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 2022, 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'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 2022, 2005, 
4. 

Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 18641933) 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. 