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An octic curve is an algebraic curve of order eight. The pear curve is an example of an octic curve.

An algebraic surface of degree eight. The maximum number of ordinary double points known to exist on an octic surface is 168 (the Endraß octics), although the rigorous upper ...

A surface which is homeomorphic to a finite collection of spheres, each with a finite number of handles, cross-handles, cross-caps, and perforations. A preliminary version of ...

A nonsingular linear map A:R^n->R^n is orientation-preserving if det(A)>0.

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.