Area of an Ellipse Without Calculus

Project a tilted circle onto a table and you get an ellipse. Because projection shrinks every area by a factor of cosθ, we can find the area of an ellipse, πab, without any calculus, then use it to solve a Kepler's second law problem about Mercury's orbit. Chapters 0:00 Goal and Motivation 0:31 Circle and Ellipse 0:59 Projecting a Length: r Becomes r cosθ 1:24 Projecting an Area: Multiply by cosθ 2:15 Conclusion: Ellipse Area = πab 2:39 Application: Kepler's Second Law #physics #math #KeplersLaws #ellipse #geometry