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Mathematical Models for Society and Biology, 2nd Edition by Edward Beltrami

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Chapter 12

The Coil of Life

12.1 Background

Although the human genome has now been decoded, the focus of investigations on the molecular form and biochemical functions of the gene continues unabated. One question of interest has been the manner in which the long strands of DNA are packed into the tiny confines of a cell. This is a complicated topic, but we can obtain a brief glimpse into some of the mathematical issues it raises.

In terms of the math, this chapter is an exercise in the differential geometry of space curves. The core idea is the linking of two such curves, and in Section 12.4 we sketch a proof, due to Carl Friedrich Gauss, that shows how many times the curves are entwined. This result is not only of interest in itself (and a good ...

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