Beyond measure: a guided tour through nature, myth, and by Jay Kappraff

By Jay Kappraff

This publication includes essays that stand all alone yet also are loosely hooked up. half I records how numbers and geometry come up in different 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 types. the point of interest is on how sure numbers, akin to the golden and silver skill, current themselves inside of those platforms. half II exhibits what percentage of an analogous numbers and quantity sequences are concerning the fashionable mathematical learn of numbers, dynamical structures, chaos, and fractals.

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Flowing movements can also be superimposed on a wave, so that as the wave moves forward, a strong wind can cause the moving current on the back of the wave to move faster than the wave and overshoot the crest and break. In this process, all that is rhythmic in a wave becomes altered. It takes on a spiral form interspersed with hollow spaces in which air is trapped. "Whenever hollow spaces are formed, water is drawn into the hollows in a circular motion, and eddies and vortices arise". This presents us with a new formative principle: The wave folds over and finally curls under to form a circling vortex.

Let's see what the effect on the growth measure is if we project the right fixed point Y to infinity. 10. , r in this case). In other words, growth measures can be viewed as double geometric series seen in perspective. , the growth measure is the identity transformation.

The stress lines, take the place of flow lines in fluids, running directly across the gap. 14 Design on a palm leaf (May River, New Guinea), Volkerkundliches Museum, Basel. 14. 9 Vortex Rings Aside from the rhythmic processes of vortex formation at the surface of the water, there is also the three-dimensional nature of the vortex to consider. 15, "every vortex is a funnel of downward suction. All flowing water, though it may seem to be entirely uniform, is really divided into extensive inner surfaces, each rotating at a different speed.

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