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In the above figure, let E be the intersection of AD and BC and specify that AB∥EF∥CD. Then 1/(AB)+1/(CD)=1/(EF). A beautiful related theorem due to H. Stengel can be stated ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...

A surface which is related to Cayley numbers.

Two quantities are said to be different (or "unequal") if they are not equal. The term "different" also has a technical usage related to modules. Let a module M in an ...

A digit sum s_b(n) is a sum of the base-b digits of n, which can be implemented in the Wolfram Language as DigitSum[n_, b_:10] := Total[IntegerDigits[n, b]]The following ...

A directed infinity in direction z is an infinite numerical quantity that is a positive real multiple of the complex number z. Directed infinity may be returned in the ...

A symbol used to distinguish a third quantity x^('') ("x double prime") from two other related quantities x and x^' ("x prime). Double primes are most commonly used to denote ...

Given a Jacobi amplitude phi in an elliptic integral, the argument u is defined by the relation phi=am(u,k). It is related to the elliptic integral of the first kind F(u,k) ...

Given a spheroid with equatorial radius a and polar radius c, the ellipticity is defined by e={sqrt((a^2-c^2)/(a^2)) c<a (oblate spheroid); sqrt((c^2-a^2)/(c^2)) c>a (prolate ...