Thread by @TamasGorbe

Follow a point on the rim of a wheel as it rolls (without slipping) on a flat road and you'll get a cycloid. It's a beautiful curve with all sorts of interesting applications. [Wiki bit.ly/2St3vmA] #50FamousCurves

Fun fact: The area under one arch of a cycloid is exactly three times the area of its generating circle. #50FamousCurves

Fun fact: The period of a cycloidal pendulum is independent of its amplitude. (This isn't the case for the simple pendulum.) This was discovered by Huygens in his search for more accurate pendulum clock designs ≈350 years ago. #50FamousCurves
[Gif source: Wikipedia, Rem088roy]

Watch @thinktwice2580's latest video for an easy-to-understand explanation.

Fun fact: The cycloid is the brachistochrone curve i.e. the curve of fastest descent. Finding this out was a challenge posed by Johann Bernoulli in 1696 and solved by several great mathematicians of the time (including Leibniz and Newton). #50FamousCurves

The history of the brachistochrone problem is fascinating. I recommend watching @3blue1brown's video that he made with @stevenstrogatz on the topic.

How to draw a cycloid? #50FamousCurves

Here's a nice video demonstrating a few features of cycloids.
For more details, visit etudes.ru/en/etudes/cycl….

#PuzzleForToday If you pull straight back on the lower pedal of a bicycle, will the bike move forward or backward?

To see the answer, click the link below 👇 simonsfoundation.org/2014/03/20/mat…

George Hart explains Martin Gardner's classic puzzle and its relation to cycloids. #FamousCurves