# Echins Ekei the Natural Architecture

Edwin VanGorder

Whereas Ekei is the Greek word for Being and Echinus is the associated architectural motif linking the panoply of spiky forms in nature as growth process:

A logarithmic spiral by definition proportions unit fields and this proportion may be demonstrated within unity as square in the form of an oblong or ratio discrimination. A liner extension of the ration is its repetition which will divide its manifold evenly to oblong form as equilibrium ie a grid. Where the grid is square per increment the equilibrium expresses the idea of square and square root and there is only a field, no figure ground or remainder process showing as complementary form… with the idea of relative complementary however linked to Morgans valence system and the idea of Gamma or the recursive structure of ‘Beth Ansatz” internally rotating infinity towards a limit as opposed to the outward spiral extending space in factorial terms as extended to complex space is essentially a view of the Greek Gnomon or comparison of the complement area to the remainder area of the figure which is always minus one and the Stirling process for determining large scale factorials ( which shows common to art and physics the process of “visualizing” that which is not in fact in plain sight)) relates the familiar Pi r squared as the operational adjustment between scales which in fact has to do with Pi as embedded in the harmonic system of roots by a relation to midline as centering the perception of magnitudes thus the square root of two stands in relation to square root of five as centering and the square root of 2 divided 5 will give 1.1416 which in relation to 3.1416 pi we can essay an understanding from the stand point of realizing from outset we are dealing with two and three as the numbers of perception ie all relative symmetry basis. The root of .618 as .788 forms a twelve fold of .3168 which is the reciprocal of pi thus the even field status of .788 in which 6 pairs of ,3168 are in each pair half .888 bt proportion and in this .6336 form = unity plus the square root of three, the square root of three and of two work simultaneously in presenting square root of two in form 1.1416 which requires then its own square to advance 3.1416 or pi while Pi develops from the reciprocal of the square root of 5 as .4473 at three fold 1.3416 plus two and minus .2 = 3.1416 … the number of rotations one introduces into a cycle then becomes the logarithmic “Big O” notation of which the Gamma subtraction for all its apparent simplicity is in fact the process described…

###### DRAWING RESEARCH NETWORK

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