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A "beam detector" for a given curve C is defined as a curve (or set of curves) through which every line tangent to or intersecting C passes. The shortest 1-arc beam detector, ...

A box-and-whisker plot (sometimes called simply a box plot) is a histogram-like method of displaying data, invented by J. Tukey. To create a box-and-whisker plot, draw a box ...

The subset B of the Euclidean plane formed by the union of the interval [0,1] of the x-axis and all line segments of unit length passing through the origin which form an ...

Cauchy's integral formula states that f(z_0)=1/(2pii)∮_gamma(f(z)dz)/(z-z_0), (1) where the integral is a contour integral along the contour gamma enclosing the point z_0. It ...

Find the figure bounded by a line which has the maximum area for a given perimeter. The solution is a semicircle. The problem is based on a passage from Virgil's Aeneid: "The ...

The Droz-Farny circles are a pair of circles of equal radius obtained by particular geometric constructions. The following amazing property of a triangle, first given by ...

The term Euclidean refers to everything that can historically or logically be referred to Euclid's monumental treatise The Thirteen Books of the Elements, written around the ...

An optical illusion named after British psychologist James Fraser, who first studied the illusion in 1908 (Fraser 1908). The illusion is also known as the false spiral, or by ...

Points, also called polar reciprocals, which are transformed into each other through inversion about a given inversion circle C (or inversion sphere). The points P and P^' ...

A Lie group is a smooth manifold obeying the group properties and that satisfies the additional condition that the group operations are differentiable. This definition is ...