__ __ () _ _ __ __ _ _ __ __ ___ ___ _ ___
| \/ |--| '(| =| | \| |/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)
/ /__\ \ / /__\_\
\/____\/ \/_____/
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