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Parametric Curves: History of The Cycloid

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First published at 22:39 UTC on February 2nd, 2018.

Math Easy Solutions

MES

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In this video I go over a brief history of the Cycloid curve as well as some of interesting problems that it makes its appearance in. The question of who first discovered the cycloid is still not resolved and many quarrels among 17th century mathematicans has led to the cycloid being called the "Helen of Geometers" (in reference to Helen of Troy). The first person to coin the term the "cycloid", as well as rigorously study it was the famous Galileo Galilei.

Two of the most famous connections to the cycloid are to the Brachistochrone and Tautochrone problems. The Brachistochrone problem involves finding the curve between 2 points (not directly above each other) that has the shortest time for a particle to move through due only to gravity. The Tautochrone problem looks at an inverted arch and finding what curve makes the time it takes for a particle anywhere on the curve to reach the bottom of the arch at exact same time. Both of these problems have their solutions in the cycloid. These are quite amazing findings, and the Tautochrone problem has given rise to pendulum clocks to be modeled after the cycloid curve because the swing of a pendulum can be scaled up or down and still retain the same time for each swing. This is a very interesting look at the history of a very unique curve so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuBDIBthz53i2dSV_Q

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-curves-history-of-the-cycloid-notes

Related Videos:

Parametric Curves: Example 10: The Cycloid: Proof Part 4: https://youtu.be/5HY7dbTezm4
Parametric Curves: Example 9: The Cycloid: Proof Part 3: https://youtu.be/4VuYJRFAI_g
Parametric Curves: Example 8: The Cycloid: Proof Part 2: https://youtu.be/_LAmOMbXXts
Parametric Curves: Example 7: The Cycloid: Proof Part 1: https://youtu.be/XmHpIZqeRKk
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw .

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