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Tomography is the study of the reconstruction of two- and three-dimensional objects from one-dimensional slices. The Radon transform is an important tool in tomography. ...

The "trefoil" curve is the name given by Cundy and Rollett (1989, p. 72) to the quartic plane curve given by the equation x^4+x^2y^2+y^4=x(x^2-y^2). (1) As such, it is a ...

Let P_i=x_i:y_i:z_i be trilinear points for i=1, 2, 3. The A-vertex of the unary cofactor triangle is then defined as the point y_2z_3-z_2y_3:z_2x_3-x_2z_3:x_2y_3-y_2x_3, and ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...

Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc. How many grains total are placed on an ...

The orthogonal polynomials defined variously by (1) (Koekoek and Swarttouw 1998, p. 24) or p_n(x;a,b,c,d) = W_n(-x^2;a,b,c,d) (2) = (3) (Koepf, p. 116, 1998). The first few ...

The ordinary differential equation y=xf(y^')+g(y^'), where y^'=dy/dx and f and g are given functions. This equation is sometimes also known as Lagrange's equation (Zwillinger ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

A series is an infinite ordered set of terms combined together by the addition operator. The term "infinite series" is sometimes used to emphasize the fact that series ...