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For a point P inside an equilateral triangle DeltaABC, the sum of the perpendiculars p_i from P to the sides of the triangle is equal to the altitude h. This result is simply ...

The nth coefficient in the power series of a univalent function should be no greater than n. In other words, if f(z)=a_0+a_1z+a_2z^2+...+a_nz^n+... is a conformal mapping of ...

A term invented by B. Grünbaum in an attempt to promote concrete and precise polyhedron terminology. The word "coptic" derives from the Greek for "to cut," and acoptic ...

A solution to a problem that can be written in "closed form" in terms of known functions, constants, etc., is often called an analytic solution. Note that this use of the ...

The word basis can arise in several different contexts. Speaking in general terms, an object is "generated" by a basis in whatever manner is appropriate. For example, a ...

A continuous map is a continuous function between two topological spaces. In some fields of mathematics, the term "function" is reserved for functions which are into the real ...

The identity element I (also denoted E, e, or 1) of a group or related mathematical structure S is the unique element such that Ia=aI=a for every element a in S. The symbol ...

If and only if (i.e., necessary and sufficient). The terms "just if" or "exactly when" are sometimes used instead. A iff B is written symbolically as A<->B, A<=>B, A<->B, or ...

A word derived from the Latin roots quad- (four) and via (ways, roads), therefore a crossing of four roads. In medieval universities, the quadrivium consisted of the four ...

The word "place" has a special meaning in complex variables, where it roughly corresponds to a point in the complex plane (except that it reflects the Riemann sheet structure ...