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Running Circles Around Circles: Part 6: Graphing Epicycloids

790 views · Published 22 January 2017 · 14:30 · Indexed 23 September 2026

Channel: Math Easy Solutions · 2017 · Education

In this video, I go over Part 6 of the Laboratory Project titled Running Circles Around Circles, and this time plot out varying types of Epicycloids. I use the same methods as in Parts 2 to 4 for which I plotted out Hypocycloids. In all the cases I assume that the outer circle has a radius b = 1, and then vary the fixed circle radius ‘a’ by considering it as a positive integer, a fraction, and an irrational number. The epicycloid shapes vary from multiple-leaf clovers, to Cardioids, to crazy spiral shapes. Also, as with hypocycloids, when the fixed circle radius, a, is an irrational number, as the range of the angle increases, the curves becomes more and more solid, and thus eventually appearing as a solid washer. This is a very cool video on once again using the amazing Desmos calculator, as well as for understanding the behavior of cool parametric curves, such as the epicycloid, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuIZHtzQvHTuqvFlpA

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/running-circles-around-circles-part-6-graphing-epicycloids

Related Videos:

Running Circles Around Circles: Part 5: Epicycloid Proof: https://youtu.be/vPxcRlzC8dk
Laboratory Project: Running Circles Around Circles: Part 4: https://youtu.be/sypHRx10RXM
Laboratory Project: Running Circles Around Circles: Part 3: https://youtu.be/uCdvK29T5Z0
Laboratory Project: Running Circles Around Circles: Part 2: https://youtu.be/-hCw2HJF0YQ
Laboratory Project: Running Circles Around Circles: Part 1: https://youtu.be/MiCqDNQN7_E
Parametric Curves: Superellipses: https://youtu.be/JqkjQjtenPQ
Parametric Curves: Example 11: Conchoids of Nicomedes: https://youtu.be/Ir1tVdwGWec
Parametric Curves: Example 7: The Cycloid: Proof Part 1: https://youtu.be/XmHpIZqeRKk
Parametric Curves: Example 6: Graphing Devices: https://youtu.be/cwpEasc9mhQ
Parametric Curves: Example 5: Lissajous Figure: https://youtu.be/0OT1OnnAQ9I
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw .

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Running Circles Around Circles: Part 6: Graphing Epicycloids

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