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The orthoptic circle of the Steiner inellipse is the circle with center at alpha_2=1/a, (1) corresponding to the triangle centroid G and radius ...

The "perp dot product" a^_|_·b for a and b vectors in the plane is a modification of the two-dimensional dot product in which a is replaced by the perpendicular vector ...

The operator I^~ which takes a real number to the same real number I^~r=r.

The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...

A set of numbers obeying a pattern like the following: 91·37 = 3367 (1) 9901·3367 = 33336667 (2) 999001·333667 = 333333666667 (3) 99990001·33336667 = 3333333366666667 (4) 4^2 ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

The standard deviation sigma of a probability distribution is defined as the square root of the variance sigma^2, sigma = sqrt(<x^2>-<x>^2) (1) = sqrt(mu_2^'-mu^2), (2) where ...

Given a formula y=f(x) with an absolute error in x of dx, the absolute error is dy. The relative error is dy/y. If x=f(u,v,...), then ...

The Lyapunov condition, sometimes known as Lyapunov's central limit theorem, states that if the (2+epsilon)th moment (with epsilon>0) exists for a statistical distribution of ...

Consider the Lagrange interpolating polynomial f(x)=b_0+(x-1)(b_1+(x-2)(b_3+(x-3)+...)) (1) through the points (n,p_n), where p_n is the nth prime. For the first few points, ...