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The Bernoulli Family

The Bernoulli Family. The Mathematical Dynasty. Jacob Bernoulli (1654-1705). Studied Mathematics against his father’s wishes Studied at University of Basel Jacob and brother Johann corresponded with Leibniz Together mastered Leibniz’ papers Found formula for isochrones. Isochrone.

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The Bernoulli Family

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  1. The Bernoulli Family

  2. The Mathematical Dynasty

  3. Jacob Bernoulli (1654-1705) • Studied Mathematics against his father’s wishes • Studied at University of Basel • Jacob and brother Johann corresponded with Leibniz • Together mastered Leibniz’ papers • Found formula for isochrones

  4. Isochrone • http://pi-nuts.soup.io/post/199542758/A-tautochrone-or-isochrone-curve-from-Greek

  5. ArsConjectandi • Jacob’s book on probability theory. • Contained his “Law of Large Numbers” • States that in a very large data set collected from a random experiment, these three measures will be approximately the same • Center of collection on numerical data measured by 3 calculations: • 1. Mean • 2. Median • 3. Mode

  6. Bernoulli Numbers • Jacob discovered a formula for e • This lead to the Bernoulli numbers • The Bernoulli numbers are calculated using a generating function: • The Bernoulli numbers are the derivatives of this function evaluated at t =0

  7. Johann (1667 – 1748) • Also studied math at the University of Basel • Also against his father’s wishes • Johann and Jacob cleaned up Leibniz’ calculus • Big Rival between brothers!

  8. Johann • Found formula for the Brachristochrone • The curve between two non-vertical points along which a free falling body would have the quickest decent. • Hydraulica • His major work on Hydrodynamics • Contained his theory: Calculus of Variations Johann was worried about a specific rival, so he pre-dated the publication date

  9. Daniel (1700-1782) • Johann’s son • And his rival • Hydrodynamica • Daniel and Johann competed for the same Grand Prize od the Paris Academy in 1734 • Joint Winners • Johann backed out, said it was “shameful” • Daniel won it 9 more times • End of relationship

  10. Bernoulli’s Principle • Daniel corrected a result of Newton’s about the rate at which a liquid flowed from a hole in a wall. • Bernoulli’s Principle • For an in viscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid’s potential energy. • Valid for gasses and how airplanes fly

  11. Family ties • Daniel worked with brothers Johann and Nicholas. • Daniel took over his father’s professor position at Basel • Daniel and Johann were offered positions at the Russian Academy in St. Petersburg which they took on the condition they could bring their colleague Leonard Euler

  12. Works Cited • http://image.slideserve.com/143100/understanding-the-bernoulli-family-tree-n.jpg

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