Online Geometry: Square, Theorems and Problems

Square, Theorems and Problems: Table of Content

Area of a Square Index.

Circle Inscribed in a Square, Theorems and Problems. Index.

Geoboard for iPad Pythagorean Theorem Proof by Leonardo.

Geoboard for iPad Gallery: Six squares with a common vertex.

Optical Prism with Square Form.
Scene created using Prism HD for iPad.

iPad Apps: fractBG.
Fractal Image with Squares.

Geoboard for iPad Gallery: Triangle with two squares (Problem 496).

Geometry Problem 870
Triangle, Median, Three Squares, Centers, Vertices, Collinear Points, Midpoint.

Geometry Problem 853
Online Geometry Problem 853: Square, Arc, Quadrant, Triangle, Perpendicular, Metric Relations.

Geometry Problem 818.
Square, Triangle, Angle.

Geometry Problem 752.
Square, Circle, Tangent, Chord, Angle.

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

Geometry Problem 725.
Kurschak's Dodecagon, Square, Equilateral Triangle, Midpoints, 30, 60 Degrees.

Geometry Problem 723.
Squares, Circumscribed Circles, Collinear points.

Geometry Problem 722.
Squares, Circumscribed Circles, Collinear points.

Geometry Problem 697.
Square, Circle, Sector, Segment, Tangent, Inscribed, Congruence, Mind Map, Polya.

Geometry Problem 693.
Square, Inscribed and Circumscribed Circle, Areas, Mind Map, Polya.

Geometry Problem 692.
Quatrefoil, Four Equal Circles and a Circle Inscribed in a Square, Areas, Mind Map, Polya.

Geometry Problem 668.
Right triangle, Incircles, Parallel, Common Tangent, Mind Map.

Geometry Problem 646.
Archimedes Book of Lemmas: Proposition 7
Square,Inscribed and Circumscribed Circles, Area.

Geometry Problem 615
Right Triangle with a Square, Diagonals, Center, Area of Quadrilateral.

Problem 599
Regular Hexagon, Square, Midpoint, Angle, Degrees.

Problem 570.
Square, Center, Right Triangles, Congruence, Collinearity.

Problem 545.
Acute Triangle, Squares, Altitudes, Area, Measure.

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 465.
Square, Arc, Angle, 90 Degrees, Measurement.

Proposed Problem 464.
Square, Arcs, Center, Angle, 90 Degrees, 120 Degrees.

Proposed Problem 462.
Square, Arcs, 90 Degrees, Circle, Tangent, Radius, Measurement.

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

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

Proposed Problem 428.
Quadrant of a circle, Square, Angle bisector, Measurement.

Proposed Problem 396.
Square, Angle Trisectors, Congruence, Area.

Proposed Problem 395.
Square, 15 Degree, Equilateral triangle.

Proposed Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle.

Proposed Problem 371.
Square, Inscribed circle, Triangle, Area.

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.

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.

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

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

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 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 1942-1943 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.
Step-by-Step construction, Manipulation, and animation.

Archimedes Arbelos and Square 1. Dynamic Geometry Software.
Step-by-Step 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

Triangle and Squares 16

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

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

Ayacucho Square (Plaza de Armas)
Ayacucho video

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

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.

Triangle and Squares 1
Squares constructed on the sides of a triangle