There is a bear

[Georgia]

Hey Toshi, you stole my thunder. I was just about to answer it.

Hey Kooper,
you stole my move! I was about to answer it ............... NOT~~ heeheehee

[Luis Ko]

i think this is not a good question and, i don't think the skin color of polar bear is black..

http://zh.wikipedia.org/wiki/%E5%8C%97% ... 5%E7%86%8A

http://blog.sina.com.tw/kisspuppy/artic ... ryid=12067

it's really surprising to see the color of skin of polar bear is black on this picture.. to see is to believe i mean. i thought it should be impossible to be real black but beige or brown, or other dark hues, because black is really hard to be covered by any other color especially white, not to mention it's said the hair of polar bear is colorless, or translucent.. ok. maybe that's why polar bear's black skin can be totally hided.

as to the question about north pole or south pole, i am wondering if the answers could be only mathematically(theoretically) correct, on a paper(map) i mean. i really doubt we will really walk a circle under the guidance of compass either going in the direction of east or west at the poles area. it's really hard to imagine for me haa.

[Georgia]

can be totally hided.

as to the question about north pole or south pole, i am wondering if the answers could be only mathematically(theoretically) correct, on a paper(map) i mean. i really doubt we will really walk a circle under the guidance of compass either going in the direction of east or west at the poles area. it's really hard to imagine for me haa.

1. hidden
2. for me to imagine

[toshi]

i think this is not a good question and, i don't think the skin color of polar bear is black..

http://zh.wikipedia.org/wiki/%E5%8C%97% ... 5%E7%86%8A

http://blog.sina.com.tw/kisspuppy/artic ... ryid=12067

it's really surprising to see the color of skin of polar bear is black on this picture.. to see is to believe i mean. i thought it should be impossible to be real black but beige or brown, or other dark hues, because black is really hard to be covered by any other color especially white, not to mention it's said the hair of polar bear is colorless, or translucent.. ok. maybe that's why polar bear's black skin can be totally hided.

as to the question about north pole or south pole, i am wondering if the answers could be only mathematically(theoretically) correct, on a paper(map) i mean. i really doubt we will really walk a circle under the guidance of compass either going in the direction of east or west at the poles area. it's really hard to imagine for me haa.

Salt is a kind of transparent cubic crystal. However the salt we have (精鹽) in our daily life looks in white. Maybe in micro scale, it looks transparent, while in macro scale, it looks in while.
Sorry maybe it's not a good example. Hmm...
Oho...now I have a question...白頭髮...is it really white? or transparent?
Let's see!!!

You are right...it's just mathematical puzzle.
First of all, the Earth is not spherically symmetric.
It's more like an orange. (像橘子一樣有一點扁平)
And its surface is not so smooth.
So, surely, the puzzle is just for "fun". ^_^
Please take it easy!

[Kooper]

========================================================================================
When I got the answer, I checked the answer in the book. It's the same.
However, later on, when I thought about the question again, I found other solution.

Me, too. In fact, there are countless set of points on the surface of earth which fit the description of the question. Here are some of them:

1. Any point ten km north of the latitude whose perimeter is 5km in the southern hemisphere of the Earth.
2. Any point ten km north of the latitude whose perimeter is 10/3 km in the southern hemisphere of the Earth.
3. Any point ten km north of the latitude whose perimeter is 2.5 km in the southern hemisphere of the Earth.
4 and the like....

[Rock]

You are right...it's just mathematical puzzle.
First of all, the Earth is not spherically symmetric.
It's more like an orange. (像橘子一樣有一點扁平)

But, somebody doesn't think the earth is orange-shaped mathematically; they take it as a pear.

The Earth is a somewhat pear shaped ellipsoid, with a slightly larger southern hemisphere than northern hemisphere.
http://www.mckinleyville.com/cart/cabinet/cab_math.html

[toshi]

You are right...it's just mathematical puzzle.
First of all, the Earth is not spherically symmetric.
It's more like an orange. (像橘子一樣有一點扁平)

But, somebody doesn't think the earth is orange-shaped mathematically; they take it as a pear.

The Earth is a somewhat pear shaped ellipsoid, with a slightly larger southern hemisphere than northern hemisphere.
http://www.mckinleyville.com/cart/cabinet/cab_math.html

Thank you for your information! ^_^

[toshi]

========================================================================================
When I got the answer, I checked the answer in the book. It's the same.
However, later on, when I thought about the question again, I found other solution.

Me, too. In fact, there are countless set of points on the surface of earth which fit the description of the question. Here are some of them:

1. Any point ten km north of the latitude whose perimeter is 5km in the southern half sphere of the Earth.
2. Any point ten km north of the latitude whose perimeter is 10/3 km in the southern half sphere of the Earth.
3. Any point ten km north of the latitude whose perimeter is 2.5 km in the southern half sphere of the Earth.
4 and the like....

I think Kooper got the "extended" answer too.

The answer : there are infinite circles, any point in these certain circles is the answer!

Let me explain it more clearly.

Untitled-7 copy.jpg

Let's draw a circle centered at the South Pole with 5 km perimeter.
This circle has a radius 5/(2π) km.
Then draw the second circle with （10 + 5/(2π)）km radius.

Start with any point of the second circle to the south for 10 km.
Then we arrive at the first circle.

Then walk to the east for 10 km.
That means we will walk along the first circle（radius 5/(2π) km）. And because 5 km is its perimeter, we will just walk 2 circles.

So, then walk to the north for 10 km, will just return to the starting point.

Similarly, draw a circle centered at the South Pole with 10/3 km perimeter.
This circle has a radius 5/(3π) km.
Then draw the second circle with （10 + 5/(3π)）km radius.

Start with any point of the second circle to the south for 10 km.
Then we arrive at the first circle.

Then walk to the east for 10 km.
That means we will walk along the first circle（radius 5/(3π) km）. And because 10/3 km is its perimeter, we will just walk 3 circles.

So, then walk to the north for 10 km, will just return to the starting point.
========================================================================================

Untitled-10.jpg

So, there are infinite solutions. Any point in these infinite circles is the answer!
The radius of these circles should be like this 10 + 10/ (2 x N xπ) km.
Where N can be 1, 2, 3, 4, 5, 6, 7,…etc. Any of positive integers.

If my explaination is not clear enough, please let me know!
Thank you for your joining this puzzle!
Is it fun? ^_^

[Georgia]

But, somebody doesn't think the earth is orange-shaped mathematically; they take it as a pear.
The Earth is a somewhat pear shaped ellipsoid, with a slightly larger southern hemisphere than northern hemisphere.
http://www.mckinleyville.com/cart/cabinet/cab_math.html

Ooooohhh...................
Probably there is another force of gravity in the Solar System or the universe...... that's why it's pulling the lower half of the Earth down.....
of course another thought, ummm... maybe the Earth needs more exercise to keep in shape haha... Rock you should teach the Earth to do some weight-lifting....

[Georgia]

Salt is a kind of transparent cubic crystal. However the salt we have (精鹽) in our daily life looks in white. Maybe in micro scale, it looks transparent, while in macro scale, it looks in while.
Sorry maybe it's not a good example. Hmm...
Oho...now I have a question...白頭髮...is it really white? or transparent?
Let's see!!!

Aahhh... I get it ~~
It's just like when a big crowd of black crows flock together ............
The color on the whole will be......................... very black !

[toshi]

But, somebody doesn't think the earth is orange-shaped mathematically; they take it as a pear.
The Earth is a somewhat pear shaped ellipsoid, with a slightly larger southern hemisphere than northern hemisphere.
http://www.mckinleyville.com/cart/cabinet/cab_math.html

Ooooohhh...................
Probably there is another force of gravity in the Solar System or the universe...... that's why it's pulling the lower half of the Earth down.....
of course another thought, ummm... maybe the Earth needs more exercise to keep in shape haha... Rock you should teach the Earth to do some weight-lifting....

The earth doesn't have to be so symmetric.

Also you know according to the continental drift theory, the land is drifting.
The MidOcean Ridges is growing up. It causes the geomagnetic field reversal.
Our earth is changing all the time, not only in local scale but also in large scale too!

http://en.wikipedia.org/wiki/Continental_drift
http://en.wikipedia.org/wiki/Geomagnetic_reversal

[technobabel]

There is a bear, and there is a bear market.
Therefore, let's take the imaginary Bi-Polar Express to Antarctica for an adventure of not-too-different kind.
Coincidentally like any expedition, the point is to get back to where we once belong.