Search Results for ""

In nonstandard analysis, the transfer principle is the technical form of the following intuitive idea: "Anything provable about a given superstructure V by passing to a ...

An abnormal number is a hypothetical number which can be factored into primes in more than one way. Hardy and Wright (1979) prove the fundamental theorem of arithmetic by ...

A proof based on a dissection which shows the formula for the area of a plane figure or of the volume of a solid. Dozens of different dissection proofs are known for the ...

If an aliquot sequence {s^0(n),s(n),s^2(n),...} for a given n is bounded, it either ends at s(1)=0 or becomes periodic. If the sequence is periodic (or eventually periodic), ...

Find necessary and sufficient conditions that determine when the integral curve of two periodic functions kappa(s) and tau(s) with the same period L is a closed curve.

All Mathieu functions have the form e^(irz)f(z), where f(z) has period 2pi and r is known as the Mathieu characteristic exponent. This exponent is returned by the Wolfram ...

A function periodic with period 2pi such that p(theta+pi)=-p(theta) for all theta is said to be Möbius periodic.

A characteristic of some systems making a transition to chaos. Doubling is followed by quadrupling, etc. An example of a map displaying period doubling is the logistic map.

A point x_0 is said to be a periodic point of a function f of period n if f^n(x_0)=x_0, where f^0(x)=x and f^n(x) is defined recursively by f^n(x)=f(f^(n-1)(x)).

An elementary theorem in geometry whose name means "asses' bridge," perhaps in reference to the fact that fools would be unable to pass this point in their geometric studies. ...