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The Lemniscate of Bernoulli

The Lemniscate of Bernoulli. The cool way to write infinity By Jonathan O’Connell. Who was Bernoulli?. Bernoulli was born in The Netherlands in 1700. Part of a predominate math family. Worked in areas of statistics, physics, and mathmatics. Developed fluid dynamics equations. How it works.

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The Lemniscate of Bernoulli

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  1. The Lemniscate of Bernoulli The cool way to write infinity By Jonathan O’Connell

  2. Who was Bernoulli? Bernoulli was born in The Netherlands in 1700. Part of a predominate math family. Worked in areas of statistics, physics, and mathmatics. Developed fluid dynamics equations.

  3. How it works

  4. Representing the Lemniscate Cartesian: Polar: Parametric:

  5. Finding the Polar equation • My cool geogebra file OC = CA = OP’ is parallel to HF’ OQ = PP’ 2QC = OH 2PQ = HH’ Then is similar to Now 2PC = OH’ = a

  6. Polar cont. • Let be and OQ be r • Segment OH = • OA =

  7. It all comes together • It’s a trig identity! • Matlab generated polar graph

  8. Changing to parametric • Matlab generated graph

  9. Interesting stuff • Delicious math =

  10. Works cited http://en.wikipedia.org/wiki/Daniel_Bernoulli Lee, Xah. "Lemniscate of Bernoulli." Visual Dictionary Of Special Plane Curves. 23 Nov. 2008 <http://xahlee.org/specialplanecurves_dir/lemniscateofbernoulli _dir/lemniscateofbernoulli.html>. A Book of Curves by E. H. Lockwood

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