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The Moses-Longuet-Higgins circle is the radical circle of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c-a, c+a-b, and ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...

A series expansion is a representation of a particular function as a sum of powers in one of its variables, or by a sum of powers of another (usually elementary) function ...

The tangential circle of a reference triangle is the circumcircle of the tangential triangle. Its center is Kimberling center X_(26), which has center function ...

The term "total curvature" is used in two different ways in differential geometry. The total curvature, also called the third curvature, of a space curve with line elements ...

The trigonometric formulas for pi/5 can be derived using the multiple-angle formula sin(5theta)=5sintheta-20sin^3theta+16sin^5theta. (1) Letting theta=pi/5 and x=sintheta ...

A technically defined extension of the ordinary determinant to "higher dimensional" hypermatrices. Cayley (1845) originally coined the term, but subsequently used it to refer ...

Polycairos are polyforms obtained from the Cairo tessellation, illustrated above. The numbers of polycairos with n=1, 2, ... components are 1, 2, 5, 17, 55, 206, 781, 3099, ...

Legendre's conjecture asserts that for every n there exists a prime p between n^2 and (n+1)^2 (Hardy and Wright 1979, p. 415; Ribenboim 1996, pp. 397-398). It is one of ...

By analogy with the outer Napoleon triangle, consider the external erection of three squares on the sides of a triangle DeltaABC. These centers form a triangle DeltaO_AO_BO_C ...