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The envelope of refracted rays for a given curve.

The symbol ∡ABC denotes the directed angle from AB to BC, which is the signed angle through which AB must be rotated about B to coincide with BC. Four points ABCD lie on a ...

The symbol | which is not used very commonly in mathematics. The double dagger is also known as the double obelisk or diesis (Bringhurst 1997, p. 275).

Let a, b, and k be integers with k>=1. For j=0, 1, 2, let S_j=sum_(i=j (mod 3))(-1)^i(k; i)a^(k-i)b^i. Then 2(a^2+ab+b^2)^(2k)=(S_0-S_1)^4+(S_1-S_2)^4+(S_2-S_0)^4.

The inverse of the Laplace transform F(t) = L^(-1)[f(s)] (1) = 1/(2pii)int_(gamma-iinfty)^(gamma+iinfty)e^(st)f(s)ds (2) f(s) = L[F(t)] (3) = int_0^inftyF(t)e^(-st)dt. (4)

An algebraic variety is called irreducible if it cannot be written as the union of nonempty algebraic varieties. For example, the set of solutions to xy=0 is reducible ...

A root-finding algorithm also called Bailey's method and Hutton's method. For a function of the form g(x)=x^d-r, Lambert's method gives an iteration function ...

The least common denominator of a collection of fractions (p_1)/(q_1),...,(p_n)/(q_n) is the least common multiple LCM(q_1,...,q_n) of their denominators.

A leg of a triangle is one of its sides. For a right triangle, the term "leg" generally refers to a side other than the one opposite the right angle (which is termed the ...

Expresses a function in terms of its Radon transform, f(x,y) = R^(-1)(Rf)(x,y) (1) = ...