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Old 3rd October 2012, 06:41 PM   #141
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Originally Posted by Cal Weldon View Post
I think because it's 40,000km, the initial reaction is: It has to be way longer, now let's go find out how much. Hmmm...
Interesting isn't it? We don't expect a cm added to 40,000km to be any bigger or smaller than a cm on its own. Why should our expectation be different with a circle? My feeling is that it's because the area added is great, being the difference between two large squares. The large addition in area leads us to expect a large difference in circumference.

It's common to confuse the equations for circumference and area. Our judgement of relative diameter is generally very poor, because our estimation is so dominated by area.

In fact, as far as circumference and radius are concerned, circles can be added arithmetically, just like lines. A small circle added to a very big circle is still a small circle. Were it not for confusion with area, that would be plainly obvious.
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Old 3rd October 2012, 07:08 PM   #142
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Thinking of confused expectations, why don't I appear upside-down in a mirror?
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Old 3rd October 2012, 07:10 PM   #143
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п П - Cyrillic alphabet has symbols similar to Greek.
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Old 3rd October 2012, 07:21 PM   #144
M Gregg is offline M Gregg  United Kingdom
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Originally Posted by PlasticIsGood View Post
Thinking of confused expectations, why don't I appear upside-down in a mirror?
Because the third eye (TV screen inside your head) is not a true representation of the real world?

Why do you look different in a mirror and different in a photo to the mirror ?

I guess the next bit may require English to be a first language, then again maybe not?

Here is an example:

7H15 M3554G3

53RV35 7O PR0V3

H0W 0UR M1ND5 C4N

D0 4M4Z1NG 7H1NG5!

1MPR3551V3 7H1NG5!

1N 7H3 B3G1NN1NG

17 WA5 H4RD BU7

N0W, 0N 7H15 LIN3

Y0UR M1ND 1S

R34D1NG 17

4U70M471C4LLY

W17H 0U7 3V3N

7H1NK1NG 4B0U7 17,

B3 PROUD! 0NLY

C3R741N P30PL3 C4N

R3AD 7H15.



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Last edited by M Gregg; 3rd October 2012 at 07:31 PM.
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Old 3rd October 2012, 07:55 PM   #145
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п П - Cyrillic alphabet has symbols similar to Greek.
There's also a swathe of orthodox Christianity stretching from Greece to Russia. Ancient trading links, perhaps.

п is such a universal symbol, at the top of many religions and ideologies, depicting the unity of opposites (body/soul, mind/matter, heaven/hell etc.), I wonder if the Greeks were responsible for associating it with the circle, or if the link is more ancient?
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Old 3rd October 2012, 08:05 PM   #146
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Quote:
Originally Posted by PlasticIsGood View Post
It's common to confuse the equations for circumference and area.
I just remembered that 2πR was the 2 dimensional one. Word association has always helped me.
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Originally Posted by M Gregg View Post

0NLY

C3R741N P30PL3 C4N

R3AD 7H15.



Regards
M. Gregg
smlr t rmvng th vwls. Y cn stll rd t.
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Old 3rd October 2012, 08:37 PM   #147
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I just remembered that 2πR was the 2 dimensional one. Word association has always helped me.
But the 2's in both The only difference is position. I have no difficulty associating a square with an area, so πr seems obvious. 2πr, OTOH, always makes me pause for thought. The linear relationship is not so obvious somehow.

Our heads don't all work the same. Reputedly, a woman grandmaster uses the face-recognition part of her brain to win at chess.
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Old 3rd October 2012, 08:53 PM   #148
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Oops, no wonder you're confused. Sometimes I should read what I type before hitting submit. Especially when I am busy.

Confusez moi.
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Old 3rd October 2012, 11:23 PM   #149
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Quote:
Originally Posted by Cal Weldon View Post
I just remembered that 2πR was the 2 dimensional one. Word association has always helped me.


smlr t rmvng th vwls. Y cn stll rd t.
You may sawp aslo ltetres in wodrs.
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Old 4th October 2012, 06:18 AM   #150
terry j is offline terry j  Australia
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Originally Posted by PlasticIsGood View Post
It took so long to find on this Windows 7 machine. I was mortified to find the top bar has lost its wiggle. What happened to extended ascii?

It's quite an instructive problem. The relationship between radius and circumference is linear, so simple superposition applies. Counterintuitive perhaps because our conception of the size of a circle is more related to area than to radius or circumference.
yep, it's a good one to win a beer at the pub! tho even if you showed them that maths..maybe it has to be an upscale bar?

I reckon...tho of course your thoughts could be the correct one, we are skewed in this prob by say looking at the 400 m track at the olympics? They start 'quite a bit apart' tho exactly the same distance to the finish line. So, 'if there is THAT much difference in a stadium, how much more around the world?' (or to reaaallly blow you mind, the entire universe!)

It pops up sometimes in the normal view of the world. "I measured the difference in my car going around australia clockwise, it is *that* much longer because I am on the outside of the road than if I went counterclockwise''.

Nope.

Dunno why, but this one seems to give me inordinate pleasure.
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