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The Dou circle is the circle cutting the sidelines of the reference triangle DeltaABC at A^', A^(''), B^', B^(''), C^', and C^('') such that ...

The normal to an ellipse at a point P intersects the ellipse at another point Q. The angle corresponding to Q can be found by solving the equation (P-Q)·(dP)/(dt)=0 (1) for ...

Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities a and b is written a=b. Equal is implemented in the Wolfram ...

Ono (1914) conjectured that the inequality 27(b^2+c^2-a^2)^2(a^2+c^2-b^2)^2(a^2+b^2-c^2)^2<=(4K)^6 holds true for all triangles, where a, b, and c are the lengths of the ...

Let the minimal length of an addition chain for a number n be denoted l(n). Then the Scholz conjecture, also called the Scholz-Brauer conjecture or Brauer-Scholz conjecture, ...

Seymour conjectured that a graph G of order n with minimum vertex degree delta(G)>=kn/(k+1) contains the kth graph power of a Hamiltonian cycle, generalizing Pósa's ...

A number of the form Tt_n=((n+2; 2); 2)=1/8n(n+1)(n+2)(n+3) (Comtet 1974, Stanley 1999), where (n; k) is a binomial coefficient. The first few values are 3, 15, 45, 105, 210, ...

There are many mathematical and recreational problems related to folding. Origami, the Japanese art of paper folding, is one well-known example. It is possible to make a ...

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

An official chessboard is an 8×8 board containing squares alternating in color between olive green and buff (where "buff" is a color variously defined as a moderate orange ...