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A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie").
The spiral approach is a technique often used in education where the initial focus of instruction is the basic facts of a subject, with further details being introduced as learning progresses. Throughout instruction, both the initial basic facts and the relationships to later details are repeatedly emphasized to help enter into long-term memory ...
The polar equation for a golden spiral is the same as for other logarithmic spirals, but with a special value of the growth factor b: [10] = or = (/), with e being the base of natural logarithms, a being the initial radius of the spiral, and b such that when θ is a right angle (a quarter turn in either direction): =.
For example, when leaves alternate up a stem, one rotation of the spiral touches two leaves, so the pattern or ratio is 1/2. In hazel the ratio is 1/3; in apricot it is 2/5; in pear it is 3/8; in almond it is 5/13. [56] Animal behaviour can yield spirals; for example, acorn worms leave spiral fecal trails on the sea floor. [57]
Starting from an empty grid or other configurations, the most commonly observed behaviours are chaotic growth, spiral growth and 'highway' construction. Rare examples become periodic after a certain number of steps.
Growth stocks vs. value stocks. There are many differences between growth and value stocks. Each of these asset types offers valuable benefits and drawbacks worth carefully considering. And ...
Meanwhile, many of the top growth stocks in the Growth ETF are still attractively priced based on their expected growth in 2025. If the AI boom continues, I expect growth to once again come out on ...
On Growth and Form is a book by the Scottish mathematical biologist D'Arcy Wentworth Thompson (1860–1948). The book is long – 793 pages in the first edition of 1917, 1116 pages in the second edition of 1942.