# The Bear

1. Mar 25, 2005

### Icebreaker

A bear starts out from a point, walks 1 kilometer due south, then changes its direction and walks 1 kilometer due east, then changes its direction once again and walks 1 kilometer due north, and ends up at the point where he began. What is the color of the bear?

2. Mar 25, 2005

### Jimmy Snyder

3. Mar 26, 2005

### Icebreaker

Yup. Why is that?

4. Mar 26, 2005

### ArielGenesis

b coz he is at the north pole. and all bear that naturally found in north pole are white.

5. Mar 26, 2005

### Icebreaker

No, why is he found at the north pole?

6. Mar 26, 2005

### Berislav

See my bad MS Paint drawing.

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7. Mar 26, 2005

### T@P

bah. humbug.

8. Mar 26, 2005

### ArielGenesis

it is because the shape of the earth is round like a ball. and he is going south,west and north direction instead of backward, leftward and foward direction.

9. Mar 26, 2005

### ArielGenesis

and also the longitude of the earth meet and one poin instead of always pararel like it's latitude.

10. Mar 28, 2005

### T@P

i posted the exact same question only harder not too long ago. it was called mr. fubini. you can look there if you are confused because there is a nother solution

11. Mar 31, 2005

### pattarkutty

it goes like this. we all know that there r no bears in the southpole.
now consider the middle of the north pole, go straight and u will reach the equator, then take a 90 degree turn east and through the equator walk the same distance, now take another 90 degree north and walk the same distance. u will find urself at the starting point. this will form a triangle with sum of angles >180 degrees = 270 degrees.
this contridction happens due to the spherical nature of the earth. so the bear ends up as a polar bear and its white. what still confuses me is ur mentioning of a specific distance of one kilometer!

12. Mar 31, 2005

### T@P

you can do the exact same thing pattarkutty without going all the way down to the equator. you can go straight south for 1 km, east for 1 km and then back north for 1 km and end up back at the north pole. the cool part about all this is that there is another solution - that i find to be the trickiest part.

13. Apr 2, 2005

### pattarkutty

i dont know how u'd reach the same point without reaching the equator. Then it should be possible to draw a triangle with angles 90 degrees with side of any dimension on any part of the sphere. i dont think so...

14. Apr 3, 2005

### T@P

take my word for it, you dont have to go to the equator :)

think about it purely non mathematically and in terms of cardinal directions for a bit:

imagine starting at the north pole. you go south 1 km, so your distance to the north pole is now 1km (on the sphere). by going directly east or west, that distance doesnt change. so go east, then back one km north again. you arrive at the pole again.

it is possible to draw a triangle that has two right angles even if it doesnt go to the equator. your problem i think is that you want it to have 3 right angles. in that case, i agree, you have to go to the equator. but thats not what the question asks, it doesnt ask you to draw a triangle with 3 right angles in it, it asks you to get back to the same point, i.e. only 2 right angles. try it on a globe, and running your hand from the top (measure it) down 1 cm, around 1 cm and up again. if you measure it, then aside from sic figs you should end up back again. really.

15. Apr 4, 2005

### pattarkutty

thanks for that. yeah i had 3 90 degrees in mind. and that was not the question.sure u can have 2 right angles anywhere. thanks.

16. Apr 4, 2005

### Galileo

I think there are an infinite number of positions where you can start such a trip, but only one of them is on the north pole, the other ones are on the south pole where there are no bears.

17. Apr 4, 2005

### T@P

actually you can get an infinite amount of solution, without resorting to south-pole-ness. its all in the topic called mr fubini