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Engineering notation is a version of scientific notation in which the exponent p in expressions of the form a×10^p is chosen to always be divisible by 3. Numbers of forms ...

Let (x_1,x_2) and (y_1,y_2) be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of ...

The function z=f(x)=ln(x/(1-x)). (1) This function has an inflection point at x=1/2, where f^('')(x)=(2x-1)/(x^2(x-1)^2)=0. (2) Applying the logit transformation to values ...

The Morgan-Voyce polynomials are polynomials related to the Brahmagupta and Fibonacci polynomials. They are defined by the recurrence relations b_n(x) = ...

Niven's theorem states that if x/pi and sinx are both rational, then the sine takes values 0, +/-1/2, and +/-1. Particular cases include sin(pi) = 0 (1) sin(pi/2) = 1 (2) ...

The set of octonions, also sometimes called Cayley numbers and denoted O, consists of the elements in a Cayley algebra. A typical octonion is of the form ...

Let alpha and beta be any ordinal numbers, then ordinal exponentiation is defined so that if beta=0 then alpha^beta=1. If beta is not a limit ordinal, then choose gamma such ...

A planar connected graph is a graph which is both planar and connected. The numbers of planar connected graphs with n=1, 2, ... nodes are 1, 1, 2, 6, 20, 99, 646, 5974, ...

A Pólya plot is a plot of the vector field of (R[f(z)],-I[f(z)]) of a complex function f(z). Several examples are shown above. Pólya plots can be created in the Wolfram ...

The positive integers are the numbers 1, 2, 3, ... (OEIS A000027), sometimes called the counting numbers or natural numbers, denoted Z^+. They are the solution to the simple ...