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.
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.
Regards
M. Gregg
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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?
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.
But the 2's in both
The only difference is position. I have no difficulty associating a square with an area, so πr² 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.
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.
Answer to mirror problem, I think...
1. As you look into a mirror, you see the top of your head at the top of the reflection, bottom of face at the bottom of the image, right side of face to the right of the image, and left to the left. The process of reflection is the same in all directions.
2. In order to compare the reflection with the original reflected object (your face in this case), the object or the image must be flipped through 180 degrees. This is how the inversion happens.
3. You choose the axis of flip. The vertical axis is strongly preferred, but you could equally correctly decide that the image is upside-down.
Perhaps it's Descartes' fault for trivialising the difference between up and down, and left to right. It's common to think the mirror problem is about having two eyes, but actually, like storks and babies, there is a common cause: gravity. The real vertical axis is fundamentally different from the horizontals.
I wonder how mirror writing seems in Chinese?
1. As you look into a mirror, you see the top of your head at the top of the reflection, bottom of face at the bottom of the image, right side of face to the right of the image, and left to the left. The process of reflection is the same in all directions.
2. In order to compare the reflection with the original reflected object (your face in this case), the object or the image must be flipped through 180 degrees. This is how the inversion happens.
3. You choose the axis of flip. The vertical axis is strongly preferred, but you could equally correctly decide that the image is upside-down.
Perhaps it's Descartes' fault for trivialising the difference between up and down, and left to right. It's common to think the mirror problem is about having two eyes, but actually, like storks and babies, there is a common cause: gravity. The real vertical axis is fundamentally different from the horizontals.
I wonder how mirror writing seems in Chinese?
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