Dangerous Shearing in Matter
The principle of the visual geometry
In principle, anything that can be calculated can be represented as patterns within Phi‑geometry.
When a 100‑centimetre bar is cut into two segments so that the longer portion measures 61.8 cm, the division follows the golden ratio. In this proportion, the ratio of the whole to the larger segment equals the ratio of the larger segment to the smaller one. Numerically, this is expressed as:
100 cm/1.618=61.8 cm
leaving the shorter segment at 38.2 cm.
In material behaviour, such a proportional coefficient can be used to describe the relative distribution of forces. This provides a conceptual basis for modelling the so‑called critical shear force, which arises from the interaction between structural geometry and applied loading. The golden‑ratio division serves as a simplified geometric analogue for this type of force relationship.
The length coefficient 1.12 corresponds to the incremental ratios found between the rows of Pascal’s triangle. These coefficients form a sequence:
(1,10 – 1,21 – 1,33 – 1,46 – 1,61)
illustrating how relative force magnitudes may increase stepwise as geometry or loading conditions evolve.
If the bar is divided repeatedly — for example, five successive cuts — the proportional calculation eventually exceeds its practical validity. At this point, the structural relationships cease to remain linear, and the system enters a regime in which proportionality no longer holds. This is a critical consideration when assessing structural capacity and the onset of dangerous shear conditions.
1 1
2 1 1 = 1 +1 = 2 1.1 x 1 = 1.1 11
3 1 2 1 1.1 x 11 = 1.21
4 1 3 3 1 = 8 1.1 x 121 = 1.331
5 1 4 6 4 1 1.1 x 1331 = 1.4641
6 1 5 10 10 5 1
1.6.2026*9:00 (43865 - 752)
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