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The Tucker cubic is the triangle cubic with trilinear equation secAsecBsecCsum_(cyclic)aalpha(b^2beta^2+c^2gamma^2) =alphabetagammasum_(cyclic)asecA(b^2sec^2B+c^2sec^2C). It ...

Except for triangles, every simple polygon has at least two nonoverlapping ears.

The integral of 1/r over the unit disk U is given by intint_(U)(dA)/r = intint_(U)(dxdy)/(sqrt(x^2+y^2)) (1) = int_0^(2pi)int_0^1(rdrdtheta)/r (2) = 2piint_0^1dr (3) = 2pi. ...

The figure formed when the midpoints of adjacent sides of a quadrilateral are joined. Varignon's theorem demonstrated that this figure is a parallelogram. The center of the ...

The figure formed when the midpoints of the sides of a convex quadrilateral are joined in order is a parallelogram. Equivalently, the bimedians bisect each other. The area of ...

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.