tomfi@tekig4.UUCP (Tom Fitzpatrick) (10/21/85)
In article <361@proper.UUCP> judith@proper.UUCP (judith) writes: >The old Polar Bear Problem: You go somewhere, set up a tent, walk a mile >south, walk a mile due west, shoot a bear. Then you drag the bear a mile north >to your tent & have him for dinner. What color is the bear? > >The sequel: (1) From how many points on Earth (assuming it's spherical, etc.) > can you make exactly these moves, i.e., walk 1 mile south, 1 > mile west, 1 mile north, and be back where you started? > > (2) Describe all of them. > >Judith Abrahms >{ucbvax,ihnp4}!dual!proper!judith There are an infinite number of points from which you can make these moves. They all lie on the line of latitude which is exactly one mile north of a latitude line with a circumference of one mile (ie. in walking one mile west, you go through 360 degrees of longitude). The Spitzer
bs@faron.UUCP (Robert D. Silverman) (10/23/85)
> In article <361@proper.UUCP> judith@proper.UUCP (judith) writes: > >The old Polar Bear Problem: You go somewhere, set up a tent, walk a mile > >south, walk a mile due west, shoot a bear. Then you drag the bear a mile north > >to your tent & have him for dinner. What color is the bear? > > > >The sequel: (1) From how many points on Earth (assuming it's spherical, etc.) > > can you make exactly these moves, i.e., walk 1 mile south, 1 > > mile west, 1 mile north, and be back where you started? > > > > (2) Describe all of them. > > > >Judith Abrahms > >{ucbvax,ihnp4}!dual!proper!judith > > There are an infinite number of points from which you can make these moves. They > all lie on the line of latitude which is exactly one mile north of a latitude > line with a circumference of one mile (ie. in walking one mile west, you go > through 360 degrees of longitude). > > The Spitzer You forgot: In walking one mile west you could also walk through 720, 1080, ... etc. degrees, i.e. multiple times around the circle. This means that there are an infinite number of starting latitudes. One is 1 mile due north of a circle that is 1 mile in circumference, another is 1 mile north of a circle 1/2 mile in circumference, 1/3 , 1/4, ... 1/n so you walk n times around a circle whose circumference is 1/n. Bob Silverman (they call me Mr. 9)