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For an undirected graph, an unordered pair of nodes that specify a line joining these two nodes are said to form an edge. For a directed graph, the edge is an ordered pair of ...

The lemniscate functions arise in rectifying the arc length of the lemniscate. The lemniscate functions were first studied by Jakob Bernoulli and Giulio Fagnano. A historical ...

The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of ...

There are two incompatible definitions of the squircle. The first defines the squircle as the quartic plane curve which is special case of the superellipse with a=b and r=4, ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

The arc length of the parabolic segment y=h(1-(x^2)/(a^2)) (1) illustrated above is given by s = int_(-a)^asqrt(1+y^('2))dx (2) = 2int_0^asqrt(1+y^('2))dx (3) = ...

A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the ...

Let s=1/(sqrt(2pi))[Gamma(1/4)]^2=5.2441151086... (1) (OEIS A064853) be the arc length of a lemniscate with a=1. Then the lemniscate constant is the quantity L = 1/2s (2) = ...

A lamp is turned on for 1/2 minute, off for 1/4 minute, on for 1/8 minute, etc. At the end of one minute, the lamp switch will have been moved aleph_0 times, where aleph_0 is ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...