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Hippocrates' Quadrature of the Lune

By Becky Taylor, Brenna Douglas, Lori Joyce and Sarah Matheson. Hippocrates' Quadrature of the Lune. The Dawn of Mathematics. The developments of math are from speculations and educated guesses. The Dawn of Mathematics. The developments of math are from speculations and educated guesses.

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Hippocrates' Quadrature of the Lune

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  1. By Becky Taylor, Brenna Douglas, Lori Joyce and Sarah Matheson Hippocrates' Quadratureof the Lune

  2. The Dawn of Mathematics • The developments of math are from speculations and educated guesses.

  3. The Dawn of Mathematics • The developments of math are from speculations and educated guesses. • Primitive arithmetic and geometry

  4. The Dawn of Mathematics • The developments of math are from speculations and educated guesses. • Primitive arithmetic and geometry • Counting livestock

  5. The Dawn of Mathematics • The developments of math are from speculations and educated guesses. • Primitive arithmetic and geometry • Counting livestock • Space for livestock

  6. The Dawn of Mathematics • The developments of math are from speculations and educated guesses. • Primitive arithmetic and geometry • Counting livestock • Space for livestock • 10,000 – 15,000 BC

  7. Math Like an Egyptian • Practical

  8. Math Like an Egyptian • Practical • Trade • Agriculture

  9. Math Like an Egyptian • Practical • Trade • Agriculture • 2000 BC

  10. Math Like an Egyptian • Practical • Trade • Agriculture • 2000 BC • Numerical system (primitive) • Geometric ideas – triangles, pyramids, etc

  11. Math Like an Egyptian • Practical • Trade • Agriculture • 2000 BC • Numerical system (primitive) • Geometric ideas – triangles, pyramids, etc • Triangles like an Egyptian ....

  12. Math Like an Egyptian • Practical • Trade • Agriculture • 2000 BC • Numerical system (primitive) • Geometric ideas – triangles, pyramids, etc • Triangles like an Egyptian .... • But!

  13. Math Like an Egyptian • Practical • Trade • Agriculture • 2000 BC • Numerical system (primitive) • Geometric ideas – triangles, pyramids, etc • Triangles like an Egyptian .... • But! • No “why” • “You will find it right” (frustum) • No 5-12-13 triangles

  14. Math: Babylonian Style • 2000 BC – 1600 BC

  15. Math: Babylonian Style • 2000 BC – 1600 BC • Better understanding of concepts than Egyptians • Pythagorean Theorem

  16. Math: Babylonian Style • 2000 BC – 1600 BC • Better understanding of concepts than Egyptians • Pythagorean Theorem • Solved problems algebraically

  17. Math: Babylonian Style • 2000 BC – 1600 BC • Better understanding of concepts than Egyptians • Pythagorean Theorem • Solved problems algebraically • Sophisticated numbering system

  18. Math: Babylonian Style • 2000 BC – 1600 BC • Better understanding of concepts than Egyptians • Pythagorean Theorem • Solved problems algebraically • Sophisticated numbering system • Base 60 instead of base 10 • Still influencing life today • 60 seconds per minute, 360

  19. Math: Babylonian Style • 2000 BC – 1600 BC • Better understanding of concepts than Egyptians • Pythagorean Theorem • Solved problems algebraically • Sophisticated numbering system • Base 60 instead of base 10 • Still influencing life today • 60 seconds per minute, 360 • But! • “how” but still no “why”

  20. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete

  21. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete • (2000) Completion of Stonehenge

  22. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete • (2000) Completion of Stonehenge • (2000) First Minoan Palace on Crete

  23. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete • (2000) Completion of Stonehenge • (2000) First Minoan Palace on Crete • (1700) Extinction of the Mammoths

  24. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete • (2000) Completion of Stonehenge • (2000) First Minoan Palace on Crete • (1700) Extinction of the Mammoths • (1600) Early Mycenaean culture

  25. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete • (2000) Completion of Stonehenge • (2000) First Minoan Palace on Crete • (1700) Extinction of the Mammoths • (1600) Early Mycenaean culture • (1500) Phoenicians develop early alphabet

  26. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete • (2000) Completion of Stonehenge • (2000) First Minoan Palace on Crete • (1700) Extinction of the Mammoths • (1600) Early Mycenaean culture • (1500) Phoenicians develop early alphabet • (1446) Moses leads the Exodus of the Jews from Egypt

  27. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete • (2000) Completion of Stonehenge • (2000) First Minoan Palace on Crete • (1700) Extinction of the Mammoths • (1600) Early Mycenaean culture • (1500) Phoenicians develop early alphabet • (1446) Moses leads the Exodus of the Jews from Egypt • (1340) Tutankhamen (King Tut)

  28. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete • (2000) Completion of Stonehenge • (2000) First Minoan Palace on Crete • (1700) Extinction of the Mammoths • (1600) Early Mycenaean culture • (1500) Phoenicians develop early alphabet • (1446) Moses leads the Exodus of the Jews from Egypt • (1340) Tutankhamen (King Tut) • (~1200) Trojan War

  29. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete • (2000) Completion of Stonehenge • (2000) First Minoan Palace on Crete • (1700) Extinction of the Mammoths • (1600) Early Mycenaean culture • (1500) Phoenicians develop early alphabet • (1446) Moses leads the Exodus of the Jews from Egypt • (1340) Tutankhamen (King Tut) • (~1200) Trojan War • (~1100) Start of Archaic Greek Period

  30. World News ca. 2000 - 1000BC • (2500) The three main pyramids in Giza complete • (2000) Completion of Stonehenge • (2000) First Minoan Palace on Crete • (1700) Extinction of the Mammoths • (1600) Early Mycenaean culture • (1500) Phoenicians develop early alphabet • (1446) Moses leads the Exodus of the Jews from Egypt • (1340) Tutankhamen (King Tut) • (~1200) Trojan War • (~1100) Start of Archaic Greek Period • Bronze/Iron Ages beginning

  31. Greece: The Classical Period • Literature, Philosophy, Architecture and politics surged • First civilization to rise above magic and superstition • Created the concept, and reality, of political freedom.

  32. Hippocrates • Born in Chios, Greece, around 470 BC, a decade after a rebellion drove out the occupying Persians. • Spent most of his life in Athens

  33. Athens • During the time of Hippocrates, Athens was experiencing it’s most successful period: The age of Pericles. • Pericles, the democratic leader of Athens and born aristocrat, weakened the aristocracy and offered many benefits to the common people. • Parthenon and the Propylaea built during this period • Herodotus, father of history, wrote a detailed history of all major events during this time

  34. Late 500th Century B.C. • Hippocrates left Athens around 430 B.C. • Peloponnesian Wars (431-404 B.C.) • Fought by Athens and its empire against the Peloponnesian League, led by Sparta • Athens Plague (430 B.C.)

  35. World Math 500BC • The Babylonian sexagesimal number system is used to record and predict the positions of the Sun, Moon and planets

  36. World Math 500BC • The Babylonian sexagesimal number system is used to record and predict the positions of the Sun, Moon and planets • Panini's work on Sanskrit grammar is the forerunner of the modern formal language theory.

  37. World Math 500BC • The Babylonian sexagesimal number system is used to record and predict the positions of the Sun, Moon and planets • Panini's work on Sanskrit grammar is the forerunner of the modern formal language theory. 465BC • Hippasus writes of a "sphere of 12 pentagons", which must refer to a dodecahedron.

  38. World Math 450BC • Greeks begin to use written numerals.

  39. World Math 450BC • Greeks begin to use written numerals. • Zeno of Elea presents his paradoxes.

  40. World Math 450BC • Greeks begin to use written numerals. • Zeno of Elea presents his paradoxes. 440BC • Hippocrates of Chios writes the Elements which is the first compilation of the elements of geometry.

  41. World Math 450BC • Greeks begin to use written numerals. • Zeno of Elea presents his paradoxes. 440BC • Hippocrates of Chios writes the Elements which is the first compilation of the elements of geometry. 430BC • Hippias of Elis invents the quadratrix which may have been used by him for trisecting an angle and squaring the circle.

  42. World Math 425 BC • Theodorus of Cyrene shows that certain square roots are irrational.

  43. World Math 425 BC • Theodorus of Cyrene shows that certain square roots are irrational. 400BC • Babylonians use a symbol to indicate an empty place in their numbers recorded in cuneiform writing.

  44. World News ca. 500 - 400BC 467BC • Greek philosopher Anaxagoras becomes the world's earliest figure to be indicted for atheism. 450BC • The Nok people of present day Nigeria began making iron tools. 427BC • Greek philosopher Plato is born

  45. Quadrature The process of constructing a square of equal area to another shape using only a straight edge and a compass.

  46. Quadrature of Rectangles Area = BE x ED

  47. Quadrature of Rectangles Area = BE x ED ED = EF

  48. Quadrature of Rectangles Area = BE x ED ED = EF BG = GF = ½ BF

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