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The "witch of Agnesi" is a curve studied by Maria Agnesi in 1748 in her book Instituzioni analitiche ad uso della gioventù italiana (the first surviving mathematical work ...

An n×n matrix whose rows are composed of cyclically shifted versions of a length-n list l. For example, the 4×4 circulant matrix on the list l={1,2,3,4} is given by C=[4 1 2 ...

A hypergeometric identity discovered by Ramanujan around 1910. From Hardy (1999, pp. 13 and 102-103), (1) where a^((n))=a(a+1)...(a+n-1) (2) is the rising factorial (a.k.a. ...

There are (at least) two graphs associated with Ellingham and Horton. These graphs on 54 and 78 nodes respectively, illustrated above, are examples of 3-connected bicubic ...

The notion of a Hilbert C^*-module is a generalization of the notion of a Hilbert space. The first use of such objects was made by Kaplansky (1953). The research on Hilbert ...

There are a number of formulas variously known as Hurwitz's formula. The first is zeta(1-s,a)=(Gamma(s))/((2pi)^s)[e^(-piis/2)F(a,s)+e^(piis/2)F(-a,s)], where zeta(z,a) is a ...

Let psi_1(x) and psi_2(x) be any two real integrable functions in [a,b], then Schwarz's inequality is given by |<psi_1|psi_2>|^2<=<psi_1|psi_1><psi_2|psi_2>. (1) Written out ...

A number (usually base 10 unless specified otherwise) which has no digitaddition generator. Such numbers were originally called Colombian numbers (S. 1974). There are ...

The singleton graph is the graph consisting of a single isolated node with no edges. It is therefore the empty graph on one node. It is commonly denoted K_1 (i.e., the ...

The point T at which the lines through the polygon vertices of a triangle perpendicular to the corresponding sides of the first Brocard triangle, are concurrent. The Tarry ...