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To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary ...

A number x is said to have "n figures" if it takes n digits to express it. The number of figures is therefore equal to one more than the power of 10 in the scientific ...

A complex number z may be represented as z=x+iy=|z|e^(itheta), (1) where |z| is a positive real number called the complex modulus of z, and theta (sometimes also denoted phi) ...

A polyhedral graph is completely regular if the dual graph is also regular. There are only five types. Let rho be the number of graph edges at each node, rho^* the number of ...

1 1 2 2 3 5 5 7 10 15 15 20 27 37 52 The Bell triangle, also called Aitken's array or the Peirce triangle (Knuth 2005, p. 28), is the number triangle obtained by beginning ...

Abstract Algebra

The imaginary part I[z] of a complex number z=x+iy is the real number multiplying i, so I[x+iy]=y. In terms of z itself, I[z]=(z-z^_)/(2i), where z^_ is the complex conjugate ...

A totative is a positive integer less than or equal to a number n which is also relatively prime to n, where 1 is counted as being relatively prime to all numbers. The number ...

The number of data points which fall within a given class in a frequency distribution.

In the archaic terminology of Whittaker and Watson (1990), the complex number z representing x+iy.