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De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

The mixtilinear circle is the circumcircle of the mixtilinear triangle, i.e., the triangle formed by the centers of the mixtilinear incircles. Neither its center not circle ...

A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

The radical circle of the mixtilinear incircles has a center with trilinear center function alpha_(999)=cosA-2, (1) which is Kimberling center X_(999). It has radius (2) ...

The mixtilinear triangle is the triangle connecting the centers of the mixtilinear incircles. It has trilinear vertex matrix (1) In has area (2) where Delta is the area of ...

A mental device used to aid memorization. Common mnemonics for mathematical constants such as e and pi consist of sentences in which the number of letters in each word give ...

There are two versions of the moat-crossing problem, one geometric and one algebraic. The geometric moat problems asks for the widest moat Rapunzel can cross to escape if she ...

A class of automata similar to cellular automata but which have a single "active" cell instead of updating all cells in parallel. In a mobile automaton, the evolution rules ...

In his last letter to Hardy, Ramanujan defined 17 Jacobi theta function-like functions F(q) with |q|<1 which he called "mock theta functions" (Watson 1936ab, Ramanujan 1988, ...

In many computer languages (such as FORTRAN or the Wolfram Language), the common residue of b (mod m) is written mod(b, m) (FORTRAN) or Mod[b, m] (Wolfram Language). The ...