


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

Proposed Problem
317.
Right triangle and Inscribed Squares. 

Geoboard
for iPad Gallery: Squares, Right Triangles. 3Squares, 4Rectangles,
Eight 345 Right Triangles,
Congruence, Areas. 

Proposed Problem
316.
Circular segments and Inscribed Squares. 

The Pythagorean Curiosity
Triangles and squares, fifteen conclusions. 

Hippocrates
and Squaring the Circle


Proposed Problem
306.
Square, Triangles, Angles, Sides. 

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

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. 

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
280.
Quadrilateral, Perpendiculars, Area of Squares. 

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

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

Proposed Problem
265.
Right Triangle, Pythagorean Theorem. 

Proposed Problem
252.
Rectangle, isosceles right triangle, square, area.


Proposed Problem
251.
Parallelogram, sides, diagonals, squares, areas. 

Parallelogram with Squares theorem Thébault's Theorem.


Sol
LeWitt Drawings: A square.


Red
Square, Moscow and the Golden Rectangle.


Homage to the Square, 1965 by Josef Albers, pioneer of Geometric abstraction. 

The
Piet Mondrian, Broadway Boogie Woogie 19421943 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
225. Viviani's Theorem Extension, Regular Polygon, Apothem, Distance. 

Proposed Problem
191. Triangle, Altitudes, Orthocenter, Squares, Areas.


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.


Huancayo Square
the Wankas 

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.


Proposed Problem 62: Square
Diagonal, Inscribed Circle. 

Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.
Triangle and Squares
in the News 

Triangle and Squares 22


Triangle and Squares 21


Triangle and Squares 20


Triangle and Squares 19


Triangle and Squares 18
Sangaku Problem 

Triangle and Squares 17

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