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For a point P inside an equilateral triangle DeltaABC, the sum of the perpendiculars p_i from P to the sides of the triangle is equal to the altitude h. This result is simply ...

A linkage used in the original steam engine to turn back-and-forth motion into approximately straight-line motion.

One name for the figure used by Euclid to prove the Pythagorean theorem.

Divide the sides of a quadrilateral into three equal parts. The figure formed by connecting and extending adjacent points on either side of a polygon vertex is a ...

The Yff central circle, a term coined here for the first time, is the circumcircle of the Yff central triangle.

The Yff contact circle is the circumcircle of the Yff contact triangle. Its center has triangle center function alpha=((b-c)(3a^3+b^3+c^3-2a^2b-2a^2c-abc))/a, (1) which does ...

The Yiu circle is the circumcircle of the Yiu triangle DeltaO_AO_BO_C. It has center function given by alpha=af(a,b,c), where f(a,b,c) is a 14th-order polynomial. Its radius ...

The Yiu triangle DeltaO_AO_BO_C is the triangle formed by the centers of the Yiu circles. It has area where f(a,b,c) is a 12th-order polynomial and Delta is the area of the ...

Complex Analysis

If three circles A, B, and C are taken in pairs, the external similarity points of the three pairs lie on a straight line. Similarly, the external similarity point of one ...