Rock and Roll (riddle)

***Ace Mercury*** · 08-09-2009, 11:27 AM

A quick little geometric riddle:

Quote:

Originally Posted by http://www.futilitycloset.com/2009/08/01/rock-and-roll-2/

Worshipful natives are rolling a giant statue of me across their island. The statue rests on a slab, which rests on rollers that have a circumference of 1 metre each. How far forward will the slab have moved when the rollers have made 1 revolution?

Related is the "Famous Wheel Question"

Quote:

Originally Posted by http://www.futilitycloset.com/2007/10/02/the-famous-wheel-question/

This question was proposed in the Scientific American, in 1868: 'How many revolutions upon its own axis, will a wheel make in rolling once around a fixed wheel of the same size?'

The question brought to the editor of that paper many replies all claiming to have solved it. Yet the replies were about equally divided as to the number of revolutions, one part claiming one revolution and the other two revolutions. So much interest was manifested in it that Munn & Co. published The Wheel, June, 1868. It contains 72 pages, giving many of the solutions, illustrated by many diagrams.

Kind of hard to visualize, for me at least =/

Mikhail Gorbachev · 08-09-2009, 12:23 PM

Spoiler Below

Having studied epicycloids and such earlier this year (on my own, not for class, because I'm that nerdy), these were pieces of cake. I'm not sure, though, if that counts as me solving it or me already knowing the answer.

To visualize it: imagine a point on the circumference of the revolving circle initially touching the figure it's revolving around, with a radius connecting this point to the revolving circle's midpoint.
The curves traced by this point as the circle revolves are the cycloid[1] and the cardioid[2]. The animated .gifs on those pages rock and make these riddles easy to visualize.

***CaptHayfever*** · 08-09-2009, 11:40 PM

Spoiler Below

2/pi meters.

And remember, "I'm-a Luigi, number one!"

***Ace Mercury*** · 08-10-2009, 07:49 AM

^^ That post only made me feel more stupid =/

By the by, the answer is supplied in the source URLs in the thread post.

Speed · 08-10-2009, 12:20 PM

The answer is Megaman.

08-09-2009, 12:23 PM	#2
Mikhail Gorbachev Senior Member Join Date: Nov 2004 Gender: Posts: 9,659 Thanks: 31 Thanked 89 Times in 71 Posts	Spoiler Below Having studied epicycloids and such earlier this year (on my own, not for class, because I'm that nerdy), these were pieces of cake. I'm not sure, though, if that counts as me solving it or me already knowing the answer. To visualize it: imagine a point on the circumference of the revolving circle initially touching the figure it's revolving around, with a radius connecting this point to the revolving circle's midpoint. The curves traced by this point as the circle revolves are the cycloid[1] and the cardioid[2]. The animated .gifs on those pages rock and make these riddles easy to visualize.

08-09-2009, 11:40 PM	#3
*CaptHayfever* Smash SuperMod Join Date: Jul 2002 Location: (n) - the place where I am Gender: Posts: 27,659 Thanks: 1,991 Thanked 2,486 Times in 1,513 Posts	Spoiler Below 2/pi meters. And remember, "I'm-a Luigi, number one!"

08-10-2009, 07:49 AM	#4
*Ace Mercury* Marshmallow Knight ☆ Supermod Join Date: Jun 2000 Location: Southern Ontario Gender: Posts: 23,274 Thanks: 568 Thanked 3,297 Times in 1,582 Posts Blog Entries: 1	^^ That post only made me feel more stupid =/ By the by, the answer is supplied in the source URLs in the thread post.

08-10-2009, 12:20 PM	#5
Speed Senior Member Join Date: Aug 2005 Location: If there's a bright center to the universe I'm on the planet it's farthest from Gender: Posts: 3,747 Thanks: 1,598 Thanked 320 Times in 224 Posts Blog Entries: 1	The answer is Megaman.