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The History of Calculus

The History of Calculus. “If I have seen farther it is by standing on the shoulders of giants .” – Sir Isaac Newton (1642-1727). Who were the giants?. The Ancient Greek Philosophers. The Ancient Egyptians. Pythagoras (570-495 BCE). The Medieval Islamic Scholars .

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The History of Calculus

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  1. The History of Calculus “If I have seen farther it is by standing on the shoulders of giants.” – Sir Isaac Newton (1642-1727)

  2. Who were the giants? The Ancient Greek Philosophers The Ancient Egyptians Pythagoras (570-495 BCE) The Medieval Islamic Scholars Omar Khayyam (1048-1131 CE)

  3. Zeno of Elea (490 – 430 BCE) Zeno’s Paradox What is a Paradox? A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition.

  4. The Dichotomy Paradox “That which is in locomotion must arrive at the half-way stage before it arrives at the goal.”—Aristotle, Physics Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on. Let D = distance travelled, then D = 1/2 + 1/4 + 1/8 + 1/16 + . . . As the series approaches infinity D approaches 1.

  5. Infinite Series What is the size of the shaded area? A = 1/4 + 1/16 + 1/64 + . . .

  6. Clue: What is 4A? 4A = 1 + 1/4 + 1/16 + 1/64. . . A = 1/4 + 1/16 + 1/64. . . Therefore. . . 3A = 1 A = 1/3

  7. Closing thought Is A = 1/3 or is A = very, very, very nearly but not quite 1/3. Now there’s a paradox!

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