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Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

The blossom algorithm (Edmonds 1965) finds a maximum independent edge set in a (possibly weighted) graph. While a maximum independent edge set can be found fairly easily for ...

The function [x] which gives the smallest integer >=x, shown as the thick curve in the above plot. Schroeder (1991) calls the ceiling function symbols the "gallows" because ...

An equation is said to be a closed-form solution if it solves a given problem in terms of functions and mathematical operations from a given generally-accepted set. For ...

In December 1920, M. Schönfinkel presented in a report to the Mathematical Society in Göttingen a new type of formal logic based on the concept of a generalized function ...

The "contiguous USA graph" is the graph whose vertices represent the contiguous 48 states of the United States plus the District of Columbia (DC) and whose edges connect ...

The probability that a random integer between 1 and x will have its greatest prime factor <=x^alpha approaches a limiting value F(alpha) as x->infty, where F(alpha)=1 for ...

The number N_d^((b))(n) of digits d in the base-b representation of a number n is called the b-ary digit count for d. The digit count is implemented in the Wolfram Language ...

A function built up of a finite combination of constant functions, field operations (addition, multiplication, division, and root extractions--the elementary operations)--and ...

Faà di Bruno's formula gives an explicit equation for the nth derivative of the composition f(g(t)). If f(t) and g(t) are functions for which all necessary derivatives are ...