Inca Trail to Machu Picchu, the Lost City of the Incas

Welcome to Theorems and Problems about Quadrilaterals! Site created and maintained by Antonio Gutierrez.

The Incas used trapezoids for all their windows and doors, which withstand earthquakes well.

 

Quadrilaterals: Table of Content

 

 

23.

Generalizing Van Aubel: Michael de Villiers' Theorems.
 

22.

Triangle and Squares. 21 theorems. Visual illustrations.

21.

Eyeball Theorem: Animated Angle to Geometry Study.

20.

Eyeball to Eyeball Theorem

Presentation: "Animated Angle to Geometry Study I & II." 46th Annual Georgia Mathematics Conference, Extreme Makeover: Mathematics Edition!, Rock Eagle, October 20-22, 2005,

19.

Hippocrates and Squaring the Circle
 

18.

Triangle with Squares Problem

17.

Thébault's Theorem. Parallelogram with Squares theorem
 

16.

Varignon and Wittenbauer paralellograms. Quadrilateral: midpoints and trisection points of the edges.

 

15.

Van Aubel

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

14.

Equilic Quadrilateral.
 

13.

Ptolemy's Theorem.
 

12.

Cyclic Quadrilateral: Ratio of the Diagonals
 

11.

Brahmagupta's Theorem Cyclic quadrilateral.

10.

Brahmagupta's Corollary Cyclic quadrilateral.

9.

Brahmagupta's Formula  Area of a cyclic quadrilateral.

8.

Brahmagupta Formula Extension Area of any quadrilateral.

7.

Newton's Theorem: Newton's Line. Circumscribed quadrilateral, midpoints of diagonals, center of the circle inscribed.

Puzzle of the Newton's Theorem: 50 pieces of circles.

6.

Sangaku Problem. The incenters of four triangles in a cyclic quadrilateral form a rectangle.

5.

Complete Quadrilateral Theorems

Presentation: "Animated Angle to Geometry Study I & II." 46th Annual Georgia Mathematics Conference, Extreme Makeover: Mathematics Edition!, Rock Eagle, October 20-22, 2005,

4.

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.
 

3.

Proposed Problem 33.
Triangle and quadrilateral.

2.

Proposed Problem 35.
Incenters and Inradii in Cyclic Quadrilateral.

1.

Proposed Problem 42. Angles and triangles.

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Last updated: April 14, 2008