Value of Pi as Visual Geometry Piin arvo näkemisen geometriana
Arkhimedes' method for calculating the value of pi (3.14)
Domenico Fetti Arkhimedes (1620 Firstly, he drew a regular n-gon inside the circle. As the value of n increases, the circumference of this inner n-gon approaches the circumference of the circle from below. Secondly, he drew another regular n-gon around the outside of the circle, whose perimeter approached the circumference of the circle from above. By doing this, Arkhimedes was able to enclose the value of pi between two perimeter values - one from below and one from above. Gradually increasing the number of sides of the n-gons reduces this interval, thereby approximating the value of pi to the desired accuracy. Using n = 96, Arkhimedes achieved the value of pi between 3.1408 and 3.1428 The Bible knew the approximate value 3 of pi, and in Mesopotamia was known as an approximation of 3 1/8 (3.125) 2000 BC. Today, the value of pi is 3.14159. What makes the determination of pi interesting is the fact that it was determined graphically using a circle and a regular n-gon inscribed within it. In EP Calculation method that mean the same thing, values are determined graphically in a similar way, so Arkhimedes solved the value of pi by visual geometry. The determination procedure of pi was by adding all polygon spans lengths and taking the ratio of the diameter of the circle. The higher the amount of n-gon spans, the closer the value of Pi. On the other hand there is a problem of measuring equipment accuracy of which is a little mention. |
Arkhimedes developed a brilliant method for determining the value of pi as accurately as possible by using the perimeters of polygons inside and outside a circle. He used regular polygons (n-gons) both inside and outside the circle to obtain lower and upper bounds for pi.