Theorem of Pappus (KristaKingMath)

[@jeffberhow]

Thanks for the response! It's quite amazing that the centroid has this property. I may be overthinking it, but we are taking the product of a one and two dimensional object and getting a three dimensional result. Very cool!

[@geraldglennmullet8665]

A segment of a circle of radius R is bounded by an arc equal to 1/3 the circumference of the circle. Find the volume of the solid generated by revolving this segment about its chord as an axis. (This solid is know as Kepler's Lemon). Note: Do note use integral calculus.

[@RaptrX]

You managed to do what my profesor couldn't in a full lesson. Thanks for clearing up some doubts that I had.

[@ahmedsaeed6556]

this video is not just helpful . it's helpful , great and awesome . actually you're doing great job . thanks for that inexpressible effort ..

[@kristakingmath]

+ahmed saeed You're welcome, I'm happy to help!

[@ptyptypty3]

very WELL DONE, KRISTA!!.. You RULE.. :) ... by the way... a Great CHECK to see if your result is Correct.. (not that I think it wasn't correct!! ) .. is to Note that the Volume of a Cone is 1/3 the Volume of a CYLINDER using the same values for "h" and "r" .. and SURE ENOUGH.. you arrived at the 1/3(Pi)(r^2)(h) !!!! BINGO!! :) ... the area of the cylinder would be (Pi)(r^2)(h) !! THANK YOU KRISTA for all your wonderful AND very Educational Videos!! ..

[@miguelalvarado5824]

Props young lady. Helped me with my Calc 2 homework, thanks!

[@kristakingmath]

You're welcome, I'm so glad it helped! :)

[@saidesmatullahhussaini9330]

Best teacher ever

[@kristakingmath]

Thank you so much!!

[@kristakingmath]

Think about the plane region, basically, a 2D triangle that sits inside the cone. The centroid of that triangle (basically the middle of it), will travel a distance when you revolve that triangle around the y-axis. That center dot will essentially form a circle when you rotate the region, and the circumference of that circle is the distance traveled by the centroid. I hope that makes sense!! :)

[@jeffberhow]

What exactly does "distance traveled by the centroid of the plane region" mean; from where to where? Thanks for the great videos!

[@kristakingmath]

I didn't see VeryEvilPettingZoo's response before I responded. Thanks for helping each other... that's awesome!! :D

[@husnainhyder6713]

your method has helped me is there any method to analyze 3D problems. Thankyou

[@lyndongaming]

thanks, never understood any of what my professor explained for 2 hours. but in this video it took only around 10 mins

[@kristakingmath]

So glad I could help simplify it for you! :)

[@hg2.]

Yes L, Krista's videos give us "working knowledge"; a whole new generation of engineers is on the way, imho.

[@kristakingmath]

Glad I could help! :)

[@Neueregel]

Well done.

[@chekurihrishikesh9022]

Thanks .

[@amairanylopez4752]

so simple! thank you!

[@DaylightDigital]

I love this theorem!!!

[@Dewatch111]

could you not also find the equation of the line and rotate it around the y-axis by using it's bounds and the disk method? not positive if that would work but i feel like it could be a substitute

[@kristakingmath]

Thanks! :)

[@jaikhanna1532]

when do we need the y coordinate..does the distance formula also change in that case?

[@rajeshagrawal4639]

hey Krista I want to find center of mass of a rigid uniform body like that semi ring please help me out

[@aubrey1008]

Where does the 1/A come from. I don't get it. Can anyone explain?

[@Boostedsoul]

hello can you state this theorem i mean statement of this theorem

[@husnainhyder6713]

video is great but still have question about Y' is the formula of Y' is correct X' is verified from my side please help me with this matter

[@kristakingmath]

thanks!! :D

[@praveenkumarsunny9158]

from where did u get the board and chalk on ur computer

[@kristakingmath]

I explain here :) www.kristakingmath.com/my-videos

[@adrieldelatorre6265]

Thank you very much! :)

[@kristakingmath]

You're welcome!

[@adi87tya]

If you're desi like me you can't stop giggling at "Pappu's theorem"

[@yopsi522]

when do you use this theorem on real life?

[@mannuposki10]

I just had one doubt. Can you explain why did we consider only the x-coordinate and not y-coordinate?

[@jasonlau1552]

+Aman Sharma well if u are trying to find the distance of a straight line (which is in this case)u can neglect ur y corrdinate

[@kunal_265]

Cos The triangle so form is rotating about y-axis, If it's rotating about x-axis, then we'll consider only y coordinate and not x centroid

[@SAAD63856]

thank you

[@kristakingmath]

You're welcome! :)

[@mayaachir1321]

can somebody recap simply the problem for me plz ? it's for a project about Descartes for school...

[@matiaharonyan9663]

inlove with you

[@Abc-tx4zr]

I don't understand why you can't just multiply 1/2 b (h)(2pi)(r)^2

[@rishirajdara]

I don't understand why the equation of F(x) is taken as the hypotenuse of the right angled triangle.

[@gadddelarosa2692]

Bcos it is the line that enclosed the cone and its equation is y=f(x)

[@thomasfox9893]

WTF is going on

[@abochaser]

thanks a lot, but there was a mistake in your solution. after the integration, r cubed was changed to r squared. and with that being done, your result is wrong.

[@Maddr33]

Yaarub Alanie it looks like the r's just canceled out. 1/3^r Xr^3

[@abochaser]

oh ok. i am sorry. thanks again

[@Maddr33]

I AM SO COOKED FROM FINALS THAT I tried and pick up my mouse and dial it.