1. The Bernoulli Family

2. The Mathematical Dynasty

3. Jacob Bernoulli ( )
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

5. Ars Conjectandi 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
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