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A right trapezoid is a trapezoid having two right angles. As illustrated above, the area of a right trapezoid is A = ah_2-1/2(h_2-h_1)a (1) = 1/2a(h_1+h_2). (2) A right ...

Let m and m+h be two consecutive critical indices of f and let F be (m+h)-normal. If the polynomials p^~_k^((n)) are defined by p^~_0^((n))(u) = 1 (1) p^~_(k+1)^((n))(u) = ...

If J is a simple closed curve in R^2, the closure of one of the components of R^2-J is homeomorphic with the unit 2-ball. This theorem may be proved using the Riemann mapping ...

Two distinct point pairs AC and BD separate each other if A, B, C, and D lie on a circle (or line) in such order that either of the arcs (or the line segment AC) contains one ...

A shortest path between two vertices of a graph is a graph path of shortest possible length between them. Such paths are also known as graph geodesics, and the matrix giving ...

A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

A Steinmetz curve is a curve of intersection of two perpendicularly placed cylinders of radii a and b comprising a Steinmetz solid. If the vertical cylinder has radius a and ...

Let sigma_0(n) and sigma_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime ...

Subtraction is the operation of taking the difference d=x-y of two numbers x and y. Here, x is called the minuend, y is called the subtrahend, and the symbol between the x ...

A surface in 3-space can be parameterized by two variables (or coordinates) u and v such that x = x(u,v) (1) y = y(u,v) (2) z = z(u,v). (3) If a surface is parameterized as ...