Eternal Triangles:
500,000 years of Pythagorean Triples
by Richard Allen Brown, Eric Rowland, Dr. John McKee and collaborators
Preliminary Outline 7/30/2001
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Chapter 1. The Rule of 3,4,5
Use in construction
Ancient Rope Stretchers
The Great Pyramids
The importance of right triangles
The Importance of A**2 + B**2 = C**2
A Short table of triples
Chapter 2. Two cuneiform tablets of Mesopotamia
A day in the Life of A Priest/Mathematician of Ur
A Map of Ancient Mesopotamia
Picture of the Plimpton 322 Tablet
Picture of the Yale Tablet
Calculating the Square Root of 2
An ordered set of Pythagorean triples-the first attempt at trigonometry?
A connection between the two tablets?
Appendix-The Mathematics of Plimpton 322
Chapter 3. Lasting Contributions of Babylonian Mathematics
Base 60 Arithmetic
Angle Measure
Time Measures
Calender Making
Map Measures
The standard in Ancient calculating
Ancient Astronomy
Ancient Navigation
Chapter 4. Pythagoras and His Theorem
The Life and Times of Pythagoras
The evolution of the concept of proof
Mathematics in the Greek world
Six proofs of the Pythagorean theorem
Pythagorean Triples and "Empirical Mathematics"
Chapter 5. Euclid's Elements of Geometry
Euclid and his role in the history of thought
The value of geometry in Ancient Greece
The importance of the "Elements"
The proof of the unbounded number of primes
The fundamental theorem of Pythagorean triples
Chapter 6. Numerology and Mathematics
Important Numbers
Chapter 7. "Almagest" The First trigonometry table
Calculating the tables
The Importance of the Law of Sines
Chapter 8. Diophantus and integer games
Five Problems of Diophantus
Chapter 9. Brahmagupta and Indian Mathematics and Astronomy
The Life and Times of Brahmagupta
The noncycling characteristic of Pythagorean Triples
Chapter10. The Invention of Algebra
The Astrolabe
The Binonial expansion
Chapter11. The Middle Ages
Fibonacci and his series
Viete and the cubic and quartic equations
Chapter12. The Renaisance
The Life and Times of Fermat
Descarte, Mersenne, and Fermat
The development of Modular artihmetic
Fermat's Last Theorem
Chapter13. Gauss and his special primes
The Life and Times of Carl Fredrick Gauss
Gaussian Primes and Pythagorean Triples
Chapter14.Galois and the development of Modern Algebra
Pythagorean triples form a group
Sophie Germain and her proof of Fermat's Last Theorem n=3
Chapter15. The Reimann Hypothesis
The Life and Times of Bernard Reimann
Calculating the density function of Triples
Chapter16. Andrew Wiles and Solution of Fermat's Last Theorem
The life and times of Andrew Wiles
Famous Problem 1: Squaring the circle
Famous Problem 2: The Four color problem
Famous Problem 3: Fermat's Last Theorem
Chapter 17. The Future
The ascendence of number theory
Unsolved Problems in mathematics
The use of the internet in mathematics
Chapter 18. Recreations in Pythagorean Triples
Ten problems
Appendix A.Chronology of Pythagorean Triples
Appendix B.Accumulated Facts about Pythagorean Triples
Tables
A. The first 3000 Pythagorean Triples
B. The first 100 1,2,3,4,5 Triples
C. The first 100 2,4,6,8,10 Triples
D. The first 100 1,2,5,12,29 Triples
E. The first 1000 triples in UAL notation
F. A special list of triples
G. Ptolemy's table of Chords
H. A listing of Gaussian Primes
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