Search Results for ""

A line segment joining the midpoints of opposite sides of a quadrilateral or tetrahedron. Varignon's theorem states that the bimedians of a quadrilateral bisect each other ...

The simplest dissection of a square into rectangles of the same areas but different shapes, composed of the seven pieces illustrated above. The square is 210 units on a side, ...

The boustrophedon ("ox-plowing") transform b of a sequence a is given by b_n = sum_(k=0)^(n)(n; k)a_kE_(n-k) (1) a_n = sum_(k=0)^(n)(-1)^(n-k)(n; k)b_kE_(n-k) (2) for n>=0, ...

The series producing Brun's constant converges even if there are an infinite number of twin primes, first proved by Brun (1919).

A change of basis is the transformation of coordinate-based vector and operator representations in a given vector space from one vector basis representation to another.

The partial differential equation u_(xx)+(y^2)/(1-(y^2)/(c^2))u_(yy)+yu_y=0.

The equation f(x_n|x_s)=int_(-infty)^inftyf(x_n|x_r)f(x_r|x_s)dx_r which gives the transitional densities of a Markov sequence. Here, n>r>s are any integers (Papoulis 1984, ...

Taking the locus of midpoints from a fixed point to a circle of radius r results in a circle of radius r/2. This follows trivially from r(theta) = [-x; 0]+1/2([rcostheta; ...

A geometric figure which touches only the vertices (or other extremities) of another figure.

A multiplicative factor (usually indexed) such as one of the constants a_i in the polynomial a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0. In this polynomial, the monomials are ...