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The altitudes of a triangle are the Cevians A_iH_i that are perpendicular to the legs A_jA_k opposite A_i. The three altitudes of any triangle are concurrent at the ...

Given a chord PQ of a circle, draw any other two chords AB and CD passing through its midpoint. Call the points where AD and BC meet PQ X and Y. Then M is also the midpoint ...

A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...

Ahmed's integral is the definite integral int_0^1(tan^(-1)(sqrt(x^2+2)))/(sqrt(x^2+2)(x^2+1))dx=5/(96)pi^2 (OEIS A096615; Ahmed 2002; Borwein et al. 2004, pp. 17-20). This is ...

An almost perfect number, also known as a least deficient or slightly defective (Singh 1997) number, is a positive integer n for which the divisor function satisfies ...

A binary bracketing is a bracketing built up entirely of binary operations. The number of binary bracketings of n letters (Catalan's problem) are given by the Catalan numbers ...

A chordless graph is a simple graph possessing no chords. A chordal graph (which possesses no chordless cycles) is not the same as (or converse of) a chordless graph (which ...

Consider a combination lock consisting of n buttons that can be pressed in any combination (including multiple buttons at once), but in such a way that each number is pressed ...

A monoid that is commutative i.e., a monoid M such that for every two elements a and b in M, ab=ba. This means that commutative monoids are commutative, associative, and have ...