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Move a point Pi_0 along a line from an initial point to a final point. It traces out a line segment Pi_1. When Pi_1 is translated from an initial position to a final ...

If the vertices A, B, and C of triangle DeltaABC lie on sides QR, RP, and PQ of the triangle DeltaPQR, then the three circumcircles CBP, ACQ, and BAR have a common point X. ...

If a cyclic quadrilateral ABCD is inscribed in a circle c_1 of a coaxal system such that one pair AC of connectors touches another circle c_2 of the system at P, then each ...

For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals AB×CD+BC×DA=AC×BD (1) (Kimberling 1998, p. 223). ...

A random polygon is a polygon generated in some random way. Kendall conjectured that the shape of a random polygon is close to a disk as the area of the polygon becomes large ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

The salinon is the figure illustrated above formed from four connected semicircles. The word salinon is Greek for "salt cellar," which the figure resembles. If the radius of ...

The 20 Cayley lines generated by a hexagon inscribed in a conic section pass four at a time though 15 points known as Salmon points (Wells 1991). There is a dual relationship ...

There are at least two theorems known as Salmon's theorem. This first states that if P and S are two points, PX and SY are the perpendiculars from P and S to the polars of S ...

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 ...