The students developed their proofs by examining how new right triangles could be created from an original right triangle.

Two students who discovered a seemingly impossible proof to the Pythagorean theorem ... which states that the sum of the ...

Researchers have demonstrated, using a novel approach, that the original solution to Dudeney’s famous dissection problem is ...

In 1907, the English author and mathematician Henry Ernest Dudeney posed a puzzle: Can any equilateral triangle be cut into ...

Henry Ernest Dudeney posed the famous dissection problem of transforming a triangle into a square by cutting it into as few ...

What it means is that in a right triangle (where one angle equals 90°), the sum of the squares of two sides equals the square of the hypotenuse (the longest side).

Their motto was "All is number." The Pythagoreans explored the "magic 3-4-5 triangle." This type of triangle was called "magic" because any triangle with sides of 3, 4, and 5 units always created ...

Angle OGH (\(y\)) = angle OHG because triangle GOH is also isosceles. Lengths OH and OG are also both radii. Angle GOH = \(180^\circ - 2y\) (because angles in a triangle add up to 180°).

hence proving that a dissection between a square and an equilateral triangle cannot be achieved with three or fewer pieces. The matching diagram played a central role in their proof. In this ...