Curve of the devil

the curve of the devil at summer studied in 1750 by Cramer and in 1810 by Lacroix.

Etymology

This curve owes its name with the closed arc which composes it partly, and which recalls the shape of a popular toy at the end of the XVIIIe century, the twin wheel (in English: “ the devil one two stick ”).

Equations

polar Equation: $r^2\; =\; b^2\; +\; \backslash \; frac\; \{a^2\}\; \{\backslash \; cos2\; \backslash \; theta\}\; \backslash ,$.

Cartesian Equation: $x^4\; -\; y^4\; -\; (a^2\; +\; b^2)\; \backslash \; cdot\; x^2\; -\; (a^2\; -\; b^2)\; \backslash \; cdot\; y^2\; =\; 0\; \backslash ,$

See too

• Lemniscate

Random links:

Soulanges (Champagne-Ardenne) | Robert Millets (architect) | The Community of communes of the Mounts of Azure | Transduction (genetic) | Sebastianus | Université_de_Toulouse

© 2007-2008 speedlook.com; article text available under the terms of GFDL, from fr.wikipedia.org