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Euler (1738, 1753) considered the series s_a(x)=sum_(n=1)^infty[1/(1-a^n)product_(k=0)^(n-1)(1-xa^(-k))]. He showed that just like log_a(a^n)=n, s_a(a^n)=n for nonnegative ...

The Van Lint-Schrijver Graph graph is a weakly regular Hamiltonian graph on 162 vertices with parameters (nu,k,lambda,mu)=(162,(6),(0),(0,1)). It is distance-regular with ...

The cubeplex graph is the cubic Hamiltonian graph on 12 nodes illustrated above in several embeddings and corresponding to the graph Gamma_1 in Fischer and Little (2001). It ...

A graph cycle.

For positive numbers a and b with a!=b, (a+b)/2>(b-a)/(lnb-lna)>sqrt(ab).

The inverse curve of the logarithmic spiral r=e^(atheta) with inversion center at the origin and inversion radius k is the logarithmic spiral r=ke^(-atheta).

The triangle graph is the cycle graph C_3, which is isomorphic to the complete graph K_3 as well as to the complete tripartite graph K_(3×1)=K_(1,1,1) and the triangular ...

The pedal curve of a logarithmic spiral with parametric equation f = e^(at)cost (1) g = e^(at)sint (2) for a pedal point at the pole is an identical logarithmic spiral x = ...

The radial curve of the logarithmic spiral is another logarithmic spiral.

An antimagic graph is a graph with e graph edges labeled with distinct elements {1,2,...,e} so that the sum of the graph edge labels at each graph vertex differ.