gandalf@hogpd.UUCP (gandalf ) (11/29/83)
V'z abg fher vs guvf fbyhgvba vf evtug fvapr V pna'g cebir vg, ohg: Fgneg ng gur ohevny fvgr naq jnyx unys jnl gb gur cnyz gerr. Znxr n 90 qrterr ghea gb lbhe yrsg naq jnyx gur fnzr qvfgnapr. QVT. Vs guvf qbrfa'g jbex, tvir hc, ynl onpx, naq fbnx hc fbzr enlf. Fbyhgvba ol tencu cncre bayl (naq crapvy). Zbagl ubtcq!tnaqnys
waf0116@ritcv.UUCP (William A. Fuss) (11/06/85)
>This is known (to me, my friends, teachers, and father) as the >infamous 'PIRATE PROBLEM'. It goes something like this... >blah, blah, blah... >A group of pirates in a ship land on an island (shape is irrelavent; >landmark the same distance that they each walked from the boat. When they >reach these new positions, they decide that they will bury the treasure >on the midpoint of the line segment that their positions now represent. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ KEY PHRASE: MIDPOINT OF THE LINE SEGMENT (OF THEIR CURRENT POSITIONS!) >PROVE (ie formal geometric proof) that regardless of where they land on >the island, provided that there is no earthquake (causing the landmarks >to move...), they will bury the treasure in EXACTLY the same place. >Erik Bailey >First off, we must note that a rotation by 90 degress takes a vector (p1,p2) to >(-/+p2, +/-p1). note that the first is minus-plus, and the second is >plus-minus. You take the top or bottom signs depending on whether you turn to >the left or the right. > etc... and (MAGICALLY) the answer is... > ((+/- y + a +/- (b-y)) / 2, (-/+ x + b -/+ (a-x)) / 2) > = ((+/- y + a +/- b -/+ y) / 2, (-/+ x + b -/+ a +/- x) / 2) > > ((a +/- b) / 2, (b -/+ a) / 2) >/Bernie where i went to school, there was only one midpoint given one segment. Of course they will bury the treasure at at the same point if >bury the treasure >on the midpoint of the line segment that their positions now represent. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ If you have any questions, look up the definition of MIDPOINT in any High School Geometry book :-) dr. billfuss -------------------------------------------- "Smile, the world may never know!" . . \_/