Math Research Spring
1. Square Roots And Pi
1. Indian Square Root Of Two
2. Tangent To A Parabola
3. Newton's Method
4. Angle Bisector Theorem
5. Angle bisector in a right triangle example
6. Archimedes Upper Bound For Pi
7. Archimedes Lower Bound For Pi
8. Trisecting an angle with the Spiral of Archimedes
9. Archimedes Spiral To Square The Circle
10. Area Under Archimedes' Spiral
11. Liu Hui Pi
12. Liu Hui Pi Under And Over
13. Liu Hui Pythagorean Theorem
14. Liu Hui Go Gou Proof 2
2. Constructions
1. Construct An Equilateral Triangle
2. Copy A Line Segment With A Collapsible Compass
3. Construct An Angle Bisector
4. Construct A Midpoint / Perpendicular Bisector
5. Create A Triangle From Three Given Sides
6. Perpendicular To A Line Through A Point On The Line
7. Perpendicular To A Line Through A Point Not On The Line
8. Copy An Angle
9. Make Parallel Line
10. I. 35
11. I. 41
12. I. 42
13. Book I.43
14. I. 44
15. Construction I. 35
16. Construction I. 42
17. Construction I. 44
18. Copy of Euclid Book I 47
19. pentagon
20. Circle through 3 points IV. 5
21. Construct Regular Pentagon Euclid IV 10

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Math Research Spring

Gary Rubinstein, Mar 2, 2016

Table of Contents

Square Roots And Pi
1. Indian Square Root Of Two
2. Tangent To A Parabola
3. Newton's Method
4. Angle Bisector Theorem
5. Angle bisector in a right triangle example
6. Archimedes Upper Bound For Pi
7. Archimedes Lower Bound For Pi
8. Trisecting an angle with the Spiral of Archimedes
9. Archimedes Spiral To Square The Circle
10. Area Under Archimedes' Spiral
11. Liu Hui Pi
12. Liu Hui Pi Under And Over
13. Liu Hui Pythagorean Theorem
14. Liu Hui Go Gou Proof 2
Constructions
1. Construct An Equilateral Triangle
2. Copy A Line Segment With A Collapsible Compass
3. Construct An Angle Bisector
4. Construct A Midpoint / Perpendicular Bisector
5. Create A Triangle From Three Given Sides
6. Perpendicular To A Line Through A Point On The Line
7. Perpendicular To A Line Through A Point Not On The Line
8. Copy An Angle
9. Make Parallel Line
10. I. 35
11. I. 41
12. I. 42
13. Book I.43
14. I. 44
15. Construction I. 35
16. Construction I. 42
17. Construction I. 44
18. Copy of Euclid Book I 47
19. pentagon
20. Circle through 3 points IV. 5
21. Construct Regular Pentagon Euclid IV 10

1.

Square Roots And Pi

1. Indian Square Root Of Two
2. Tangent To A Parabola
3. Newton's Method
4. Angle Bisector Theorem
5. Angle bisector in a right triangle example
6. Archimedes Upper Bound For Pi
7. Archimedes Lower Bound For Pi
8. Trisecting an angle with the Spiral of Archimedes
9. Archimedes Spiral To Square The Circle
10. Area Under Archimedes' Spiral
11. Liu Hui Pi
12. Liu Hui Pi Under And Over
13. Liu Hui Pythagorean Theorem
14. Liu Hui Go Gou Proof 2

1.1.

Indian Square Root Of Two

1.2.

1.3.

1.4.

1.5.

1.6.

1.7.

1.8.

1.9.

1.10.

1.11.

1.12.

1.13.

1.14.

2.

Constructions

1. Construct An Equilateral Triangle
2. Copy A Line Segment With A Collapsible Compass
3. Construct An Angle Bisector
4. Construct A Midpoint / Perpendicular Bisector
5. Create A Triangle From Three Given Sides
6. Perpendicular To A Line Through A Point On The Line
7. Perpendicular To A Line Through A Point Not On The Line
8. Copy An Angle
9. Make Parallel Line
10. I. 35
11. I. 41
12. I. 42
13. Book I.43
14. I. 44
15. Construction I. 35
16. Construction I. 42
17. Construction I. 44
18. Copy of Euclid Book I 47
19. pentagon
20. Circle through 3 points IV. 5
21. Construct Regular Pentagon Euclid IV 10

2.1.

Construct An Equilateral Triangle

Euclid I.1

Use the tools to create an equilateral triangle with AB as one of the sides

2.2.

2.3.

2.4.

2.5.

2.6.

2.7.

2.8.

2.9.

2.10.

2.11.

2.12.

2.13.

2.14.

2.15.

2.16.

2.17.

2.18.

2.19.

2.20.

2.21.

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