In this video I go over some of the amazing real-world applications of ellipses due to their unique reflective property which I derived in my last video, so make sure to watch that proof video! Some of the applications include Lithotripsy, Whispering Galleries, and even in Ellipse Billiards Tables. In Lithotripsy, device known as a Lithotripter which is usually ellipsoidal (a 3D ellipse) in shape, and involves sending high-intensity soundwaves, known as shockwaves, from a source located at one focus of the ellipsoid which bounce of the reflective walls and towards the other focus, which is usually aimed at kidney stones or gallstones through an X-Ray targeting device. Whispering Galleries use the ellipse reflection property to send sound from one focus towards the other, which allows for even the smallest of sounds to be overheard many feet away! Playing pool (or billiards) with an ellipse shaped table adds the unique ability to aim the ball at the focus which could make putting the ball in the hole, at the other focus, an interesting trick shot.
The reflective property of the ellipse, as proved in my earlier video, matches the Law of Reflection which states that the angle of light, or sound, that hits a reflective surface such as a mirror gets reflected off in the same angle as intuitively expected. Thus this explains why the ellipse has very cool real-world applications. In this video I also go over some amazing architecture and artwork involving ellipses, which make real-life appear to be photoshopped. This is a very instructive video on the real world applications of mathematics so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvlkta0VwPQjAIWVUw
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-conic-sections-ellipses-applications-lithotripsy-and-whispering-galleries-elliptical-artwork
Conic Sections: Ellipses: Example 3: Amazing Reflective Property: https://youtu.be/H5IPfg3HSRU
Conic Sections: Ellipses: Example 2: Vertical Ellipse: https://youtu.be/cK0z2ZMC1fU
Conic Sections: Ellipses: Example 1: https://youtu.be/m9FXGv3kMkk
Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M
Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE .
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