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A quadrilateral in which a pair of opposite sides have the same length and are inclined at 60 degrees to each other (or equivalently, satisfy <A>+<B>=120 degrees). Some ...

Consider Kimberling centers X_(20) (de Longchamps point Z; intersection L_S intersection L_E of the Soddy line and Euler line), X_(468) (intersection L_E intersection L_O of ...

A graph is said to be H^*-connected if it is either Hamilton-connected or Hamilton-laceable. S. Wagon (pers. comm., May. 20, 2013; Dupuis and Wagon 2014) conjecture that all ...

With three cuts, dissect an equilateral triangle into a square. The problem was first proposed by Dudeney in 1902, and subsequently discussed in Dudeney (1958), and Gardner ...

Home plate in the game of baseball is an irregular pentagon with two parallel sides, each perpendicular to a base. It seems reasonable to dub such a figure (i.e., a rectangle ...

Suppose a line L^' meets sidelines BC, CA, and AB in points A^', B^', and C^', respectively. Let A^('') be the reflection of A^' about the midpoint of segment BC, and ...

Since each triplet of Yff circles are congruent and pass through a single point, they obey Johnson's theorem. As a result, in each case, there is a fourth circle congruent to ...

The MacBeath circumconic is the dual conic to the MacBeath inconic, introduced in Dec. 2004 by P. Moses (Kimberling). It has circumconic parameters x:y:z=cosA:cosB:cosC, (1) ...

A maltitude ("midpoint altitude") is a perpendicular drawn to a side of a quadrilateral from the midpoint M_i of the opposite side. If the quadrilateral is cyclic, then the ...

The Napoleon-Feuerbach cubic is the pivotal isogonal cubic with nine-point center N as the pivot point. It therefore has trilinear equation ...