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Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...

The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of ...

A simplex, sometimes called a hypertetrahedron (Buekenhout and Parker 1998), is the generalization of a tetrahedral region of space to n dimensions. The boundary of a ...

A solid of revolution is a solid enclosing the surface of revolution obtained by rotating a 1-dimensional curve, line, etc. about an axis. A portion of a solid of revolution ...

In the arbelos, consider the semicircles K_1 and K_2 with centers A and C passing through B. The Apollonius circle K_3 of K_1, K_2 and the large semicircle of the arbelos is ...

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

What is the probability that a chord drawn at random on a circle of radius r (i.e., circle line picking) has length >=r (or sometimes greater than or equal to the side length ...

A roulette is a curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. The roulettes described by the foci of ...

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a ...

The Lemoine axis is the perspectrix of a reference triangle and its tangential triangle, and also the trilinear polar of the symmedian point K of the reference triangle. It ...