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LBRY Claims • running-circles-around-circles-part-5

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Running Circles Around Circles: Part 5: Epicycloid Proof
In this video I go over Part 5 of the Laboratory Project titled Running Circles Around Circles and this time derive the parametric equations for an Epicycloid. An epicycloid is a curve formed by the path a point on a circle takes as it rotates around the OUTSIDE of another fixed circle. This is similar to a hypocycloid, which I covered in Parts 1 to 5, but for a hypocycloid the circle rotates around the INSIDE of the fixed circle. The derivation for the parametric equations for the epicycloid is also very similar to that for the hypocycloid. In the derivation I set up two right angle triangles in order to apply basic trigonometry to obtain the coordinates of the point on the outer circle.

The derivation also involves using the definition of arc length, as well as simplifying the final equations by first deriving the trig identities for sin(π-x) and cos(π-x). Although the derivation gets a bit messy because of the many angles and trigonometric ratios, it is definitely worth following the video very closely to see how distances can be derived using trigonometry. So make sure to watch this video, and watch it slowly!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuIFzu-V4_zu15qzyQ

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/running-circles-around-circles-part-5-epicycloid-proof

Related Videos:

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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