What Color is the Bear's Snowball Adventure?

  • Context: High School 
  • Thread starter Thread starter Icebreaker
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Discussion Overview

The discussion revolves around a thought experiment involving a bear that walks in a specific pattern and returns to its starting point. Participants explore the implications of this scenario, particularly focusing on the geographical and mathematical reasoning behind the bear's location and color. The conversation touches on concepts related to spherical geometry and the nature of the Earth's shape.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that the bear is white because it is at the North Pole, where polar bears are found.
  • Others question the assumption that the bear must be at the North Pole, asking for clarification on why it is located there.
  • A participant suggests that the spherical nature of the Earth allows for the described path to return to the starting point without reaching the equator.
  • Another participant mentions that there are multiple solutions to the problem, referencing a previous discussion titled "mr. fubini."
  • Some argue that it is possible to return to the starting point without going to the equator, while others express confusion about how this is possible.
  • One participant highlights that there are infinite positions where the described trip can start, but only one is at the North Pole.
  • Another participant emphasizes the distinction between having two right angles versus three in the context of the problem.

Areas of Agreement / Disagreement

Participants express differing views on the location of the bear and the implications of the path taken. There is no consensus on the necessity of the equator in the solution, and multiple competing interpretations of the problem remain unresolved.

Contextual Notes

Some participants express confusion regarding the specific distances mentioned and the geometric implications of the bear's journey. The discussion includes assumptions about the Earth's shape and the nature of geographical coordinates.

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?
 
Mathematics news on Phys.org
Same color as this reply
 
Yup. Why is that?
 
b coz he is at the north pole. and all bear that naturally found in north pole are white.
 
No, why is he found at the north pole?
 
No, why is he found at the north pole?

See my bad MS Paint drawing.
 

Attachments

bah. humbug.
 
Icebreaker said:
No, why is he found at the north pole?


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.
 
and also the longitude of the Earth meet and one poin instead of always pararel like it's latitude.
 
  • #10
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
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
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
i don't 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 don't think so...
 
  • #14
take my word for it, you don't 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 doesn't 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 doesn't 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 that's not what the question asks, it doesn't 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
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
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
actually you can get an infinite amount of solution, without resorting to south-pole-ness. its all in the topic called mr fubini
 

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