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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 ...

If each of two curves meets the line at infinity in distinct, nonsingular points, and if all their intersections are finite, then if to each common point there is attached a ...

Define the first Brocard point as the interior point Omega of a triangle for which the angles ∠OmegaAB, ∠OmegaBC, and ∠OmegaCA are equal to an angle omega. Similarly, define ...

The map projection having transformation equations x = (lambda-lambda_0)cosphi_s (1) y = sinphisecphi_s (2) for the normal aspect, where lambda is the longitude, lambda_0 is ...

The center of an inner Soddy circle. It has equivalent triangle center functions alpha = 1+(2Delta)/(a(b+c-a)) (1) alpha = sec(1/2A)cos(1/2B)cos(1/2C)+1, (2) where Delta is ...

Let A and B be two classes of positive integers. Let A(n) be the number of integers in A which are less than or equal to n, and let B(n) be the number of integers in B which ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...

The golden triangle, sometimes also called the sublime triangle, is an isosceles triangle such that the ratio of the hypotenuse a to base b is equal to the golden ratio, ...

An isosceles trapezoid (called an isosceles trapezium by the British; Bronshtein and Semendyayev 1997, p. 174) is trapezoid in which the base angles are equal and therefore ...

The "kurtosis excess" (Kenney and Keeping 1951, p. 27) is defined in terms of the usual kurtosis by gamma_2 = beta_2-3 (1) = (mu_4)/(mu_2^2)-3. (2) It is commonly denoted ...