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Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, configuration spaces, etc.) that ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function. Then the sequence of numbers s^0(n)=n,s^1(n)=s(n),s^2(n)=s(s(n)),... ...

Consider decomposition the factorial n! into multiplicative factors p_k^(b_k) arranged in nondecreasing order. For example, 4! = 3·2^3 (1) = 2·3·4 (2) = 2·2·2·3 (3) and 5! = ...

The alternating factorial is defined as the sum of consecutive factorials with alternating signs, a(n)=sum_(k=1)^n(-1)^(n-k)k!. (1) They can be given in closed form as ...

An amphichiral knot is a knot that is capable of being continuously deformed into its own mirror image. More formally, a knot K is amphichiral (also called achiral or ...

The term analysis is used in two ways in mathematics. It describes both the discipline of which calculus is a part and one form of abstract logic theory. Analysis is the ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...

The anticomplementary triangle is the triangle DeltaA_1^'A_2^'A_3^' which has a given triangle DeltaA_1A_2A_3 as its medial triangle. It is therefore the anticevian triangle ...

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. Its Schläfli symbol is {infty}. The apeirogon can produce a ...