A simple drill for the Pythagorean theorem with scissors on circles!

Note on an n-dimensional Pythagorean theorem

A famous theorem in Euclidean geometry often attributed to the Greek thinker Pythagoras of Samos (6th century, B.C.) states that if one of the angles of a planar triangle is a right angle, then the square of the length of the side opposite the right angle equals the sum of the squares of the lengths of the sides which form the right angle. There are less commonly known higherdimensional version...

The Pythagorean Theorem: I. The finite case.

The Pythagorean Theorem and variants of it are studied. The variations evolve to a formulation in terms of noncommutative, conditional expectations on von Neumann algebras that displays the theorem as the basic result of noncommutative, metric, Euclidean Geometry. The emphasis in the present article is finite dimensionality, both "discrete" and "continuous."

The Pythagorean Theorem: What Is It About?

Although twenty five centuries old, the Pythagorean theorem appears vigorous and ubiquitous. A key to the distance formula in Descartes’s method of coordinates, the theorem is implicitly present in all scientific models and engineering computations involving spatial relationships or trigonometry. An invisible companion to the dot-product operation, it is inherent in equations of mathematical ph...

The Six Circles Theorem revisited

G Pythagorean hodograph quintic transition between two circles

Walton & Meek [13] obtained fair G Pythagorean hodograph (PH) quintic transition Sand C-shaped curves connecting two circles. It was shown that an S-shaped curve has no curvature extremum and a Cshaped curve has a single curvature extremum. We simplified and completed their analysis. A family of fair PH quintic transition curves between two circles has been derived. We presented an algorithm wi...