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Origami is the Japanese art of paper folding. In traditional origami, constructions are done using a single sheet of colored paper that is often, though not always, square. ...

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

A vector perpendicular to a given vector a is a vector a^_|_ (voiced "a-perp") such that a and a^_|_ form a right angle. In the plane, there are two vectors perpendicular to ...

The 60 Pascal lines of a hexagon inscribed in a conic section intersect three at a time through 20 Steiner points. There is a dual relationship between the 15 Plücker lines ...

Given an obtuse triangle, the polar circle has center at the orthocenter H. Call H_i the feet. Then the square of the radius r is given by r^2 = HA^_·HH_A^_ (1) = HB^_·HH_B^_ ...

The chord through a focus parallel to the conic section directrix of a conic section is called the latus rectum, and half this length is called the semilatus rectum (Coxeter ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

The total graph T(G) of a graph G has a vertex for each edge and vertex of G and an edge in T(G) for every edge-edge, vertex-edge, and vertex-vertex adjacency in G ...

A weak snark is a cyclically 4-edge connected cubic graph with edge chromatic number 4 and girth at least 4 (Brinkmann et al. 2013). Weak snarks therefore represent a more ...