__ __ () _ _ __ __ _ _ __ __ ___ ___ _ ___ | \/ |--| '(| =| | \| |/o \ " /|_/ O | O )|/( _| |_\__/_|__|_|_|__| |_|\__|_/\_|_|___|__/|_\_\ |___) __ ___ ,___ () () __ __ ___ ____ /o \ ( _| _/.--.--. (__) /o \| O )_ _| |_/\_|___) \__\|__|__| |_/\_|_\_\/__\
Mathscii -------- -- Impossibles Three-Pronged, One-Slot Widgets _____________________ / __________________() / /|_________________ / /_/________________() /______________________ |_____________________() ____________________ /___________________() | ___________________ | | |_______________() | |/_________________ |___________________() mn ____ /\ \ Moebius Triangle / \ \ / \ \ / \ \ / /\ \ \ / / \ \ \ / / \ \ \ / / / \ \ \ / / / \ \ \ / / /---------' \ / / /_______________\ \ / / \/_____________________/ -- Fourth Dimensionals Hypercube (2-dimensional representation of a 3-dimensional cross-section of a 4-dimensional cube) +___________+ /:\ ,:\ / : \ , : \ / : \ , : \ / : +-----------+ +....:../:...+ : /| |\ +./.:...`...+ / | | \ ,`/ : :` ,`/ | | \ /`. : : ` /` | | , +-----------+ ` | |, | `+...:,.|...`+ +...|...,'...+ | / \ | , ` | / \ | , ` | / \|, `|/ mn, 7/97 +___________+ I read a story once about a genie who comes out of a Klein bottle. A Klein bottle is a bottle which twists through four-dimensional space (oh, yes, here we go again!) to connect to the "inside" of the bottle without actually making a hole as this picture suggests. The interesting feature of this bottle is that it has no inside or outside, just like a mobius strip has no topside or bottomside. In fact, if you slice the bottle in half, you end up with two separate mobius strips. ,-"~"-. / ._. \ : / \ : ! ! : ! ; ! ; ; / \ / / / \/ / / /`/ / / /\ | .`-' | | .'.' | | : : | | ..: :.. | |.' .' `. '.| `\ ' ` /' `--___--' mn If I were a genie, I would definitely live "inside" one of these! -- Fractals /\ /__\ /\ /\ Sierpinsky Gasket /__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\/__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\ /__\/__\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\/__\/__\/__\/__\/__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\ /__\/__\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\/__\/__\ /__\/__\/__\/__\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\ /__\/__\ /__\/__\ /__\/__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\ Cantor Dust ____________________________________________________________________ | | | | |____________________________________________________________________| ______________________ ______________________ | | | | |______________________| |______________________| _______ _______ _______ _______ |_______| |_______| |_______| |_______| === === === === === === === === - - - - - - - - - - - - - - - - " " " " " " " " " " " " " " " " -- mnaylor@math.fsu.edu /\ "Abacabadabacaba!" /\ / \ /\ /\ / \ /\ / \ /\ / \ /\ /\/ \/\/ \/\/ \/\/ \/\/ \/\/ \/\/ \/\ (What do you suppose "abacabadabacaba" means?) -- Miscii Mathscii __ __ /\ \ Moebius Strip /\ \ Moebius Strip / /\ \ (1/2 twist) / /\ \ (1 & 1/2 twists) / /__\ \ / /__\_\ \/____\/ \/_____/
Back to Ascii Gallery