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Geometry

The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

In his last letter to Hardy, Ramanujan defined 17 Jacobi theta function-like functions F(q) with |q|<1 which he called "mock theta functions" (Watson 1936ab, Ramanujan 1988, ...

The adjacency matrix, sometimes also called the connection matrix, of a simple labeled graph is a matrix with rows and columns labeled by graph vertices, with a 1 or 0 in ...

The Cantor set T_infty, sometimes also called the Cantor comb or no middle third set (Cullen 1968, pp. 78-81), is given by taking the interval [0,1] (set T_0), removing the ...

A portion of a disk whose upper boundary is a (circular) arc and whose lower boundary is a chord making a central angle theta<pi radians (180 degrees), illustrated above as ...

A connex is a geometric form introduced by Clebsch (1872) that included as special cases the curve considered as a point locus and the curve considered as a line envelope ...

If P is a pedal point inside a triangle DeltaABC, and P_A, P_B, and P_C are the feet of the perpendiculars from P upon the respective sides BC, CA, and AB, then ...

For s>1, the Riemann zeta function is given by zeta(s) = sum_(n=1)^(infty)1/(n^s) (1) = product_(k=1)^(infty)1/(1-1/(p_k^s)), (2) where p_k is the kth prime. This is Euler's ...