Editing Logarithmic spiral (section)

==''Spira mirabilis'' and Jacob Bernoulli==
'''''Spira mirabilis''''', [[Latin]] for "miraculous spiral", is another name for the logarithmic spiral. Although this curve had already been named by other mathematicians, the specific name ("miraculous" or "marvelous" spiral) was given to this curve by [[Jacob Bernoulli]], because he was fascinated by one of its unique mathematical properties: the size of the spiral increases but its shape is unaltered with each successive curve, a property known as [[self-similarity]]. Possibly as a result of this unique property, the spira mirabilis has evolved in nature, appearing in certain growing forms such as [[nautilus]] shells and [[sunflower]] heads.  Jacob Bernoulli wanted such a spiral engraved on his [[headstone]] along with the phrase "[[Eadem mutata resurgo]]" ("Although changed, I shall arise the same."), but, by error, an [[Archimedean spiral]] was placed there instead.<ref name="livio">{{cite book |last=Livio |first=Mario |year=2002 |title=The Golden Ratio: The Story of Phi, The World's Most Astonishing Number |publisher=Broadway Books |location=New York |isbn=978-0-7679-0815-3 |url-access=registration |url=https://archive.org/details/goldenratiostory00livi }}</ref><ref>Yates, R. C.: ''A Handbook on Curves and Their Properties'', J. W. Edwards (1952), "Evolutes". p. 206.</ref>