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The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

In general, the catacaustics of the astroid are complicated curves. For an astroid with parametric equations x = cos^3t (1) y = sin^3t, (2) the catacaustic for a radiant ...

Let C_1, C_2, C_3, and C_4 be four circles of general position through a point P. Let P_(ij) be the second intersection of the circles C_i and C_j. Let C_(ijk) be the circle ...

The Kenmotu circle is the circle passing through the six contact points of the congruent squares used in the construction of the Kenmotu point with the triangle sides. It is ...

Members of a coaxal system satisfy x^2+y^2+2lambdax+c=(x+lambda)^2+y^2+c-lambda^2=0 for values of lambda. Picking lambda^2=c then gives the two circles (x+/-sqrt(c))^2+y^2=0 ...

The south pole is the point on a sphere with minimum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

Through a point K in the plane of a triangle DeltaABC, draw parallelians through a point as illustrated above. Then there exist four points K for which ...

Let theta(t) be the Riemann-Siegel function. The unique value g_n such that theta(g_n)=pin (1) where n=0, 1, ... is then known as a Gram point (Edwards 2001, pp. 125-126). An ...

The point on a line segment dividing it into two segments of equal length. The midpoint of a line segment is easy to locate by first constructing a lens using circular arcs, ...

A phase curve (i.e., an invariant manifold) which meets a hyperbolic fixed point (i.e., an intersection of a stable and an unstable invariant manifold) or connects the ...