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Except for convex polygons, every simple polygon has at least one mouth.

Given an acute angle in a right triangle, the opposite side is the leg of the triangle which is not incident on the angle. Lengths of opposite and adjacent sides appear ...

If two pairs of opposite sides of a complete quadrilateral are pairs of perpendicular lines, the quadrilateral is said to be orthocentric. In such a case, the remaining sides ...

The orthoptic circle of the Steiner inellipse is the circle with center at alpha_2=1/a, (1) corresponding to the triangle centroid G and radius ...

A parallelotope whose edges are all mutually perpendicular. The orthotope is a generalization of the rectangle and cuboid.

The fraction eta of a volume filled by a given collection of solids.

A papal cross is a cross having three crossbars. A schematic polyomino version of a papal cross is illustrated above.

The inverse curve for a parabola given by x = at^2 (1) y = 2at (2) with inversion center (x_0,y_0) and inversion radius k is x = x_0+(k(at^2-x_0))/((at^2+x_0)^2+(2at-y_0)^2) ...

The involute of a parabola x = at^2 (1) y = at (2) is given by x_i = -(atsinh^(-1)(2t))/(2sqrt(4t^2+1)) (3) y_i = a(1/2t-(sinh^(-1)(2t))/(4sqrt(4t^2+1))). (4) Defining ...

A cyclide formed by inversion of a standard torus when inversion sphere is tangent to the torus.