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The intersection H of the three altitudes AH_A, BH_B, and CH_C of a triangle is called the orthocenter. The name was invented by Besant and Ferrers in 1865 while walking on a ...

Given a source S and a curve gamma, pick a point on gamma and find its tangent T. Then the locus of reflections of S about tangents T is the orthotomic curve (also known as ...

A curve y(x) is osculating to f(x) at x_0 if it is tangent at x_0 and has the same curvature there. Osculating curves therefore satisfy y^((k))(x_0)=f^((k))(x_0) for k=0, 1, ...

An egg-shaped curve. Lockwood (1967) calls the negative pedal curve of an ellipse with eccentricity e<=1/2 an ovoid.

The Pappus spiral is the name given to the conical spiral with parametric equations x(t) = asin(alphat)cost (1) y(t) = asin(alphat)sint (2) x(t) = acos(alphat) (3) by ...

For a parabola oriented vertically and opening upwards, the vertex is the point where the curve reaches a minimum.

A quadratic surface given by the equation x^2+2rz=0.

Rings produced by cutting a strip that has been given m half twists and been re-attached into n equal strips (Ball and Coxeter 1987, pp. 127-128).

The function f(x,y)=(2x^2-y)(y-x^2) which does not have a local maximum at (0, 0), despite criteria commonly touted in the second half of the 1800s which indicated the ...

A curve given by the Cartesian equation b^2y^2=x^3(a-x). (1) It has area A=(a^3pi)/(8b). (2) The curvature is kappa(x)=(2b^2(3a^2-12ax+8x^2))/(sqrt(x)[4b^2(a-x)+(3a-4x)^2x]). ...