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nydus/On Growth and FormPublic
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CHAPTER XI THE LOGARITHMIC SPIRAL

radial direction of any two whorls ( W ). We have then merely to apply the formula

which we may simply write r =ã€₤eÿ£¢ö¡ã€₤cotã€₤öÝã€₤, etc.; since our first radius or whorl is regarded, for the purpose of comparison, as being equal to unity.

Thus, in the diagram, OCã€₤いã€₤OEã€₤, or EFã€₤いã€₤BDã€₤, or DCã€₤いã€₤EFã€₤, being in each case radii, or diameters, at right angles to one another, are all equal to eÿ£¢(ü€ã€₤いã€₤2)ã€₤cotã€₤öÝã€₤. While in like manner, EOã€₤いã€₤OFã€₤, EGã€₤いã€₤FHã€₤, or GOã€₤いã€₤HOã€₤, all equal eÿ£¢ü€ã€₤cotã€₤öÝã€₤; and BCã€₤いã€₤BAã€₤, or COã€₤いã€₤OB =ã€₤eÿ£¢2ü€ã€₤cotã€₤öÝã€₤.

A geometric diagram showing a logarithmic spiral expanding outward from a central origin, labeled with points along its curve.

As soon, then, as we have prepared tables for these values, the determination of the constant angle öÝ in a particular shell becomes a very simple matter.

A complete table would be cumbrous, and it will be sufficient to deal with the simple case of the ratio between the

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