Evolute of Ellipse
- Author:
- Michael Borcherds
Equation of the evolute of an Ellipse from Greg Egan
https://twitter.com/gregeganSF/status/1267463035242737664
Version to copy and paste:
a⁴y⁸+(a²-b²)²(a²-d²)²(b²-d²)²+x⁶(2b²y²(a²+b²)+2b²(a²(d²-2b²)+b⁴-2b²d²))-2y²(a-b)(a+b)(a-d)(a+d)(a⁴(b²+d²)-2a²(b⁴+d⁴)+b²d²(b²+d²))+x⁴(a⁴(6b⁴-6b²d²+d⁴)-2a²(3b⁶-5b⁴d²+3b²d⁴)+y⁴(a⁴+4a²b²+b⁴)-2y²(a⁴(3b²+d²)-a²b²(b²+d²)+b⁶+3b⁴d²)+b⁸-6b⁶d²+6b⁴d⁴)+2y⁶(a⁶-2a⁴(b²+d²)+a²b²d²)+x²(2a²y⁶(a²+b²)-2(a-b)(a+b)(b-d)(b+d)(a⁴(2b²-d²)-a²(b⁴+d⁴)-b⁴d²+2b²d⁴)-2y⁴(a⁶-a⁴b²+3a²b⁴+d²(3a⁴-a²b²+b⁴)) +2y²(a⁶(3b²+2d²)+a⁴(-5b⁴-3b²d²+3d⁴)+a²(3b⁶-3b⁴d²-5b²d⁴)+2b⁶d²+3b⁴d⁴))+y⁴(a⁸-6a⁶(b²+d²)+2a⁴(3b⁴+5b²d²+3d⁴)-6a²b²d²(b²+d²)+b⁴d⁴)+b⁴x⁸=0
