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The Lemniscate of Bernoulli: Exploring Infinity Graphically and Mathematically

Discover the fascinating world of the Lemniscate of Bernoulli through this insightful guide by Jonathan O'Connell. Learn about the life of Bernoulli and his contributions to mathematics, physics, and statistics. Explore the representation of the Lemniscate in Cartesian, polar, and parametric forms. Dive into concepts such as fluid dynamics equations and trigonometric identities with step-by-step explanations. Delve into the practical applications with a Geogebra file and Matlab-generated graphs. References and further reading are included for in-depth exploration.

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The Lemniscate of Bernoulli: Exploring Infinity Graphically and Mathematically

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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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