By Jay Kappraff
This booklet involves essays that stand all alone yet also are loosely attached. half I files how numbers and geometry come up in numerous cultural contexts and in nature: the traditional musical scale, percentage in structure, old geometry, megalithic stone circles, the hidden pavements of the Laurentian library, the shapes of the Hebrew letters, and the shapes of organic kinds. the focal point is on how yes numbers, equivalent to the golden and silver capability, current themselves inside of those structures. half II exhibits what number of an analogous numbers and quantity sequences are regarding the trendy mathematical learn of numbers, dynamical platforms, chaos, and fractals.
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Extra info for Beyond measure: a guided tour through nature, myth, and number
I shall also examine the possibility that ancient civilizations were aware of such astronomical phenomena as the precession of the equinoxes, and that die stars were pictured as rising in helices [de-D]. Finally, I will present an outline of the observations and ideas of Theodor Schwenk [Schw] on the creative force of water in the genesis of organic forms. 2 The Australian Aborigines The Aborigines are a nomadic people who believe that in ancient times, known as the "epoch of die sky", gods inhabited the territory.
16 shows the planets being carried about in the sun's vortex S, and the moon being carried around the earth in the same way. " T h e vortex h a s a n o t h e r quality t h a t suggests [astronomical] connections". If a small floating object with a fixed pointer is allowed to circulate in a vortex, it always points in the direction that it was originally placed, remaining parallel to itself. In other words, it is always directed to the same point at infinity, "just as the axis of the Earth points in the same direction as it revolves around the sun".
Stevens. B;y permission of Little Brown and Co. G. de Bruin, Kon. Ned. Akad. Wetensch. Proc. Ser. A84 (indaginationes Mathimaticae 43) 27-37. 8 From Chaos, Fractals, and Power Laws by M. Schroeder. H. Freeman. Used by permission. 3 P. Bak and R. Bruinsma, Phys. Rev. Lett. 49, 249-251. Part I Essays in Geometry and Number as They Arise in Nature, Music, Architecture and Design This page is intentionally left blank 1 The Spiral in Nature and Myth The ocean wave... in essence is a kind of ghost Freed from materiality by the dimension of time.