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Consider a string of length 2L plucked at the right end and fixed at the left. The functional form of this configuration is f(x)=x/(2L). (1) The components of the Fourier ...

Let f be a real-valued function defined on an interval [a,b] and let x_0 in (a,b). The four one-sided limits D^+f(x_0)=lim sup_(x->x_0+)(f(x)-f(x_0))/(x-x_0), (1) ...

The pedal curve of the parabola with parametric equations x = at^2 (1) y = 2at (2) with pedal point (x_0,y_0) is x_p = ((x_0-a)t^2+y_0t)/(t^2+1) (3) y_p = ...

A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid. For a right pyramidal frustum, let s be the slant height, h the ...

A trapezoid is a quadrilateral with two sides parallel. The trapezoid is equivalent to the British definition of trapezium (Bronshtein and Semendyayev 1977, p. 174). An ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

Suppose f(x) is continuous at a stationary point x_0. 1. If f^'(x)>0 on an open interval extending left from x_0 and f^'(x)<0 on an open interval extending right from x_0, ...

The term two-sided ideal is used in noncommutative rings to denote a subset that is both a right ideal and a left ideal. In commutative rings, where right and left are ...

A paradox mentioned in the Greek work Mechanica, dubiously attributed to Aristotle. Consider the above diagram depicting a wheel consisting of two concentric circles of ...

Given a chord PQ of a circle, draw any other two chords AB and CD passing through its midpoint. Call the points where AD and BC meet PQ X and Y. Then M is also the midpoint ...