the remarkable character of its placement on the face of the Earth. The Pyramid lies in the center of gravity of the continents. It also lies in the exact center of all the land area of the world, dividing the earth's land mass into approximately equal quarters. This is visual geometry, which the ancient people carried out through monumental engineering structure. (197)


Pyramids location on the largest mass concentration on the Earth

5.   Cheops Pyramid - Speed of Light

The base of the pyramid has the dimensions of 230.3 x 230.3 m


When drawing two circles around the circle, one outsides the pyramid and the second inside as the image shows.

The outside circle perimeter - the inside cirle perimeter = the speed of the light


Pii x 230.3 = 723.509
Pii x 230.3 x sgrt (2) = 1023.196
1023.196 - 723.509 = 299.687
(The speed of light 299.792 km/s)

Whatever you think of the calculation, it undeniably demonstrates equivalence to the speed of light. (1088)

6.   Time Dilation in Pascal's Triangle

E = m c2


Time dilation table


Pascal's Triangle as  Visual Geometry

1 dim                   1                 m          (1.0328)

2 dim               1      1            m2           1.03283

3 dim           1      2      1        m3            1.03286

4 dim      1       3      3     1     s / t         1.03289

1.03283  = 1.1    -    1,03286  = 1.21    -    1.03289 = 1.337



The Theory of Proportionality

One hundred years after the general theory of relativitythe theory of proportionality explains how the identified astronomical scale matters affect at low speed phenomena on the Earth. This is shown in EP-Calculation.


The first argument is Albert Einstein's theory, which has not been used at low speed phenomena, even the next phrase exhorts to this. (1148)

Special theory of relativity applies to all physical phenomena except gravity

The second argument is that time dilation joins to phenomena on the Earth

At slow speed momentum p is transformed into Lorenz - variant factor 1/L when

L = sqrt (1-( v/c )2)

==>    time dilation 1.0328 when the speed of light 0,25 c

7. Plato, the Cave Metaphor

Visual geometry has its historical background thousands of years' backwards. The calculation is however from this day. I write about the history and today's reality. The calculation is divided in to two different ways to study mathematical phenomena. This is a description of the physics, starting the text of Some Basics of Physics. In the end, quite a lot of things are geometry.

platon_small.jpgPlato used his well known cave metaphor (figure of speech). In which he compared our position in the nature chart to a person who has lived since born in a cave. According to him, the picture of reality has born of real objects which have formed shadows onto the cave's back wall of the moving images. This happened thus, that outside the cave aperture, the real objects in the sun light cast these shadows onto the cave's back wall. Like those who were in a cave, we scrape the surface of reality. We do the same using our sense and ability to understand things around us. More about this can be read in physics website.

8.   Space Filling

The idea of filling the ​​space with similar pieces is 2300 years old. It is believed that the first who considered it was Plato (427 - 347 BC). According to Plato, materia consisted of a polyhedrons satisfying the condition, determining the five regular polyhedrons, and calling these to five regular pieces. These represented his vision of the perfect symmetry of space geometry.


Kuviot Wikipediasta


The regular polyhedron is a piece in which all the facets have the same size and shape, also the angles between adjacent facets are the same. The cube is a good example. The facets are square-shaped, and the angle between the adjacent facets is always 90 degrees. A certificate stating that there are only five such pieces is a large Greek mathematical achievement.

Plato's the most famous student Aristotle suggested that the teacher did not have the right idea. This was based on the fact that many polyhedron, did not meet the space completely, but left a blank space when packing them tightly. Only six-facet pieces of cubes and four-facet tetrahedras filled the space completely. The other was left gaps. For some reason the tetrahedron filled the Platonic idea of ​​the perfect filled space? The perception of the possibility of a tetrahedron fill space completely, remained 1800 years. Today, we know only the six-facet cube to be able to fill the space completely. Now we are coming to number five.

There are nine regular polyhedrons:

Five Plato's pieces:  Dodecahedron, icosahedron, octahedron,Tetrahedron, cube.

Four Kepler-Poinsot'n are star-shaped pieces of regular polyhedrons.  (897)

9.   Calculation is Divided Into Two Way Study the Phenomena

a) Things are studied by calculating and definning phenomena. This trying to avoid formulas.

b) Things are studied by way of patterns, which show the same as calculations do. The procedure is often raised that we are not able to calculate.


Visual objects as the shadows of reality

Pentagon in photo describes human being. There are  two legs, two hands and head. Pentagon expresses the dimensioning of the human body. Not just of human being, all entity being located to construction. More patterns later.


Leonardi da Vinci, Vitruvian man

An ellipse is a particular class of mathematical shapes that resemble a stretched out circle. Ellipse has two focal points. Circle is a special case of an ellipse that is not stretched out and in which both focal points coincide at the center.

10.   Pythagorean Pentagon


The pentagram is a symmetrical 5-pointed star that fits inside a pentagon. From times of Pythagoras pentagon has been the most studied to understand the Golden Ratio 1.618. Today, Pythagoras is not associated with the pentagon, but to the theorem of Pythagoras. Pythagoras does not be connect in any way to Pythagorean theorem, relation in Euclidean geometry among the three sides of a right triangle, this because it was known for a thousand years before Pythagoras. Maybe Sumerians had in the first figured pentagram around 3000 BC.The different thing is how Pythagoras interpreted the pattern and whether there is evidence not even today. Pentagon contains in many sense the ratio of 1.618. Pythagoras took pentagram as a symbol to established selected brotherhood. Among other things, Cheops pyramid includes the golden section ratio of 1.618 in its structure. I mention the pyramids, therefore, that Pythagoras traveled to Egypt, and well acquainted with these works and also the Egyptian mathematics, which was largely based on the geometry.

There is no evidence of that, but let us think so. The pyramids can say that they were thousands of years old when Pythagoras visited to the country. Structures, whose construction does not to this day to be able to explain or repeat due to lack of financial resources. Egyptian mathematical knowledge has been devalued, its accession to a large extent beeing to the flooding of the Nile and the consequent of land areas determination to the farmers. In short, the Egyptians are said to be connected by the number and shape of Mathematics. It can be said the Egyptians determined the mass, ie the farmers grains to a surface area which sides are a times a and this can be a harvest. In a later well-known equation for energy "harvest" obtained by multiplying the mass with surface area, which has the side length of speed of lightThis can be put in the form of E = m c c. This is explained more in my pages, but back to the pentagon.

I will open the pentagon pattern by writing of the history, the strength formation in a matter, and to carry out the Equivalent Proportional Calculation of the products. Many of the things that are countable, can be presented as a geometric patterns. This, because the nature wants to reveal the value as a pattern and present the harmony between things.

The starting point for everything is energy, of which the matter after cooling has condensed. Matter is based on the energy, which is to us visibly detectable mass. When calculating the mass and energy, they have the same meaning to each others. (851)

11.   Number Five to EP-Calculation

viisikulmiot.jpgCalculation introduces pentagon and writings of Pythagoras? Some books warn of this kind of thinkingas if the numbers or figures would include the concept of a mathematical objectStill, a few of the Leonardo da Vinci's name forward and backward have connection to number five and to ratio of 1.618. Visual Geometry is a reality of which has been written.

The following text does not join to the topic, still I put it here. I think it is just fun to do it in this context. You know Leonardo da Vinci as a well-known artist and you will be able to list his works. Do it now, but you say it to be impossible. Some of the preserved paintings (approx. 15 pieces), his notes including drawings, scientific diagrams, and ideas on the nature of paintingmake up a significant effort to later artists, that has competes with only his contemporaries Michelangelo. Leonardo da Vinci was thus one of the most important artists of paintingwithout being actually a painter. Is your understanding of the phenomena at the same level with your knowledge of the Leonardo da VinciYou know a lot, but you do not know everything. If the calculator in your hand does not present the same as I write, please leave my website. I grant you this with pleasureto go back to the fantasy world. The above sentence, because I believe the calculator tells more of the real world than the idea world which are not demonstrable.


Area of ​​the Circle

a) Radius  r = 1
A = π x r = 3.14
b) Radius  r = 2
A = π x r = 12.56
 1 - 1.03 - 1.06 - 1.12 - 1.25 - 1.6 - 2 - 2.5 - 3.15 - 4 - 5 - 6.3 - 8 - 10 (- 12.5)
Full Angle 360o
2 x π rad =6.28 rad.  
1 - 1.03 - 1.06 - 1.12 - 1.25 - 1.6 - 2 - 2.5 - 3.15 - 4 - 5 - 6.3 - 8 - 10
6.28 rad / 2 = 3.14 rad
1 - 1.03 - 1.06 - 1.12 - 1.25 - 1.6 - 2 - 2.5 - 3.15 - 4 - 5 - 6.3  - 8  - 10
3.14 rad / 2
1.570796 rad   => 1.03 x 1.5707 rad = 1.618
1 - 1.03 - 1.06 - 1.12 - 1.25 - 1.6 - 2 - 2.5 - 3.15  - 4 - 5 - 6.3  - 8  - 10
SQRT (1.570796)  = 1.2533
6.28  rad / 5 = 1.256 rad
1 - 1.03 - 1.06 - 1.12 - 1.25 - 1.6 - 2 - 2.5 - 3.15 - 4 - 5 - 6.3  - 8  - 10
SQRT (1.2533)  = 1.12
1 - 1.03 - 1.06 - 1.12 - 1.25 - 1.6 - 2 - 2.5 - 3.15 - 4 - 5 - 6.3  - 8  - 10
SQRT (1.12)  = 1.06
1 - 1.03 - 1.06 - 1,12 - 1.25 - 1.6 - 2 - 2.5 - 3.15 - 4 - 5 - 6.3  - 8  - 10
SQRT (1.06)  = 1.03
1 - 1.03 - 1.06 - 1.12  - 1.25 - 1.6 - 2 - 2.5 - 3.15 -4 - 5 - 6.3  - 8  - 10

The above is visual geometry and calculatings, without apparent patterns. After all, can not see the phenomena themselves, although they certainly exist. On the other hand, we know well phenomena consequencesThey possess (owns) in many cases, the above form in one way or anotherWhy the title of this page is "Number Five", even if it is not present on the page. The reason for this is trying to tell on this pagethat all is not possible to see. I could tell of five finger used to open the computerFive fingerswhich the early counting is based on and continue to pentagon image on this page. (879)

20.   Mother and Child Example

In this time is possible an example, in which someone hides behind a stone. To this intention suits a little child. The child is behind the stone and thinks being well hidden. In addition to this, the mother knows her child's existence commonly - as we know about the matters and values those existence commonly - mother sees the child behind the stone of the formed shadow.


Time is the shadow of the event


The child is behind the stone when the sun shines. The mother cannot see directly the child, but through the shadow mother can see things. Of the child's position the mother is able to conclude an exciting moment in child's life. Do not have to see any children,which in this metaphor describes phenomenons, products and so on. The shadow is something we cannot touch, such as time in connection with the sport result. (774)

21.   Euclid's Geometry

Geometry is not due to the geometry, but in reality due to the necessary specifications. We understand the geometry to calculate surface areas and volumes. However, expressions are finally as surface of a area.

Energy                     M = m c2                 Covering of the light

Paine                         kg/cm2                   Covering of the pressure

Tension                      kN/cm2                   Covering of the force

Velocity                        m/s2                      Covering of the acceleration



Euclid Wrote


One can draw a straight line from any point to any point

Phi-Geometry; the curve can be plotted in any transaction between the two more, if these are known. By the Equivalent Proportional Calculation, even to the events which are not known in advance.


Things equal to the same thing are also equal to one another

Visual Geometry geometry as the surface area, expands the concept of phenomena and events. Euclides saw farther in this sentence. Of the geometry the sentence has no mention.

The extremities of lines are points

Visual Geometry; event or phenomenon is a point of the curve from the beginning, between and at the end of the range. The curve is defined by an infinite number of points.

A line is a breathless length

Visual Geometry; between the two-event or phenomenon is not a vacuum or openings

A straight line lies equally with respect to the points on itself

Visual Geometry; a curve line lies equally events and phenomenas with respects to the point on itself      (733)

22.   EPC and Visual Geometry

Equivalent Proportional Calculation is an approach to understand the structure of the world, the sense in which it affects everyday life. It is startling to read of the three calculations and find that you are writing of two other calculations. Because these are my pages, I can write this. I understand the idea behind the four calculations, but the Category Theory will not open to me. This unintentionally, that the calculation would not have any place alongside the others.  (341)


        Equivalent Proportional Calculation                               Visual Geometry


                 Set Theory                                                     Category Theory            
   Mathematical Logic


More information from the Wikipedia


23.   Nature Modular Structure

Imagine the blue lines to be steel tubes and structure forming the half of the roof truss. The relative lengths of the tubes are 1, 1.618 and 2.618. The tubes form a module, so the structure can be prepared of three different length of tubes. The angles between the tubes are 36, 72 and 108 degrees, i.e. the angle of 36 degrees multiples. In the end, 5 x 36 degrees = 180 degrees = pi () radians. Full Angle 10 x 36 degrees = 360 degrees = 2 pi () radians = 6.28.



1.618 x 1 = 1.618      => 1.618 x 1.618 = 2.618     => 2.618 - 1 = 1.618


The nature has the symmetry concept. When the left side is known, the right side is at the same known. Do you think the nature does the support constructions by different way as we humans are them doing? Constructions in the nature look different, but have you calculated them? No, you have not, but the roof truss is familiar to you. Yes, they are familiar to many of us, but we have not strength calculated them.

When the calculation proceeds, we load the truss and look the distribution of the forces. Only a limited mind determines the image as only the roof truss. A similar grid structure have values and phenomena, but the calculation is not known. Through the EP-calculation, the patterns and formulas have the same meaning. Everything is formed of the surface area, length, volume and time. We are dealing with the visual geometry. Looking at the images, there is not a simpler functional measure of the relationship than the golden ratio 1.618. Finally, the nature modular thinking, is the industry requested modular structure. A good example of this Lego blocks.  (925)

24.   Right Angle Proportionality


An angle equal to 1/4 turn (90° or π/2 radians) is called a right angle.
EP-Calculation is non-Euclidean geometry, where the phenomena at a right angle or deviating from the angle, form curves and radian angle like patterns.

0.125 x 90° = 11.25° = sin 11,25° = 0.195         (1.253 x 1.0328 =2.0)

0.1618 x 90° = 14.562° = sin 14.562° = 0.251   (1.254 x 1,0328 =2.52)

0.20 x 90° = 18° = sin 18° = 0.31                       (1.255 x 1,0328 =3.15)

0.25 x 90° = 22.5° = sin 22,5° = 0.382               (1.256 x 1,0328 =3.94)

0.315 x 90° = 28.35° = sin 28.35° = 0.475         (1.257 x 1,0328 =4.92)

0.40 x 90° = 36° = sin 36° = 0.59                       (1.258 x 1,0328 =6.16)

____________________________________________________ _ Proportional limit five steps

0.50 x 90° = 45° = sin 45° = 0.70                       (1.259 x 1.0328 =7.67)

0.63 x 90° = 56,7° = sin 56,7° = 0.836               (1.2510 x 1.0328 =9,62)

0.80 x 90° = 72° = sin 72° = 0.951                     (1.2511 x 1.0328 =12.0)


viisikulmiot.jpgPascal's triangle; the figures are blurred after five or six stepsThe table above shows the same.

The first six rows of the calculation goes quite accurately - as well in phenomena - the line is over the calculation

Below being => chain deserves a review.

0.125 x 90° = 11.25° => sin 11.25° = 0.195 => 1.253 = 1,95 => 0.1253 = 0.0195 => arc sin 0.0195 = (1 +) 0.12 = 1,12 = 1.122 = 1.25 => 1.252 x 1.03 = 1.618 => 1.618 x 1.25 = 2 => 1.25 x 2 = 2.5 => 1,25 2,5 = 3.15 => 1.25 x 3.15 = 4 => 1.25 x 4 = 5 => 1.25 x 5 = 6.25 => 6.25 x 1,25 = 8 => 1.25 x 8 = 10


0.125 x 90° = 11.25° => cos 11.25° = 0.981.

Calculation is suitable for energy based calculation due the value of 0.981, the overall force of gravity on the Earth. Decimal points, it should be forgotten and keep the focus on the overall perceptionDuring the calculation, errors are forfeited. (998)

Time Dilation

Time dilation joins to phenomena on the Earth

At slow speed momentum p is transformed into Lorenz - variant factor 1/L when

L = sqrt (1-( v/c )2)

==>    time dilation 1.0328 when the speed of light 0,25 c    (1 + 0.25 = 1.25)

25.   Point

1   Point In Geometry

1.1   In geometry, topology and to other such parallel areas of mathematics, point is the simplest objects that other objects can be defined. For example a line is an infinite set of points.


1.2   Point determines the position on a two-dimensional map page and in the three-dimensional volume.

2.   Equivalent Proportional Calculation

tuotearvokayra.jpgIn EP-calculation the importance of a point is a geometrical description of zero-dimensionality and  it describes the location of the phenomenon on a value curve. 

Points are determined in one-dimensionality, in other words the distance between them.

Points are in the value space, but their location of view of the phenomenon is not relevant. The phenomena do not ask for location coordinates. 

3.   History

3.1   Euclid defined point in his book The Elements, saying that " the point is something that can not be divided ". The idea is ​​reflecting the Demokritos idea of ​​the atom, the smallest part of a substance, which could no longer be shared.

3.2  The ancient geometry were measured points and the distances used to detect the coordinates of the points in place. The point of the place was considered an unambiguous only if it could be linked to the fixed points of a sufficient number of distance allows .

3.2   EP-calculation principle has much the same way as the Greeks had with a well-known places. These places determined the location of one point. This is comparable to EP-calculation well-known data about the value. Conversly in EP-calculation at least one well-known point determines other points.

26.   Pi 3.14 the Length of Rivers

In time, Archimedes developed a method to calculate the value of pi to a arbitrary precision. Pythagoras made ​​the law of physics, which revealed a phenomenon of physics, showing the fundamental existing relationship between mathematics and science.



At the University of Cambridge, Geography Professor Hans-Henrik Stollum calculated lengths of rivers from their source to a river mouth and the rivers had a math length of more than three times the nominal length of the indicted beeline. Moreover, the figure was 3.14, which is a circle and the diameter ratio. This is not the length of each river, but a mathematical average.

1.252 x 2 = 3.13


Albert Einstein introduced, the river increases the meander, because the river flow rate increases at the outer side of a curve. Chaos do not arise because the increased curvature of the river, turns back the bed and generates ultimately the cutting loop. The river itself adjusted the bed, the river has left beside an arc-shaped lake.

At the same time, these lakes form the intelligently shaped flood pockets. It is known that the more even the inland ground passes, the lower meanders river. Ostrobothnia rivers in Finland flow into the flat ground, the rivers meander is less pronounced, but the stronger the spring floods.

In examples, the figure pi (3.14) has very odd occasions. The figure of pi (3.14) is associated with the Golden Ratio, and in this sense, is not a separate chapter.
Pi is perceived as the best in a circle, the ratio of the circumference to the diameter. All the circulars are still not round, such as the length of the rivers. The length of the rivers from the starting point to the end point corresponding to the diameter of the circle and the total length corresponding the circumference of a circle.  (882)

27.   Circle Description

The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.14159. A circle is a simple shape of Euclidean geometry that is the set of all points in a plane that are at a given distance from a given point, thecentre. The distance between any of the points and the centre is called the radius. It can also be defined as the locus of a point equidistant from a fixed point.

27.1   Circle and Ellipse


The area of unit circle (1) determines the specific gravity of steel. Patterns inside the circle (ellipse and circle) having the golden section proportion, determine the mechanical properties of steel.

27.2   The Fear of Physics

A guide for the Perplexed. Book author is an American Theoretical Physicist Lawrence Krauss. In the book he writes how the physics has changed the picture of the world.

"Anyhow, on the wall being separate reflections were succeeded to guess straight perceptions of the background being uniformity". Before being joins to Plato's description of the shadows on the cave wall. The particle physics today exposes the same to the researcher. On this basis, Plato had in his mind reflectance of electricity-magnetism and weak interaction essence. These are basis of one physical (types of) embodiments

Before mentioned written in our time. The science can find out, plato was with his thoughts ahead of his time thousands of years. Plato processes in writing metaphysics, after physics. The metaphysics is undefined and on the other hand unverified.

Author of the book has narrated that physicists often begin to explain the phenomenon, drawing a circle. In this way of seeing visual geometry has always been involved in the making of science.

27.3   Describing a Circle of Steel

When the human birth, the first seen objects have often round shapes. Light (lamp) on the ceiling, the Sun in the sky, Moon, ball etc. Let us assume the round shape for the steel as a unit circle. Steel is in connection with the Big Bang, containing from this point the calculation base.



 Steel unit circle; diameter one unit and length one unit

a) the specific gravity of iron 7.87 g/cm3

b) steel is iron, from which has taken off some coal. Still teel has a few percent of carbon, so the specific gravity value of 7.87 g/cm3 is functional to calculation.


6.181 x 1.618 = 10            =            0.6181 x 1.618 = 1

Units of the calculation does not matter, because they are invented by humans. In this case, the design program calculated the weight in grams, thinking the numbers to value ​​of 0.6181.

Plato's dungeon dustbin, in this case steel casted the shadow in form of a geometrical shape as a unit circle. In calculation the unit circle is what ever circle having diameter of one unit. The specific fravity of steel is three-dimensional (area x depth) value which the image shows.  (791)

28.   Circle and Square Areas

Gravitational Force

There are two steel rods of cross-sections a square and circle. The cross-sections of bars has the proportion to gravitational and Newton (N) force. Nominal rod dimensions are 1, without significance of the units. By calculating the circular surface area, the square surface area is known or vice versa.


The circle surface area is ​​0.785 units

 =>                     A = 0.785 x 1.25 x 1.034 = 1.02 (Newton N)
A = 0.785 x 1.25 = 9.82 (gravitational force g)

The square area 1,02 units is logical, because materials have + tolerance.

Phi-geometry notes the value of the gravitation and Newton force. Calculation sets the same meaning, between the surface area and gravitation force​​. Phi-geometry has an ingenious way of approaching things and phenomena through patterns and areas. Calculation is calculating through different figures.  (30)


29.   Equilateral Triangle and Circle

We believe to proportionality between things, because the word of proportionality is in our speeches. The figure shows a triangle and circle and can not avoid the ratio of 1.618 as the Golden Ratio. Relationship is maintained, any of the dimensions of the image is selected. In our minds we necessarily do not make a picture of them. A similar idea is linked to all presented images.


1 / 1.618 = 0.618

Through the visual geometry, things are shaped by way of the patterns, which often do not shape by way of the formulas.  (984)

1 - 1.12 - 1.25 - 1.6 - 2.0

   Area of the triangle: 2 units2

Area of the circle: 1.1998 units2

Ratio between areas 

2 units2 / 1.1998 units2  = 1.6669  => 1.6669 / 1.03* = 1.618

* 1.03 = the fatigue factor from time dilation

30.   Golden Ratio in the Circle

Golden Ratio

The golden ratio consists of an active earth time dilation coefficient 1.0328 which belongs to the speed of light 0.25 c . It should not pay too much attention to decimals.

1.25(2)2 x 1.0328 = 1.618
1.571 x 1.03(28) = 1.618


31.   Speed of Light as Geometry

We get the energy from the Sun which has the round shape. In the well-known energy equation, the speed of light C is in the second power. To it has to be some shape of geometry. Its geometrical shape is square. Have you never thought the Moon and Sun appear to be of same sizen on the sky. The Moon is 400 times smaller but 400 times closer the Earth. This makes the eclipses possible. The both round shapes are the first seen shapes in the childhood. In addition, the light on the ceiling and the ball. This is visual geometry.


Length   -  Area  -  Volume  -  Time
The speed of light is area c2

The speed of light  is 3 x 108 m/s, exactly 299 792 458 meters per second.

The EP-calculation use the light coverage (area) => C2 = 9 x 1016m/s. We are in the same meaning with the Golden Ratio 1.618 which is the power entry (16).


The circle radius has the value 1 as the speed of light (300.000 km/s)
2 x Pi / 4 = 1.5708
1.03 x 1.5708 = 1.618

In the EP-calculation the first value gets the value of 1. The other values are determined through this comparing. Therefore, the value of the radius of a circle is one but not three.

1  -  1.25  - 1.6  - 2  - 2.5  - 3.2  -  4  - 5  -  6.3  -  8  -  10

1 / 1.6(18) = 0.63
0.25 x 0.25 = 0.63
1.25 x 1.25 = 1.56
1.57 x 1.03 = 1.62

32.   The Angles of a Pentagon

Viisikulmio_kulma-asteet_b.jpgIs it possible to draw a different pattern, in which the symmetry of the pattern is corresponding? The figure is worth to show, even if this does not contain anything.

The angle of 0.628 radian is a calculated value of some fruits. Fruits convey the message of a full angle, 2 pi radians = 6.28 rad. This corresponds to a 360 degrees angle.

Let us divide the value of one with the Golden Ratio => 1 / 1.618 = 0.618.

Let us divide the value of 0.628 radians with value 0.618 => 0.628 / 0.618 =1.01618 Newtons = 0.1 kg.

Let us divide the value of 1 with value 1.01618 => 1 / 1.01618 = 9.84 = 9,83 m/s2 the gravitational constant. This is reduced by the centrifugal force caused by rotation of the Earth => gravity g 9,82 m/s2.

It is possible study the pentagon through calculations and by this way understand the Pythagorean interest in to this pattern two and a half thousand years ago. Pentagon edges determine the number five and the time of the running 200 m World Record. The well-known data of 100 m WR-time is 9.58 seconds. It is also generally known that, when the span increases two-times longer, increases deflection 23-times bigger. Running along the increased length of time is an increase of the deflection of the load caused by the increasing fatigue. 200-meter running is an exceptional case, but of that later. (604)

2 pii rad / 5 = 1,256637061


1.2566370613 x 9.58 s = 19.01 s (200 m WR 19.16 after running into the wind. 0.78% error)

6.28 rad / 10 = 0.628 rad

Pentagon in the middle of the fruit


39.   Pentagon in Oranges


Orange have a pentagon-shaped central sectionOf the image, this is difficult to detect because the fruit flesh is softIntentionally the shape of the image is not too easy.

From the image can calculate segment numberin which case you can try to find a fruit, which has a different number of segmentsThis becausesome people also have a different number of fingers.

10 segments        

Pythagorasthe Catholic Church and Satan worshipers have found the pattern, but science notThe theologians at the University are representing the faculty, so how the science has not found the patternHow the pattern can be so powerful. Perhaps there is more rear the figureas it has awared. (1090)

40.   Pentagon in Apples

leikattu_omena.jpgThe story has told the Catholic Church (at least sometimes) banned the presentation of a pentagon. Last, as the figure shows in a contrary view the symbol of Satan worshipers. Most likely you do not cut the apple as the photo shows.

Split an apple and the seed space forms a flower-shaped pentagon. Pentagon forms around the perimeter, which is a multiple of five, ie the regular double pentagon. The distance between the perimeters is the golden ratio of 1.618. Detecting of the points is sometimes difficult. In the photo the pentagon and outer perimeter has marked with green colour. The shown cross section occurs also in other fruits and farmed in plants.   (896)

41.   Pentagon in the Hand



Seek it out of the hand, of the world's most complete tool(836)

42.   Surface Areas of the pentagon

viisikulmion_pinta-alat.jpgIn the pentagon image, the top part is marked with honey cells and the lower part with stars. In the drawing, the upper triangle has the width of 100 units. The image areas are below. The ratio of the areas stays by any dimensions change in the drawing. The idea is the same as the issues and phenomena have.

By knowing one case, the other cases are known. Later observed the pentagon areas having the same ratio as the matter has under load. This is visual geometry of the forces in the matter.

The ratio of the surface areas

 4755.3078 / 1816.3659 = 2.618


The total area of a pentagon

4755.3078 + 1816.3659 = 6571.6737


The total surface area ratio to the smaller area

6571.6737 / 1816.3659 = 3.618


1.618 review

1.618 x 1.618 = 2.618

1.618 +1 = 2.618

2.618 +1 = 3.618

100 / 1.618 = 61.8

Is there any other pattern, which has potential for the pentagon? The golden section ratio has an undeniable connection to pentagon and by calculating made reviews. (335)

43.   Johannes Kepler

Ellipses Description of Planetary Orbits

johannes_kepler_a.jpgIn the time, the Sun, Moon and planets were assumed to have a perfect circular orbits. Kepler rejected the idea of circular planetary orbits, and ended up the idea of their elliptical paths, as known nowadays.

Kepler discovered basing the calculations of planetary orbits to be elliptical. The minor axis ratio to longer axis in our solar system is 99 - 100%. A small "epicycle" of planetary orbits would be so small. The location of the sun is an ellipse focal point, and that is located at the other end of the orbit. This attention was not required to accept at first.

 Johannes Kepler, Wikipedia
Freely translated

Your ellipses leads to the loss of roundness and smoothness of movements, which it seems to me foolish, I wonder what the deeper it. - If only you could keep perfectly circular orbit, and to explain the elliptical orbit with a small second episycle, the situation would be much better. - Astronomy David Fabricius


 The Image belongs to the calculation

The planetary orbits are elliptical in shape. The minor axis ratio to longer axis in our solar system is 99 - 100%. A small "epicycle" of planetary orbits is so small. The location of the sun is an ellipse focal point, and that is located at the other end of the orbit. One description of the calculation is the light bulb, a mathematical sun on the earth. Still the calculating is description of the matter and physiology, not astronomy.    

It is possible to draw an ellipse by several ways, having any understanding of it. You can ask almost anyone the importance of an ellipse, without the answer. The same when is asked drawing an ellipse with a pencil.  (917)

44.   Ellipse Drawing  

44.1   Ellipse with the Rope and Two Pins

An another way to draw an ellipse with the rope through two pins, of which a description. Put two pins eight centimeters in front of each other, ie the image of 80 mm from each other. Connect between the pins 10 cm long string. Take a pen and place it against the string on a red dot. Draw a pattern pins around and you draw an ellipse, the "drawing of a world".


         50 / 40 = 1,25

         50 / (30 x 1,03) = 1,618   the Golden Ratio

We study through the time dilation the factor 1,25 and 1,03(3) which the image shows as Visual Geometry.


44.2   Ellipse With Two Circles

Ellipse can be configured in many ways, of which the following two circle, one for smaller and one for the major axis. Blue line, which, unfortunately, shows little drawing, consists of an ellipse.



a)  From the center of the circles is drawn a straight line to a larger circumference.

b)  From the smaller circle intersection is drawn a horizontal line

c)  From the larger circle intersection is drawn a verticall line


d)  The horizontal and vertical line intersection is the point of a ellipse curve.


x = a cos (angle)°

y = b sin (angle)°


x = 8,09 x cos 55,10°                   y = 5 x sin 55,10°

x = 4,63                                          y = 4,1

Ellipse Can Be Drawn

1. Drawing with the rope through two pins

2. By drawing a compass and straightedge

3. Through technical drawing program

4. By calculating

In practice, the ellipse is drawn through some technical drawing program, still hand-made ​​ellipse is good to know. The other thing is the ellipse's accession to the reality. This because the phenomena form generally an ellipse. Johannes Kepler brought this up first to orbit of a celestial body. Of this we will continue to phenomena. At first, one thing is seen in this image, and later the infinite number through the Visual Geometry.  (916)

44.3   Ellipse Inside the Circle

The image shows one principle of the calculation. On the basis of the known, others are known. In the image the measure of 0.75 determines the diameter of the circle (1) and the ellipse minor axis length of 0.5.


 Surface area of circle: 0,7854 units2

Surface area of ellipse: 0,3927 units2

The measure 0.5 (that cannot see in the image) shows the area of ​​the ellipse which is halve of the circular area. About what the ratio we choose, the area is divided proportionally between the circle and the ellipse. The perception of this, is not self-evident, what the visual geometry holds. The ellipse and circle shape a tool for the forces examination in the matter.

45.   The World's Picture, Areas of the Circles

Johannes Kepler observed the Earth's elliptical orbit around the sun. Calculation shows the equivalence between an elliptical shape and phenomena. The elliptical shape of the phenomena is associated with the concept of product space. When looking the global picture of the areas, which Johannes Kepler did not present it in this format - describes the Pythagorean harmony of the golden section. This requires a static fatigue factor (Universal friction) of 1.03. The showed calculation is not alone in these observations in relation to Plato, Johannes Kepler, and in this context, we add to this group one person.


Galileo Galilei played a major role in the Scientific Revolution. His insistence was that the book of nature was written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it. - Galileo Galilei

The educational system learned us the geometry, and there is no reason learn it again. Still I tell the formula of areas in ellipse. There is no need for any unit, because we are calculating universal mathematics.

                                                             A = pii x a x b

a = half semimajor axis 50 units

b = half semiminor axis 30 units

                                                             A = 3,14 x 50 x 30   = 4712,3890

Circle d = 60, inside the ellipse        (you have to imagine this circle)

                                                             A = 2827,4334

Circle D = 100, outside the ellipse    (you have to imagine this circle)


                                                             A = 7853,9816


                                     7853,9816 / (4712,3890 x 1,03) = 1,618

                                     4712,3890 / (2827,4334 x 1,03) = 1,618

The educational system learned the geometry, and there is no reason learn it again. Still I tell the formula of areas in ellipse. There is no need for any unit, because we calculate universal mathematics.

                                                             A = pii x a x b

a = half semimajor axis 50 units

b = half semiminor axis 30 units

                                                             A = 3,14 x 50 x 30   = 4712,3890

Circle d = 60, inside the ellipse        (you have to imagine this circle)

                                                             A = 2827,4334

Circle D = 100, outside the ellipse    (you have to imagine this circle)


                                                             A = 7853,9816


                                     7853,9816 / (4712,3890 x 1,03) = 1,618

                                     4712,3890 / (2827,4334 x 1,03) = 1,618




        Circumference of ellipse = 255,270

        Circumference of d60    = 188,4956

        Circumference of D100  = 314,1593


                                    314,1593 / (188,4956 x 1,03) = 1,618

                                    (314,1593 + 188,4956) x 1,03/ 255,270 = 2

46.   Friction Coefficient 1.03

Light and shadow hide the same meaning. You can think the image below is composed of lines as the light. Products, phenomena and values generally ​​have the friction​​, which the black color describes. But do not say, the geometry has not tried to show the coefficient.




Without the force of gravity there is no friction to stops the movement. Atmosphere and material should spread into space. The world we see, would not be. Pentagon describes gravitational force. A coefficient of 9.82, often in Europe used the coefficient of 9.81.

                               0.3633 + 0.6181 = 0.9814

The universal friction coefficient 1.03(4) occurs in a number of examples and patterns. This  is derivated from equation E = m c2. We swim in the universal gravitational field, which can be calculated through the friction. (893)

                               ( 0.3633 + 0.6181 ) x 1.03 = 1.0

47.   Universal Friction 1.03

Visual Geometry describes in many ways the Universal friction.


The circle diameter of 2 units        => the length of the circumference Pi x D = 6.28 units

The quarter length of the circle  = 2 x 3.14 .../ 4 = 1.5708 units

1,5708 x 1,03 = 1,618

It is said that the Golden Ratio 1,618 is an irrational constant that cannot understand; when some phenomenon, we loose something, but this something cannot observe. This is the character of the Universal Friction 1,03(4). In the image the Universal Friction is the missing part of the red line, being the character of the friction. (895)


48.   Stopping Distance as Visual Geometry

I dare say that even this approach has not been presented elsewhere. The below shows the braking distance, calculated by using the formula in physics. The reaction time is generally accepted one second. This gives the travelled total stopping distance, for example a speed of 50 km/h, 26,2 m. Another method at the right is using natural logarithms.

Braking on a dry and clean asphalt

Speed       Reaction time    Braking    Tot.           Logarithmic Calculation

km/h               m                      m            m                                   

  30                8.33                   4.42        12.8           Known data 13 m

  40               11.1                    7.9          19,0             40/(Ln pii)6 =   17.8 m

  50               13.9                  12.3          26.2             50/(Ln pii)5 =   25.5 m  

  63               17.5                  19,5          37.0             63/(Ln pii)4 =   37.0 m

  80               22.2                  31.4          53,6             80/(Ln pii)3 =   53.3 m

100               27,8                  49,2          77,0           100/(Ln pii)2 =   76.3 m

120               33,3                  70.6        103,9           120/(Ln pii)  =  104.8 m

125               34.7                  76.6        111.3           125/(Ln pii)  =  109.2 m

Visual Geometry


The stopping distance is increased by a factor of

1,252 /1,03(3)2 = 1,4641

When the speed is increased by 25 %, increases the stopping distance, but proportionally reduces. The stopping distance "get tired", as a runner get tired.

Stopping distance is four-dimensional phenomenon, involving dimensionalities of length, width, height and time. Time is assiciated to time dilation, which is part of the essence of value space. After these comes proportionality in things, including the value of the golden ratio 1.618.


The value space

                            Pascal's Triangle

  1 dim                            1.1

  2 dim                      1.1 x 1.1                  = 1.21

  3 dim                  1.1 x 1.1 x 1.1             = 1.331

  4 dim            1.1 x 1.1 x 1.1 x 1.1          = 1.4641        Length - Width - Height - Time

  Propo        1.1 x 1.1 x 1.1 x 1.1 x 1.1     = 1.61051     (The Golden ratio 1.618)

EP-calculated stopping distances 

km/h     Stopping distance          Calculation

    30                12.8                       13 m the known data

    40                19.0                       13.00 m x 1.4641              = 19.03 m                   1.

    50                26.2                       19.03 m x 1.4641 / 1.033  = 26.97 m                    2.

    63                37,0                       26.97 m x 1.4641 / 1.033  = 38.22 m                    3.

    80                53.6                       38.22 m x 1.4641 / 1.033 = 54.18 m                     4.

  100                77.0                       54.18 m x 1.4641 / 1.033 = 76.79 m                     5.

  125              111.3                       76.78 m x 1.4641 / 1.033 = 108.83 m

 The speed of 100 km can calculate:

13 m x 1.46415 / 1.0334 = 76.80 m

The calculated 76.79 m is the exact value

EP-Calculation accuracy is five steps

The fifth step of the time dilation are values of 0.25 and 1.033

Many of the readers say them to be better brakers than the table shows. My best heard is 21 meters starting from 100 km/h. The tabled value 49.2 m. That was a motor cycle and police did measure the braking length. Now this is up to you believe the braking distance, but then we have a new physics. (1011)

49.   Volume of a Pyramid

1/3 × Base Area × Height (H)


Cheops Pyramidpyramidi_egypti2.jpg

                                      V= 1/3 x 230.3 m x 230.3 m x 146.41 m

                                      V = 2 588 436 m3

Visual geometry

                            V = 1.254 x 1.06 = 2.588

                            ( length x width x height x time x fatiquing of 3d + time)

                             (1,25 = 1/4)

                             (1.032 = 1.06)

Surface Area of the Pyramid

All side faces are the same:

Base Area + 1/2 × Perimeter of Base × Slant Length (L)

                              A = 230.3 m x 230.3 m + 1/2  x( 4 x 230.3 m) x 186.3 m

                              A =  138848 m2

Golden ratio

                      (186,3 m/146.41 m = 1.2724    =>  1.27242 = 1.618 )


50.   Volume of a Ball

The Earth is a sphere on the basis of its name.

jalkapallo_1.jpg50.1   By formula

V =  π x d 3                        V =  4 x π r3

          3                                           6

V = 4.189                           V = 4.189


50.2   Equivalent Proportional Calculation

V  =   π d3                               V  =   π d3

  2 (π /1,034*)                     ((1,25665 ) /1,034) x 2      Note ! 1,12(1)2 = 1,2566 **

V =  4,14                       V =  4,14

*1.034  Time dilation, relates to the speed of light 0.25 x C

** 1.12 and 1.25 are the coefficients of the calculation


50.3   The Golden Section and Gravity

V  =   π d3 x1,618         


V  =  4,14


50.4   Lifetime to Machine Elements

V  =   π d3              

      2 x 1,253

V =  4,12

There is very few who remember the formula for ball volume. The volume of the ball is guided on through the calculation. The calculation has the average accuracy of 2%, but the examples above exceed the accuracy

50.5   Volume of a Ball

Area of the circle / (π / 1,034)

A = 12.566370614359172953850573533118 / (3.1415926535897932384626433832795 /1,033)

A = 4.13

The volume of the ball has the same meaning with the ball cross-sectional area. Time - Fatigue - strength - tension - productivity - lifetime, etc. become familiar and meant the same.

60.   Pascal's Triangle - Phi 1.618

Many formulae from mathematics to science and engineering involve pi (3.14), which makes it one of the most important mathematical constants.

In formula Pi (3.14) often determines the round shaped area? Phi (1.618) determines the proportion between matters and phenomena like the two halves of the round shape in the picture.

When you brake up you will loose something like saw dust when sawing or friction when moving something. This has called the Static Fatique Factor 1,03. This friction or loss has nothing to do with what we think between the two surfaces friction. This friction is universal loss between issues. This may initially prove the calculation at the bottom, which converts the 1.618 value of the golden ratio and pi 3.14 with each other. This is the continuation of most of the phenomena having similar principle of mutually mating


                         0.1  0.1

                    0.1   0.2   0.1           1.6(18)

                0.1   0,3   0.3   0.1

            0.1   0.4   0,6   0.4   0,1

            0.1   0.4   0.6   0.4   0.1.

                0.1   0.3   0.3   0.1

                   0.1   0.2    0.1           1.6(18)

                        0.1   0.1


 0.1 +  0.4 +  0.6 +  0.4 +  0.1= 1.6


(2 x 1.618) / 1.03 = 3.14

61.   Pascal's Triangle & Pi (3.14)

61.1   The Nature Factor 1.1

                          1                                                             1

                   1             1                                       1.1 x 1 = 1.1

             1            2           1                              1.1 x 1,1 =1.21

       1           3            3          1                      1.1 x 1,21 = 1.331

  1         4             6           4         1              1.1 x 1,331 = 1.4641


We have read of the row factor eleven (11), but does the nature have it?

Pi (π) is the ratio of any circles's circumference to its diameter. If something grows eleven times bigger, its relative position grows 1,112 = 3,14 times bigger. For example 110 cm has its relative position 1,1 to length of 100 cm. Everything has its relative position 1,1 to something else. Is the constant Pi a shadow of Pascal's Triangle or contraversary? Finally the showed can visually calculate from the image.



62.   Fibonacci Numbers


                                                               1        1

                                                         1        2        1                     Pascal's Triangle

                                                    1        3         3        1

The fift row                           1       4         6        4        1                16  =  1.618


0 - 1 -  1 -  2 -  3 -  5 -  8 - 13 - 21 - 34 -  55  (Double five)

The first eleven numbers of Fibonacci numbers

Sometimes the Fibonacci numbers begin omitting the initial 0, and the sequence is written this way. The first two numbers in the Fibonacci numbers are 0 and 1, and each subsequent number is the sum of the previous two. We find the Fibonacci numbers to begin, such as Pascal's triangle.

Relation to The Golden Ratio

      1/1 = 1.000

          3/2 = 1.5000                             This is more Phi-Geometry than mathematics

                5/3 = 1.666...

                     8/5 = 1.600

                          13/8 = 1.625

                                21/13 = 1.615

                                     34/21 = 1.619         The value closest to the Golden Ratio

                                          55/34 = 1.617647    

                                                89/55 = 1.6181818

                                                       ......  =  ...............

Kultainen leikkaus                       1.61803398874989

Pascal's Triangle                                          1

The Eleventh row is 1,618                    1              1

Finally, phenomena follow the formation as described, each in its own way. Pascal's triangle is a pattern that includes the formation of the description.  (397)

63.   Golden Ratio in Products

All around of us we are affected by various proportions, as exemplified by the golden ratio 1.618 in products. I will add products to this page and the first is commercial calculator HP 12 C. The products include visual geometry, which does not need to calculate. (821)


Hewlett Packard 12C Financial calculator, has a ratio of 1.6125.

Mitat  - Dimensions (W x D x H)
8.0 x 1.52 x 12.9 cm

12,9 / 8,0 = 1,6125

64.   The Specific Gravity of Steel

64.1   Circle and Ellipse


The area of unit circle (1) determines the specific gravity of steel (0.785). Ellipse and circle patterns inside the circle, have between them the golden section proportion, determine the mechanical properties of steel. This is a simple summing function.

0.3000 + 0.4854 = 0.7854

1,618 x 0,3000 = 4.854

64.2   Steel Unit Circle and Aluminium

The material of the calculation is steel. The steel is in connection with Big Bang, containing the calculation base.



 Steel unit circle; diameter one unit and length one unit

a) the specific gravity of iron is 7, 87 g/cm3.

b) the steel is iron, from which is taken off some coal. Carbon steel has a few percent, and the specific gravity value of 7.87 g/cm3 is functional.

The specific gravity of the steel and the unit area of ​​the circle can be measured using coefficient 1.618 and 1

6.181 x 1.618 = 10            =            0.6181 x 1.618 = 1

Units of the calculation does not matter, because they are invented by humans. In this case, the program calculated the weight in grams and lets think the numbers to values ​​of 0.6181 and 1. This is a good workout at the same values. Calculated do not have to be steel. We will calculate the weight of a piece of aluminum plate on the basis of the specific gravity of steel. Specific gravity of aluminum is 2.7 g/cm3.

1.618 / 0.618 x 1.034 = 2.70

Calculation through gravitation 9.82 m/s2

1.618 /(0.618 x 9.82) x 1.034 = 0.275


We go through the whole mathematical palette, from a piece of steel as shown, and we stop to values ​​of the final product formation. This only requires patience and logic simplification. How necessary is to calculate the weight of aluminum, as shown, is another story.  (209)

65.   Steel Strength as Visual Geometry

According to Plato, the picture of the reality had born of real objects which formed shadows onto the cave's back wall. In Plato's example, the prisoners came for the first time freedom, but had to return back to the cave. Before only shados seen prisoner told of the real objects behind the shadows, but the other prisoners did not want to believe. As a result, other prisoners rather wanted to kill the prisoner, than to change their own idea of the reality. These others may not differ from us, if the not casted shadows are not familiar to us. Knowledge gives the opportunity to see the kind, which, without the knowledge is not possible. Let me to explain the idea a little more.

wikiped.jpgPlato´s cave example

Allegory of the Cave

1 - 1.12 - 1.25

That what we have a lot of, it is the world's iron subsoil. Normal structural steel S235 hardness for the strength calculation is HB 112, the average value from HB 100 to 125. The round shape of a diameter 112 (*units are yours), includes the diameter of the scale, the hardness of the steel S235. Anyone can do the circle having diameter of 112 units, when the two-dimensional circle represents the hardness onto the paper. The circle forms the area of 9852 square units, gravity 9,82 units/s2 in other words .

By making a three-dimensional ball of the circle, it can determine the hardness of the steel. Pressing the ball onto the surface of the steel, is the used method to determine hardness. Below is a pattern, of which can continue to determine the strength. Not onto the wall casting shadow, of the invisible phenomenon called strength. In the same way as the visible is seen as a shadow, invisible has the calculable not seen shadow.

* Units are human fabrications, such as mm, inch, light year, etc.  (906)


65.1   Steel Hardness Golden Ratio

Dividing the circle area by bigger ellipse area, the areas includes the ratio of 1:1.618. The diameter of the circle per the ellipse minor axis length, includes the Golden Ratio. The larger elliptical area per the smaller elliptical area, has also the ratio 1.618. 



When drawing an ellipse inside the ellipse having the ratio of 1.618, the  area is 1:2.618 of the previous ellipse.

1 + 1.618 = 2.1618         1.618 x 1.618 = 2.618


Area of ​​the circle is 2.0561 units The larger ellipse has the area of ​​1.2708 units => 2.0561 / 1.2708 = 1.618 The smaller ellipse has the area of ​​0.4854 units => 1.2708 / 0.4854 = 2.618

The circular shape has the hardness of the material, strength ellipses.

Why to do this. This I'll expain through the strength calculation ...

The Golden Ratio joins to machine engineering most common material, steel. However, we do not notice the golden ratio, choosing the quality of steel, or examining the strength of steels. The tensile strength of steel is proportional to the hardness, in a such a way up to 100 kN/cm2, the ultimate tensile strength of carbon steel is 36% and alloy steel 34% of the Brinell hardness. The percentual share has been observed, but not the joining to the Golden Ratio.

The ratio φ (1.618). The ultimate tensile strength of carbon and low alloy steels, can be quite precisely determine by dividing the steel hardness HB by ratio 1.618. => HB 112 / 1.618 = 69.221 => σM = 112 - 69.221 = 42.8 kN/cm2. The value 42.8 kN/cm2 corresponds to S235 steel grade with a guaranteed ultimate tensile strength of at least 37 kN/cm2.


HB = Brinell hardness                      σM = The ultimate tensile strength

Structural steel S235                     HB   100...125

65.2   Shadow of the Bending

The loaded girder can be pre-calculated, deflection, stresses etc. We use to like the calculation result as axiom. Still, however, there is no long time as the strength calculation was not possible. Thinking about the matter, the deflection shadow is caused by the load. This shadow under beam can see in the bigger image. It depends on the direction of the light, whether to see the shadow of the deflection or not. Issues in the analysis is the same, depending on the viewer's point of view under review.



The force of gravity bends the beam, whereby in many meanings, it is question of the power. In connection with the power, it is often used the name of energy. The energy conversation is known, but has bending the parallel meaning to other matters? Shadows  generally are something that cannot touch as the calculation result, as can not touch any energy. Of these shadows, is partly ask on my pages. (995)

66.   Strength, such as Visual Geometry

rakennusmaa.jpgThe calculation includes an explanation to the mathematical ratio of 1.618. This is presented in steel and different kind of structures having strength perspective. Data is common for architects, engineers and professional people in all areas. The calculation does not limit anyone.

Product Designer is not an actual designer, but using the number ratio of 1.618 and its squared ratio of 1.25 is a great opportunity to design a pleasant-looking objects. We find the strength of the structure to comply with the ratio of 1.618.

In the examples we go through the calculation of the strength of bending to fatigue. We find the strength to move relative to products. By calculating correct one product, the other a series of products are with high probability proportionate. The Equivalent Proportional Calculation is a mathematical construct that has no end.

These studies, we do not just in products, we make it to all possible phenomena. Constraint is our experience in managing a normal solution. Previous, because we need the experience to compare the traditional calculation and The Equivalent Proportional Calculation.  (299)

66.1   The Golden Triangle

In the triangle the lengths of the margins are 1 and 0.5 unit => hypotenuse is 1.1(18) units and perimeter 2.618 units. The Golden Ratio is square root of 2,618 and means 1.618 x 1.618 = 2.618. In the phenomenon, when studying the alteration of value. The known value has its proportional value 1 => the one dimensional (1d) change is 1.118 (1.12). The value alteration is 1.4641 times as the Pascal's Triangle shows.

Image above lefft:              1 / 1.618 = 0.618        Golden ratio 1.618

Image below on the left:         1 - 1.12 - 1.25        Ratio sequence

Image below on the right:     2 x 0.5 + 0.618        Golden ratio 1.618


0,618 + 0,500 = 1,118

0,618 / 0,500 = 1,236

1 + (2 x 0,118) = 1,236

1 / 1,618 = 0,618

0,138  / 0,089  = 1,55

1,2362 = 1,527

 1,618 x 1,618 = 2,618

1 + 1,618 = 2,618


aikadilaatio_small.jpgThe girder is loaded and the length of the span increases 1,1(18) times the original length. Deflection increases 1,46 times the original deflection.

We calculate something what is the whole and something what is not. The whole is the triangle and its area of 0,25 units, the factor 1.25 of the ratio numbers.

The value (1.118) that is not the whole, consists of two sector values (0.618 + 0.5). There are no units, because we calculate universal mathemathics.

In addition to an invisible, there is the universal friction of 1.03 (1,25 => 1,03 in the table).

It is good to remember that the whole is not decimals.

0,089 + 0.138 = 0,227

Sector 1 + sector 2 = 0.227

0,25 / 0,227 = 1,1

The whole / part wholes = 1.1

The lost part of the whole is Pascal's Triangle and its row factor 1.1.

0.1                         1

0.2                   1         1                        1,1 x 1,0 = 1,1     

0.4               1        2        1                   1,1 x 1,1 = 1,21 

0.8          1        3       3       1                1,1 x 1,21 = 1,33

1.6      1       4        6       4      1            1,1 x 1,331 = 1,46

  1     6        1        1       6      1             1,1 x 1,4641 = 1,61

                                                                   Together = 6,71 ( x 10 -11 )




Finally the Pascals triangle formulates the Gravitational Constant. This is an example how the areas of phi geometry are the same as the calculation. Gravitation is still unresolved, in which a few decimal difference is not significant. (954)

67.   Products, Such as Visual Geometry

67.1   Lifting Lugs from 500 to 40,000 kg



The leftmost lifting lug is the smallest in size. On the basis of one ligfting lug, the other lifting lugs can be detemined. For example, the weight of the 40,000 kg lifting lug differs 5 kg of the manufactured lifting lug. The difference in weight between the smallest and the largest is about 200 times the smallest. The calculation takes a moment to calculate on the paper and on spreadsheets, only for a few seconds.

125 kg x 1.25 x 1.12 = 175 kg is the last line of the calculation of the 40,000 kg lifting lug.

Of the product weight formation, there is a need to understand the proportionality in different dimensions. Calculation shows later the weight determination of the lifting lugs. The parabola of the curve joins to
visual geometry. (593)

68.   Visual Geometry as Physiology

68.1   Short Run Events in Pascal's Triangle

Pascal's triangle as visual geometry


Pascal's triangle                                Run Events                         Distances

                 1                                                 100                                  100 m

             1      1                                       100       100                            200 m

         1      2       1                           100       200       100                      400 m

    1      3       3      1                  100       300      300      100                  800 m

1       4      6       4      1        100     400       600       400     100           1600 m

Cheops pyramid


Pascal's triangle determines the five shortest running distances. Pascal's triangle is a two-dimensional pattern, which corresponds to a three-dimensional pyramid.

You think the pyramid has nothing to do with running, and ancient Egyptian did not run a race. To that there is no need at all, because the phenomena included in the pyramid pattern. Science for some reason does not want to understand this. I guess you can see the pyramid similarity between Pascal's triangle and the fact this context, derived from the short run events. 1600 m run event prefer today to be 1500 m. The British Commonwealth of Nations has called the length of 1609 m as a mile. Today to be run for a shorter 1500 meter, runners are still referred to Mailer. The distance is said to be killing, which can be demonstrated by calculating the time period. After this, Pascal's pattern will continue with other issues and values. It is quite sufficient to begin with this observation. (972)

29.9 2015*20:40


E-mail:  karikolehmainen53@gmail.com

Kari Kolehmainen +358 44 200 3207

Equivalent Proportional Calculation

Visual Geometry