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The hexyl circle is the circumcircle of the hexyl triangle. Amazingly, its center is at the incenter I and its radius is 2R, where R is the circumradius. Its circle function ...

Also known as the a Lorentz transformation or Procrustian stretch, a hyperbolic transformation leaves each branch of the hyperbola x^'y^'=xy invariant and transforms circles ...

Pick a point O in the interior of a quadrilateral which is not a parallelogram. Join this point to each of the four vertices, then the locus of points O for which the sum of ...

The surface of revolution generated by the external catenary between a fixed point a and its conjugate on the envelope of the catenary through the fixed point is equal in ...

A mensuration formula is simply a formula for computing the length-related properties of an object (such as area, circumradius, etc., of a polygon) based on other known ...

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]). ...

A transformation in which all points along a given line L remain fixed while other points are shifted parallel to L by a distance proportional to their perpendicular distance ...

A closed geometric figure on the surface of a sphere which is formed by the arcs of great circles. The spherical polygon is a generalization of the spherical triangle. If ...

The triquetra is a geometric figure consisting of three mutually intersecting vesica piscis lens shapes, as illustrated above. The central region common to all three lenses ...

The figure formed when the midpoints of the sides of a convex quadrilateral are joined in order is a parallelogram. Equivalently, the bimedians bisect each other. The area of ...