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One of the beautiful arrangements of circles found at the Temple of Osiris at Abydos, Egypt (Rawles 1997). The pattern also appears in Italian art from the 13th century ...

Half a circle. The area of a semicircle of radius r is given by A = int_0^rint_(-sqrt(r^2-x^2))^(sqrt(r^2-x^2))dxdy (1) = 2int_0^rsqrt(r^2-x^2)dx (2) = 1/2pir^2. (3) The ...

Two figures are said to be similar when all corresponding angles are equal and all distances are increased (or decreased) in the same ratio, called the ratio of magnification ...

A plane shape constructed by Reinhardt (1934) that is conjectured to be the "worst" packer of all centrally-symmetric plane regions. It has a packing density of ...

Given three mutually tangent circles, there exist exactly two nonintersecting circles which are tangent circles to all three original circles. These are called the inner and ...

The spherical distance between two points P and Q on a sphere is the distance of the shortest path along the surface of the sphere (paths that cut through the interior of the ...

A hypotrochoid generated by a fixed point on a circle rolling inside a fixed circle. The curves above correspond to values of a=0.1, 0.2, ..., 1.0. Additional attractive ...

The Steiner triangle DeltaS_AS_BS_C (a term coined here for the first time), is the Cevian triangle of the Steiner point S. It is the polar triangle of the Kiepert parabola. ...

The symmedial triangle DeltaK_AK_BK_C (a term coined here for the first time), is the triangle whose vertices are the intersection points of the symmedians with the reference ...

The lines AK_A, BK_B, and CK_C which are isogonal to the triangle medians AM_A, BM_B, and CM_C of a triangle are called the triangle's symmedian. The symmedians are ...