


The Pythagorean Curiosity
Triangles and squares, fifteen conclusions. 

Albert Einstein
and the Pythagorean theorem.
A preteen Albert Einstein devised a new proof of the Pythagorean theorem. 

Proposed Problem
305.
Square, Triangles, Angles, Sides. 

Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 18641933) An elegant and a purely geometric
way of finding the area of a regular dodecagon.
A square with an equilateral triangle drawn inwards on each side. 

Euclid's
Elements, Book X, Lemma for Proposition 33
One page visual illustration. 

Archimedes' Book of Lemmas: Proposition 7
Square and inscribed and circumscribed Circles


Proposed Problem 286:
Square, Midpoints, Octagon. 

Proposed Problem
273.
Triangle, Perpendiculars, Area of Squares. 

Proposed Problem
276.
Square, 90 degree Arcs, Circle, Radius. 

Proposed Problem
265.
Right Triangle, Pythagorean Theorem. 

Red
Square, Moscow and the Golden Rectangle.


Proposed Problem
244. Square, Diagonals, Centers, Distance.


Proposed Problem
239. Square, Midpoints, Lines, Congruence, Pythagoras.


Proposed Problem
238. Square, Midpoints, Lines, Congruence.


Archimedes Arbelos and Square
2.
Dynamic Geometry Software.
StepbyStep construction, Manipulation, and animation. 

Archimedes Arbelos and Square 1.
Dynamic Geometry Software.
StepbyStep construction, Manipulation, and animation. 

Proposed Problem
189. Squares, Distances. 

Proposed Problem
188. Square, Diagonal, 45 Degrees Angle. 

Proposed Problem
179. Rhombus, Square, Diagonal, Angle. 

Proposed Problem
112. Area of square and triangle.


Inca Skull
Surgery
Inca Skull Surgeons Were "Highly Skilled," Study Finds.
Trepanation = square hole in the skull. 

Huancayo Square
the Wankas 

Ayacucho Square
(Plaza de Armas)
Ayacucho video 

Triangle and Squares Theorem 1:
with Interactive Geometry Software
StepbyStep construction, Manipulation, and animation. 

Bottema's Theorem: Triangle and Squares with Interactive
Geometry Software
StepbyStep construction, Manipulation, and animation. 

Proposed Problem
70: Squares inscribed in a triangle, Similarity.


Proposed Problem
69: Square inscribed in a triangle, Similarity.


Interactive Hinged tessellation. Square tessellation  Dynamic Geometry.
Please be patient while the applet loads on your computer. This Java applet requires Java 1.3 or higher. 

Generalizing Van Aubel: Michael de Villiers' Theorems.
Triangle and Squares
in the News 

Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.


Triangle and Squares 22


Triangle and Squares 21
See also:
Triangle and Squares 19 

Triangle and Squares 20


Triangle and Squares 19


Triangle and Squares 18
Sangaku Problem 

Triangle and Squares 17


Triangle and Squares 16


Triangle and Squares 15 

Triangle and Squares 14 

Triangle and Squares
13 

Triangle and Squares
12 

Triangle and Squares
11 

Triangle and Squares
10 

Triangle and Squares 9


Triangle and Squares 8 

Triangle and Squares 7 

Triangle and Squares 6 

Triangle and Squares 5 

Triangle and Squares 4 

Triangle and Squares 3 

Triangle and Squares 2 

Triangle and Squares 1 