Breaking the Cycloid: A Geometry Problem

[@LearnPlaySolve]

When Galileo discovered that the ratio of the areas of the cycloid and circle was 3 to 1, he initially thought that it was actually π to 1. He assumed that the small discrepancy was due to the precision limits of his scale.

[@FORTUNECHOMBA]

Wow 😮

[@bonfacemuthuri9840]

Thanks you are the best

[@enzotsunoda]

this video's animation is top tier, keep the good work! btw which program do you use?

[@TheJara123]

Hi man I just discovered your videos few days back, superb video math content... Amazing way of explaining, you have nice gift to present math!! I realy enjoyed the breaking cycloid video. No one makes video like this about calculus and trignometry... I am so excited to check out the rest. Please keep posting more videos... On trignometry, calculus, geometry, number theory as you said you have great collection!!

[@LearnPlaySolve]

Thank you so much for that compliment!!'

[@ahmedbloul01]

Extraordinary video, what a joyful watching you. Thank you very much

[@abacaabaca8131]

Thanks to this video I was able to draw cycloid in code. I want the computer to slowly draw the cycloid. Before this, I just prepare all the coordinates before hand in a data structure before drawing them i.e using factory method. But it draws the cycloid but not draw it slowly. What I need to do is that: angle+=1.0f*fElapsedTime; Then update x and y coordinate And draw using those.

[@juniorcyans2988]

It's already over 1 am and I'm still rushing my physics homework. To understand cycloid, I found this video. I liked it and I subscribed!

[@gopalsamykannan2964]

Good narration and explained well !!!

[@thonloai]

dat ...so cool

[@odysseytkl7261]

This video is amazing, top tier. No idea how you don't have more subs

[@Neemakukreti5421]

That was a fantastic demonstration! Simply wonderful! Just one question--how did you conclude that the arc length of the circle should be equal to the horizontal distance covered by it?

[@LearnPlaySolve]

Imagine that you cut the circle and unwrap it into a straight line. Every point on the circle would correspond to another point on the ground that it touched as it rolled. For example, if a circle rolls for one complete revolution, the length of the path it rolled would be equal to the circumference of the circle.

[@mdabusayem8755]

fantastic broooo

[@dragonlovesdiamond9512]

Im confused why the arc length of the circle = the = x+a

[@David1AAA]

Amazing explanation, keep up the good work, humanity will thank you

[@sarthaksharma2880]

I know i will never meet you SIR but you have saved some one out there❤❤🫡🫡🫡,i was solving a problem of particle on edge of rim ,had to prove the path is cycloid for observer situated outside,,you just described cycloiddddd so weell(i touch your feet),thankyouuuuuu,😄😄😄😄

[@arturo.1895]

I just didn't understand why x+a is the same as the arc length of the circle. 2:31

[@konoveldorada5990]

Same bro

[@LearnPlaySolve]

You could take that line segment (x+a) and wrap it along the circle, it would equal that specific arc length. We know this because the circle rolled along that same line segment without slipping

[@arturo.1895]

​@@LearnPlaySolveyeah, so since the circle rolled without slipping, all of its points touched the line, forming a segment which is, by definition, is the arc length.

[@nazishahmad1337]

Please let me know which software do you use for creating your animations , they're really good . Please if possible make a video on how do you create your videos .

[@c3physics772]

Software ka pata chala kya

[@no1_cheema543]

man! you are doing great. I request you to never give up

[@LearnPlaySolve]

Thank you for that! 😃

[@legend5951]

Great explanation 👍, keep it up dude

[@DragonYeng]

best video on cycloid

[@LearnPlaySolve]

Thank you so much!

[@ziaulhaq3066]

Good yar!! Very nice animation and explanation

[@juniorcyans2988]

I watched twice, then I kinda get it. Very nice video! Thanks a lot!

[@leexavier44]

Great learning experience thank you

[@c3physics772]

Wonderful.

[@dakerbal]

Excellent video

[@Mo_ducky]

Keep up the work I like ur channel it's very entertaining

[@tanner1985]

Cycloids are very intriguing

[@OskarSevillaCardenas]

Hey, awesome video

[@scienceandtech4497]

This was amazing

[@zenmonk29]

great video man

[@sarfarazshaikh7334]

Subscribed ❤️

[@igorjasenovski4313]

You did a greate job on this video and explanação!!!

[@LearnPlaySolve]

Thank you 🙏

[@albertyeung5787]

excellent

[@wyattwatters172]

Awesome video bro!!

[@thickmomson]

Underrated af

[@RaulLopez-rq6wh]

How could you calculate the point new position in the x.y plane if the circle rotates in place?

[@LearnPlaySolve]

The circle does not rotate in place. It rolls along a straight line.

[@RaulLopez-rq6wh]

@@LearnPlaySolve sorry, I meant an hypothetical scenario where it rotates in place, or do you mean it gets calculated the same?

[@LearnPlaySolve]

Then I suppose you could just treat it like a unit circle. Every point could be defined as (cosx,sinx).

[@sebastianramirezcaseres2965]

Great explanation bro, thznks a lot

[@c3physics772]

Sir which software you use to make such vedio

[@c3physics772]

@@LearnPlaySolve so nice of you Sir

[@LearnPlaySolve]

No problem. Thank you for watching my videos.

[@c3physics772]

@@LearnPlaySolve i have subscribed it also. I will regularly watch. Thanks