bundy@oasys.UUCP (12/12/85)
We all remember the old first semester calculus question asking what
is the longest board (i.e. 1-dimensional rigid body) that can fit
around a 90 degree turn between two corridors. What is the biggest
two dimensional rigid body that can fit around the turn and can also
slide freely down both corridors:
______________________________
I
I
I
_________________ I
I I
I I
I I
I I
I I
I I
I I
I I
Both corridors are infinite length, width a, and we are interested in
the 2-d rigid body of greatest area that goes around the corner.
Certainly the square of width a fits, but a little thought will reveal
shapes of significantly greater area.
--
Bruce Bundy
{ucbvax,hao,allegra}!nbires!oasys!bundyjankok@zuring.UUCP (Jan Kok) (12/16/85)
In article <167@oasys.UUCP> bundy@oasys.UUCP writes: >. . . . What is the biggest >two dimensional rigid body that can fit around the turn and can also >slide freely down both corridors: > . . . I have seen the problem been posed about 15 years ago by Hammersley in a British journal. The solution method is elementary and I won't spoil it for you. -- jan kok, cwi (afd. nw), amsterdam, nederland UUCP: {seismo, decvax, philabs, okstate, garfield}!mcvax!zuring!jankok --------------------------------------------------------------- " For people who like this sort of things, this is the sort of thing they will like. " (I have seen this quotation attributed to pres. Lincoln, but I can't check this. Perhaps someone can send me the correct source. Do not attribute it to Aldous Huxley, who was himself quoting his whole life.)