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Index
Epigraph
Title Page
Introduction
The Evolution of BaseTen
The Pythagorean Theorem
Optical Illusions and Computer Graphics
The Cycloid – The Helen of Geometry
A triangle to a square
Halley’s Comet
The Impossible Tribar
The Quipu
Calligraphy, Typography &
The Wheat &the Chessboard
Probability and π
Earthquakes and Logarithms
The parabolic ceiling of the Capitol
Computers, Counting, &
Topo – A Mathematical Game
Fibonacci Sequence
A twist to the Pythagorean Theorem
Trinity of Rings – a topological model
Anatomy & the Golden
The catenary & the parabolic curves
The T Problem
Thales & the Great Pyramid
Hotel Infinity
Crystals – Nature’s Polyhedra
Pascal’s triangle, the Fibonacci sequence & binomial formula
Mathematics of the
The geometry of an electron’s path
The Moebius Strip & The Klein Bottle
A Sam Loyd Puzzle
Mathematics & paperfolding
The Fibonacci Trick
The Evolution of Mathematical Symbols
Some geometric designs of Leonardo
Ten Historical Dates
Napoleon’s Theorem
Lewis Carroll – The Mathematician
Counting on Fingers
A Twist to the Moebius Strip
Heron’s Theorem
A look at Gothic architecture & geometry
Napier’s Bones
Art & Projective Geometry
Infinity & the Circle
The Amazing Track
The Persian Horses & Sam
Lunes
Hexagons in Nature
Googol & Googolplex
A Magic Cube
Fractals—real or imaginary?
Nanoseconds – measuring time on computers
Geodesic Dome of Leonardo da Vinci
Magic Squares
THE STAIRCASE METHOD
The “Special” Magic Square
Chinese Triangle
The Death of Archimedes
A Non-Euclidean World
Cannon Balls & Pyramids
Conchoid of Nicomedes
The Trefoil Knot
The Magic Square of Benjamin Franklin
Irrational Numbers & the Pythagorean
Prime Numbers
The Golden Rectangle
Making a Tri-Tetra Flexagon
Finding infinity in small places
The Five Platonic Solids
The Pyramid Method for making magic squares
The Kepler – Poinsot Solids
The False Spiral Optical Illusion
The icosahedron & the golden rectangle
Zeno’s Paradox —Achilles &
The Mystic Hexagram
The Penny Puzzle
Tessellations
Diophantus’ Riddle
The Königsberg Bridge Problem &Topology
Networks
Aztec Calendars
The Impossible Trio
Ancient Tibetan Magic Square
Perimeter, Area & the Infinite Series
The Checkerboard Problem
Pascal’s Calculator
Isaac Newton & Calculus
Japanese Calculus
The proof of 1=2
The Symmetry of Crystals
The Mathematics of Music
Numerical Palindromes
The Paradox of the Unexpected Exam
Babylonian Cuneiform Text
The Spiral of Archimedes
Evolution of Mathematical Ideas
The Four Color Map Problem – Topology turns the tables on map coloring
Art & Dynamic Symmetry
Transfinite
Logic Problem
The Snowflake Curve
Zero—Where & When
Pappus’ theorem & the nine coin puzzle
A Japanese Magic Circle
Spherical Dome & Water Distillation
The Helix—Mathematics & Genetics
Magic “Line”
Mathematics & Architecture
History of Optical
Trisecting & the equilateral triangle
Wood, Water, Grain Problem
Charles Babbage – the Leonardo da Vinci of modern computers
Mathematics & Moslem Art
A Chinese Magic Square
Infinity & Limits
Counterfeit Coin Puzzle
The Parthenon —An Optical & Mathematical Design
Probability and Pascal’s Triangle
The Involute
The pentagon, the pentagram & the golden triangle
Three men facing the wall
Geometric fallacy & the Fibonacci sequence
Mazes
Chinese “Checkerboards”
Conic Sections
The Screw of Archimedes
Irradiation Optical illusion
The Pythagorean Theorem and President Garfield
The Wheel Paradox of Aristotle
Stonehenge
How many dimensions are there?
Computers & Dimensions
The “Double” Moebius Strip
Paradoxical Curve – space-filling curve
The Abacus
Mathematics & Weaving
Mersenne’s Number
Tangram Puzzle
Infinite vs Finite
Triangular, Square & Pentagonal Numbers
Eratosthenes measures the Earth
Projective Geometry & Linear Programming
The spider & the fly problem
Mathematics & soap bubbles
The coin paradox
Hexaminoes
The Fibonacci sequence & Nature
The monkey and the coconuts
Spider & Spirals
APPENDIX
INDEX
Copyright Page
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