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Given a sequence {a_n}_(n=1)^infty, a formal power series f(s) = sum_(n=1)^(infty)(a_n)/(n^s) (1) = a_1+(a_2)/(2^s)+(a_3)/(3^s)+... (2) is called the Dirichlet generating ...

Consider two mutually tangent (externally) spheres A and B together with a larger sphere C inside which A and B are internally tangent. Then construct a chain of spheres each ...

A hyperbola for which the asymptotes are perpendicular, also called an equilateral hyperbola or right hyperbola. This occurs when the semimajor and semiminor axes are equal. ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

The self-intersection of a one-sided surface. The word "cross-cap" is sometimes also written without the hyphen as the single word "crosscap." The cross-cap can be thought of ...

If a, b, c, and d are points in the extended complex plane C^*, their cross ratio, also called the cross-ratio (Courant and Robbins 1996, p. 172; Durell 1928, p. 73), ...

An incircle is an inscribed circle of a polygon, i.e., a circle that is tangent to each of the polygon's sides. The center I of the incircle is called the incenter, and the ...

Kepler's equation gives the relation between the polar coordinates of a celestial body (such as a planet) and the time elapsed from a given initial point. Kepler's equation ...

Starting with the circle P_1 tangent to the three semicircles forming the arbelos, construct a chain of tangent circles P_i, all tangent to one of the two small interior ...