Current Events > Can you solve this SAT math question?

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Naysaspace
03/19/24 5:18:52 PM
#1:


Two coins. These coins are the exact same and have the same radius and circumference.

Roll the top coin around the bottom coin until it gets back to it's starting position. How many full rotations does the top coin make?
https://gamefaqs.gamespot.com/a/forum/8/8a275a1e.png

This is known as the coin roll paradox.

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R1masher
03/19/24 5:20:44 PM
#2:


360

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Naysaspace
03/19/24 5:21:05 PM
#3:


This is a handy explanation

https://graphicmaths.com/recreational/paradoxes/rotating-coin/

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bigblu89
03/19/24 5:23:23 PM
#4:


Yes. I can.

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LonelyStoner
03/19/24 5:24:33 PM
#5:


720 degrees. You have to account for the first coins area and circumference. It takes two rotations to match up perfectly.

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VideoboysaysCube
03/19/24 5:30:53 PM
#6:


Naysaspace posted...
This is a handy explanation

https://graphicmaths.com/recreational/paradoxes/rotating-coin/

This makes me wonder what other assumptions I've made about life are wrong.

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EndOfDiscOne
03/19/24 5:32:07 PM
#7:


I had to visualize it, and I realized my initial guess was wrong. I haven't looked up the answer, but I would have gotten it wrong on an SAT since I'd be working faster.

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RetuenOfDevsman
03/19/24 5:32:35 PM
#8:


It would have to be two. If it just did one, the top of Washington's head would always be away from the eagle, which would be sliding instead of rolling. Then since the circumferences are the same, it would have to roll once in addition.

Or to think of it another way, if you drew a line the length of the circumference and rolled it along ng it would rotate once, then there's another rotation when the path is curved into a circle.
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NeonOPPAl
03/19/24 5:34:28 PM
#9:


I guess 2 because it rotates once from the circumference being the same, and another for the viewing angle (ie: when it's halfway around, it will be right side up for us)

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MarcoRubio
03/19/24 5:37:35 PM
#10:


It's fucking two

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Naysaspace
03/19/24 5:46:19 PM
#11:


Why it's 2 and not one: The stationary coin is also technically rolling. Think like they are two gears, there is no "sliding". But the camera/view is "locked" to the "stationary" coin. It still moves, so the movement is "transferred" to the outside/rolling coin.

When i found this out it blew my mind. The problem i worked on was a bit tougher (two different sized circles, one circumference 1, other circumference 3, and the answer is 4, not 3). AFAIK, the formula for rotations is Large R/ small r + small r.

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Naysaspace
03/19/24 5:49:50 PM
#12:


RetuenOfDevsman posted...
It would have to be two. If it just did one, the top of Washington's head would always be away from the eagle,
1 full rotation actually has the top of the head facing the eagle, but it's at the bottom rather than back in the starting position

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DDP886
03/19/24 6:01:45 PM
#13:


Reminds me of the GRE

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Evening_Dragon
03/19/24 6:05:52 PM
#14:


Just visualized it and only 2 looked right. Thanks for that explanation link.

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kelemvor
03/19/24 6:07:14 PM
#15:


Isnt this a question that was wrong on an official SAT test?
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Naysaspace
03/19/24 6:18:13 PM
#16:


kelemvor posted...
Isnt this a question that was wrong on an official SAT test?
it was, i believe that was a long time ago however.

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radical_rhino
03/19/24 6:28:00 PM
#17:


Thats not what a paradox is.

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Baphometa
03/19/24 6:40:59 PM
#18:


radical_rhino posted...
Thats not what a paradox is.
https://gamefaqs.gamespot.com/a/forum/2/2fee5932.jpg

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Robot2600
03/19/24 6:48:44 PM
#19:


weird!

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Seaman_Prime
03/19/24 7:12:51 PM
#20:


Holy shit im doing this with my fingers and its blowing my mind
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