Bicorn

The following curve is the locus of point X resulting in the classical proof of Pythagora's theorem.
Usually X is defined as the intersection point of BL with the polar of L with respect to the circle
with diameter AC, the hypotenuse of the right angled triangle ABC. The figure below indicates the
paths described by various moving points related to the triangle as vertex B varies on the circle
with diameter AC. The parameter a entering the formula is a=AC/2 and the origin is at the middle
O of AC (See Pythagoras.html , Polar.html ).

Bicorn                                 y²(a²-x²) = (x²+2ay-a²)² ,
parametric equations:
                                                  x = asin(t),
                                                  y = (acos²(t)/(2-cos(t)).

[Mathcurve, /courbes2d/bicorne/bicorne.shtml].

Bibliography

[Mathcurve] Robert Ferreol Curves remarquables Encyclopedie des formes mathematiques remarquables

Return to Gallery

http://users.math.uoc.gr/~pamfilos/

Bicorn

See Also

Bibliography