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nydus/On Growth and FormPublic
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Table of Contents

CHAPTER XI THE LOGARITHMIC SPIRAL

breadths of adjacent, or immediately succeeding, whorls.

Here we have r =ã€₤eÿ£¢2ü€ã€₤cotã€₤öÝã€₤, or logã€₤r =ã€₤logã€₤eã€₤û—ã€₤2ü€ã€₤û—ã€₤cotã€₤öÝã€₤, from which we obtain the following figures19:

Ratio of breadth of each whorl to the next preceding r ã€₤いã€₤1Constant angle öÝ
1ôñ1〇89ô¯ô 〇8ÿ£¢ã€ý
1ôñ2587〈ô 58〈
1ôñ5〇86〈ô 18〈
2ôñ0〇83〈ô 42〈
2ôñ5〇81〈ô 42〈
3ôñ0〇80〈ô 〇5〈
3ôñ5〇78〈ô 43〈
4ôñ0〇77〈ô 34〈
4ôñ5〇76〈ô 32〈
5ôñ0〇75〈ô 38〈
10ôñ0〇69〈ô 53〈
20ôñ0〇64〈ô 31〈
50ôñ0〇58〈ô 〇5〈
100ôñ0〇53〈ô 46〈
1,000ôñ0〇42〈ô 17〈
10,000〈〇〇34〈ô 19〈
100,000〈〇〇28〈ô 37〈
1,000,000〈〇〇24〈ô 28〈
10,000,000〈〇〇21〈ô 18〈
100,000,000〈〇〇18〈ô 50〈
1,000,000,000〈〇〇16〈ô 52〈

We learn several interesting things from this short table. We see, in the first place, that where each whorl is about three times the breadth of its neighbour and

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