Online Geometry: Triangle and Squares, Theorems and Problems

Geoboard for iPad Pythagorean Theorem Proof by Leonardo.

Geometry Problem 608
Square with Right Triangles, Metric Relations, Congruence, Measurement.

Geoboard for iPad Pythagorean Theorem Proof, Squares (Problem 540).

Problem 540.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.

Problem 539.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.

Problem 534.
Right Triangle, Squares, Perpendicular, Dissection, Areas.

Problem 521.
Triangle with three Squares, Altitude, Rectangle, Area.

Problem 520.
Triangle with six Squares, Ratio, Area.

Problem 519.
Triangle, Squares, Altitude, Perpendicular, Rectangle, Area.

Problem 518.
Parallelogram, Five Squares, Centers, 45 Degrees, Measure.

Problem 517.
Right Triangle, Six Squares, Areas.

Problem 514.
Triangle, Five Squares, Line, Area.

Problem 512.
Triangle with three squares and concurrency.

Problem 510.
Triangle, Three Squares, Midpoints, Concurrency.

Problem 508.
Triangle with three Squares, Four triangle of equal Area.

Problem 506.
Triangle with Three Squares, Center, Midpoint, Perpendicular.

Problem 503.
Triangle with Three Squares, Perpendicular, Congruence, Concurrency.

Problem 502.
Triangle, Two Squares, Midpoint, Perpendicular, Half the measure.

Problem 501.
Triangle, Two Squares, Center, Midpoint, another Square.

Problem 499.
Triangle, Two Squares, Perpendicular.

Problem 497.
Triangle, Two Squares, Centers, Midpoint, 90 Degrees.

Problem 496.
Triangle, Two Squares, 90 Degrees, Concurrency, Angle Bisectors.

Problem 491.
Square, Right Triangle, Incircle, Inscribed Circle, Radius.

Problem 485.
Square, Side, Circles, Tangent, Radius, Measurement.

Problem 484.
Square, Angle, 90 degrees, Triangle, Measurement, Proportion.

Problem 483.
Square, Angle, 90 degrees, Measurement.

Proposed Problem 459.
Right triangle, Squares, Distance, Measurement.

Proposed Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement.

Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles.

Proposed Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity.

Proposed Problem 357.
Square, Exterior point, Triangles, Area.

Proposed Problem 356.
Square, Point inside, Triangles, Area.

Proposed Problem 354.
Rhombus, Square, 45 degrees.

Proposed Problem 336.
Two equal circles, a Common Tangent and a Square.

Proposed Problem 331.
Square, Point on the Inscribed Circle, Tangency Points.

Proposed Problem 322.
Square, Inscribed circle, Tangent, Triangle area.

Proposed Problem 317.
Right triangle and Inscribed Squares.

Proposed Problem 316.
Circular segments and Inscribed Squares.

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

Kurschak's Tile and Theorem. Jozsef Kurschak (Hungary, 1864-1933) 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.

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 265.
Right Triangle, Pythagorean 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 1942-1943 and the Golden Rectangle

Paris Review by Sol LeWitt, Sol LeWitt was an American artist linked to various movements, including Conceptual art and Minimalism.
Sol LeWitt Index

Arithmetic Composition, 1929-1930 by Theo van Doesburg, pioneer of Geometric abstraction.

Composition II in Red, Blue, and Yellow by Piet Mondrian, pioneer of Geometric abstraction.

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.
Step-by-Step construction, Manipulation, and animation.

Archimedes Arbelos and Square 1. Dynamic Geometry Software.
Step-by-Step 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
Step-by-Step construction, Manipulation, and animation.

Bottema's Theorem: Triangle and Squares with Interactive Geometry Software
Step-by-Step 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