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Given two bicentric points P=p:q:r and U=u:v:w, their bicentric sum is defined by p+u:q+v:r:w.

A line segment joining the midpoints of opposite sides of a quadrilateral or tetrahedron. Varignon's theorem states that the bimedians of a quadrilateral bisect each other ...

The quartic with implicit equation x^4=x^2y-y^3. (1) The bow has vertical tangents at (+/-2/9sqrt(3),2/9) and horizontal tangents at (+/-1/4sqrt(2),1/4). Its curvature is ...

In a cyclic quadrilateral ABCD having perpendicular diagonals AC_|_BD, the perpendiculars to the sides through point T of intersection of the diagonals (the anticenter) ...

Let A_1, B_2, C_1, A_2, and B_1 be five points determining a conic. Then the conic is the locus of the point C_2=A_1(L·C_1A_2)·B_1(L·C_1B_2), where L is a line through the ...

One name for the figure used by Euclid to prove the Pythagorean theorem. It is sometimes also known as the "windmill."

Brocard geometry is that part of triangle geometry concerned with the Brocard points, Brocard triangles, etc.

The stylized cross illustrated above.

The "cannabis" curve is the name given here to the polar curve whose shape resembles that of a cannabis leaf. The cannabis curve encloses an area A=(27619209)/(16000000)pia^2.

For the cardioid given parametrically as x = a(1+cost)cost (1) y = a(1+cost)sint, (2) the negative pedal curve with respect to the pedal point (x_0,y_0)=(0,0) is the circle ...