This work reconstructs the basic trigonometric functions from a process-logical perspective and shows that sine and cosine do not originate from geometric forms, but rather from the dynamics of a radial process space. The starting point is a center from which a maximum radius unfolds. This radius forms two stable process spaces, which traditionally appear as semicircles, but must be understood ontologically as dynamic spaces of possibility. The so called 90 -degree rule becomes apparent as a stability condition that prevents either of the two process spaces from collapsing. It is not a geometric convention, but rather the prerequisite for a maximum radius to support two independent process components. Within this framework, sine and cosine do not appear as triangular quantities, but rather as components of a radius process expressed in two orthogonal process spaces. The legs are interpreted as subprocesses of the radius, not as sides of a triangle. The geometric representation of trigonometry thus becomes visible as a historical projection that obscures, but does not replace, the underlying process. Modern times have largely transformed this process space with grids, polygons, and coordinate systems, thereby obscuring its original dynamic. The processual reconstruction shows that trigonometric functions can be formulated without a geometric foundation. This opens a bridge to quantum mechanics, which also operates in states, transitions, and radial processes and does not require geometric forms to describe physical reality. The work demonstrates that geometry does not need to be refuted, but rather becomes superfluous once the processual structure is revealed. Trigonometry thus appears not as a system of forms, but as a system of states whose mathematical representation emerges from a deeper ontological logic.
Manfred Thiele (Fri,) studied this question.
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