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Can you solve the maths question for Singapore schoolkids that went viral?

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It is running around another circle.

rollingcircle1.png.0205e44d664fe86fc61d2ec9c9c02222.png

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Now if after it had run on the flat and rotated 3 times, you then rotated both the circle and the line around one more time - you'd have rotated the circle in total 4 times:

rollingcircle4.thumb.png.9f766a2e79d264dc9bd55485f1f0c422.png

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And this is the same thing as if you rotated the line, while the circle was rotating along it:

rollingcircle5.thumb.png.9b3c802c116cad2da51ebd0b6f505126.png

The circle rotates three times by rolling, and is also rotated a further time as the line is rotated, carrying the circle with it.

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But this is identical to the situation you get when you roll the small circle around the large one - the line is the equivalent of the tangent line parallel to the surface of the join of the two circles:

rollingcircle6.thumb.png.f3f1c30e6705462ec6e6427741e3e89f.png

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Try it in the pub with two coins of the same size - roll one around the other.

Most people expect it to rotate once as it rolls around, but in fact it rolls twice.

rollingcircle7.png.f7b2ac14538c02065a7890eae20dfe8d.png

I'm currently reading Measurement by Paul Lockhart and couldn't recommend it more.  It is a most wonderfully concise and clear explanation of the mathematics of geometry and the joys of mathematics.  I wonder if Woolley, or dilligaf or even PGW would ever pick up such a book and find something of wonder inside its pages.

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I’d have selected the ‘3’ answer and moved on to the next question within about 2 seconds. China would no doubt have written a long explanation in the margin as to why all the available answers were wrong. I’d have ended up studying at Harvard, China would be the janitor there solving the puzzles on the blackboard :D

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In celebration of Doug Hofstadter's 75th birthday - do read Godel, Escher and Bach it is awesomely thought provoking, I present the following paradox:

How many errors do you see in the sentence below?
"This sentense has three erors."

 

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26 minutes ago, Chinahand said:

In celebration of Doug Hofstadter's 75th birthday - do read Godel, Escher and Bach it is awesomely thought provoking, I present the following paradox:

How many errors do you see in the sentence below?
"This sentense has three erors."

 

All three

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Erm. So is it correct that there are three errors or not?

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45 minutes ago, Chinahand said:

Erm. So is it correct that there are three errors or not?

That’s why I answered  how I did. It’s the same as Frederick in the Gilbertian “little boy of 5”. 
 

A paradox, a paradox, a most ingenious paradox. 

 

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2 hours ago, Chinahand said:

In celebration of Doug Hofstadter's 75th birthday - do read Godel, Escher and Bach it is awesomely thought provoking, I present the following paradox:

How many errors do you see in the sentence below?
"This sentense has three erors."

 

Nice. 
 

I read it aged 19 or 20 I think. I then studied Gödel’s incompleteness theorem later on as part of my OU maths degree. I still have difficulty getting my head round it, despite working through his original paper line by line. 

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Isn't it wonderful you can list a series of sentences and it is easy to say how many errors they have, and then at 3 you enter into a strange self-referential blackhole. 

image.png.0171a1745c7e98a8152e7586e4fc2b05.png

上士闻道,勤而行之;

中士闻道,若存若亡;

下士闻道,大笑之。

不笑不足以为道。

Shàng shì wén dào, qín ér xíng zhī;

zhōng shì wén dào, ruò cún ruò wáng;

xiàshì wén dào, dà xiào zhī.

Bù xiào bùzú yǐwéi dào.

Scholars of the highest class, when they hear about the Tao, earnestly carry it into practice.

Scholars of the middle class, when they have heard about it, seem now to keep it and now to lose it.
Scholars of the lowest class, when they have heard about it, laugh greatly at it.

If it were not (thus) laughed at, it would not be fit to be the Tao.
 

 

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