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The second Yff triangle is the Cevian triangle DeltaA^'B^'C^' of the second Yff point. The area of the second Yff triangle is Delta=(u^3)/(2R), where R is the circumradius of ...

A portion of a disk whose upper boundary is a (circular) arc and whose lower boundary is a chord making a central angle theta<pi radians (180 degrees), illustrated above as ...

A curve of order n is generally determined by n(n+3)/2 points. So a conic section is determined by five points and a cubic curve should require nine. But the Maclaurin-Bézout ...

A pivotal isotomic cubic is a self-isotomic cubic that possesses a pivot point, i.e., in which points P lying on the conic and their isotomic conjugates are collinear with a ...

An inconic with parameters x:y:z=a(b-c):b(c-a):c(a-b), (1) giving equation (2) (Kimberling 1998, pp. 238-239). Its focus is Kimberling center X_(101) and its conic section ...

Pre-Calculus

Bubbles can meet only at angles of 120 degrees (for three bubbles) and cos^(-1)(-1/3) approx 109 degrees28^'16^('') (for four bubbles), where cos^(-1)(-1/3) is the ...

A statement about theorems. It usually gives a criterion for getting a new theorem from an old one, either by changing its objects according to a rule (duality principle), or ...

A bounded plane convex region symmetric about a lattice point and with area >4 must contain at least three lattice points in the interior. In n dimensions, the theorem can be ...

Two polygons are congruent by dissection iff they have the same area. In particular, any polygon is congruent by dissection to a square of the same area. Laczkovich (1988) ...