1 / 10

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.

dianebrock
Download Presentation

The Lemniscate of Bernoulli

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related