zq06 summer 2013
Article Spiral Hegira
Author: Tom McKeag
Spiral Hegira A Universal Recipe PAX Scientific CEO and Founder, Jay Harman has a recipe for cleaning our air that is based on the fundamental properties of fluids. Now he has to convince the rest of the world that the universal model he claims to have found can be used to alleviate smog in one of the world’s grittiest cities.
bigger and bigger curves around the center point as it moved outward. Vectors drawn from its center would intersect the curve at different angles. If one pulled our two spirals out into three dimensions, the logarithmic spiral would describe a cone, while the Archimedean spiral would describe a cylinder.
The importance of the logarithmic geometry to living forms has long been noted, The universal property that Mr. Harman for it is the only curve to possess the folhas become obsessed with is the spiral, lowing property: radial growth and intrinor, more precisely and three-dimensionalsic growth in the direction of the curve ly, the vortex. Vortices (or vortexes) are bear a constant ratio to each other. D’Archy complex physical phenomena within the W. Thompson, in observing the nautilus in turbulent flow of fluids that appear at all his classic 1917 text, On Growth and Form, scales in our tangible world, from nebwrote: ulae to DNA. Air, water and even fire can assume this shape, and many of the solid “In the growth of a shell we can conforms in living organisms will reflect their ceive no simpler law than this, namely, once plastic state in this twisting form. that it shall widen and lengthen in the same unvarying proportions: and this A two-dimensional “slice” of the spiral simplest of laws is that which Nature found typically in nature, the spira miratends to follow. The shell, like the creabilis described by Bernoulli, is a logarithmic ture within it, grows in size but does not or equiangular spiral, unlike the Archimedchange its shape; and the existence of ean or cylindrical spiral found in a watch this constant relativity of growth, or spring. It is called equiangular because the constant similarity of form, is of the esangle in which a radius vector intersects sence, and may be made the basis of a the curve at any point is constant. definition, of the equiangular spiral.” If one were to draw these two spirals as center points from which one traced curves radiating around these centers, It is not that such vortices have escaped then the logarithmic spiral would trace notice in our world; quite the contrary.
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