Search Results for ""

The Pappus configuration is the 9_3 configuration illustrated above that appears in Pappus's hexagon theorem. It is one of the three 9_3 configurations. The Levi graph of the ...

Given a regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the n=5 case of polygon triangle picking, A^_ = ...

The pentagonal cupola is Johnson solid J_5. Its faces consist of 5 equilateral triangles, 5 squares, 1 pentagon, and one decagon. The surface area and volume of the ...

A perfect cubic polynomial can be factored into a linear and a quadratic term, x^3+y^3 = (x+y)(x^2-xy+y^2) (1) x^3-y^3 = (x-y)(x^2+xy+y^2). (2)

A square matrix A such that the matrix power A^(k+1)=A for k a positive integer is called a periodic matrix. If k is the least such integer, then the matrix is said to have ...

An analog of the determinant for number triangles defined as a signed sum indexed by set partitions of {1,...,n} into pairs of elements. The Pfaffian is the square root of ...

The symbol +/- is used to denote a quantity which should be both added and subtracted, as in a+/-b. The symbol can be used to denote a range of uncertainty, or to denote a ...

Let {y^k} be a set of orthonormal vectors with k=1, 2, ..., K, such that the inner product (y^k,y^k)=1. Then set x=sum_(k=1)^Ku_ky^k (1) so that for any square matrix A for ...

To find the minimum distance between a point in the plane (x_0,y_0) and a quadratic plane curve y=a_0+a_1x+a_2x^2, (1) note that the square of the distance is r^2 = ...

Polynomial identities involving sums and differences of like powers include x^2-y^2 = (x-y)(x+y) (1) x^3-y^3 = (x-y)(x^2+xy+y^2) (2) x^3+y^3 = (x+y)(x^2-xy+y^2) (3) x^4-y^4 = ...