`sin^2x + cos^2x = 1`

`y = frac (-b +- sqrt(b^2 - 4ac)) (2a)`

`(x + 2)^2 + (y - 3)^2 = 16`

`slope = m = frac (\text(change in y)) (\text(change in x)) = frac (Deltay) (Deltax)`

Lover of math. Bad at drawing.

No irrationals required.... Read more

Math with Bad Drawings... the paperback.... Read more

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Life's constraints may be simple, but life's objectives are irreducibly complex.... Read more

My third book comes out today.... Read more

Why do some wizards know no spells?... Read more

Lover of math. Bad at drawing.

No irrationals required.... Read more

Math with Bad Drawings... the paperback.... Read more

By popular demand. (From a demanding populace.)... Read more

Life's constraints may be simple, but life's objectives are irreducibly complex.... Read more

My third book comes out today.... Read more

Why do some wizards know no spells?... Read more

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**Abstract**. The so-called "Japanese theorem" dates back over 200 years; in its original form it states that given a quadrilateral inscribed in a circle, the sum of the inradii of the two triangles formed by the addition of a diagonal does not depend on the choice of diagonal. Later it was shown that this invariance holds for any cyclic polygon that is triangulated by diagonals. In this article we examine this theorem closely, discuss some of its consequences, and generalize it further.

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**Abstract**. The so-called "Japanese theorem" dates back over 200 years; in its original form it states that given a quadrilateral inscribed in a circle, the sum of the inradii of the two triangles formed by the addition of a diagonal does not depend on the choice of diagonal. Later it was shown that this invariance holds for any cyclic polygon that is triangulated by diagonals. In this article we examine this theorem closely, discuss some of its consequences, and generalize it further.

This article explores analogues of the Pythagorean Theorem in non-Euclidean geometries.

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