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In this illusion, the vertical lines in the above figure are parallel, but appear to be tilted at an angle. In 1860, F. Zöllner sent his discovery in a letter to physicist ...

A zonal harmonic is a spherical harmonic of the form P_l(costheta), i.e., one which reduces to a Legendre polynomial (Whittaker and Watson 1990, p. 302). These harmonics are ...

The de Longchamps ellipse of a triangle DeltaABC is the conic circumscribed on the incentral triangle and the Cevian triangle of the isogonal mittenpunkt X_(57). (Since a ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

de Rham's function is the function defined by the functional equations phi_alpha(1/2x) = alphaphi_alpha(x) (1) phi_alpha(1/2(x+1)) = alpha+(1-alpha)phi_alpha(x) (2) (Trott ...

An n-tuple, sometimes simply called a "tuple" when the number n is known implicitly, is another word for a list, i.e., an ordered set of n elements. It can be interpreted as ...

When p is a prime number, then a p-group is a group, all of whose elements have order some power of p. For a finite group, the equivalent definition is that the number of ...

A q-analog of the Chu-Vandermonde identity given by where _2phi_1(a,b;c;q,z) is the q-hypergeometric function. The identity can also be written as ...

The q-digamma function psi_q(z), also denoted psi_q^((0))(z), is defined as psi_q(z)=1/(Gamma_q(z))(partialGamma_q(z))/(partialz), (1) where Gamma_q(z) is the q-gamma ...

A continuous distribution defined on the range x in [0,2pi) with probability density function P(x)=(e^(bcos(x-a)))/(2piI_0(b)), (1) where I_0(x) is a modified Bessel function ...