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The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a ...

Formulas expressing trigonometric functions of an angle 2x in terms of functions of an angle x, sin(2x) = 2sinxcosx (1) cos(2x) = cos^2x-sin^2x (2) = 2cos^2x-1 (3) = ...

The exterior angle bisectors (Johnson 1929, p. 149), also called the external angle bisectors (Kimberling 1998, pp. 18-19), of a triangle DeltaABC are the lines bisecting the ...

Let X be a locally convex topological vector space and let K be a compact subset of X. In functional analysis, Milman's theorem is a result which says that if the closed ...

Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2x) = ...

An angle theta drawn on the coordinate plane is said to be in standard position if its initial side lies on the positive x-axis so that its vertex coincides with the origin ...

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...

There are so many theorems due to Fermat that the term "Fermat's theorem" is best avoided unless augmented by a description of which theorem of Fermat is under discussion. ...

Specifying two adjacent side lengths a and c of a triangle (with a<c) and one acute angle A opposite a does not, in general, uniquely determine a triangle. If sinA<a/c, there ...

The triangle center with triangle center function alpha=A.