Paradromic rings are shapes created by cutting a Möbius strip across its width. This CLI can be used for computing their basic structural properties.
The main goal of the project was to explore Scheme's capabilities as a general purpose programming language. It's implemented in R5RS Scheme and uses SRFI-28 for string formatting.
The idea for a subject was inspired by Dr Tadashi Tokieda's course Topology & Geometry.
Some surprising properties show up when dissecting Möbius strips and similar structures.
A mathematician confided
That a Mobius band is one-sided,
And you'll get quite a laugh,
If you cut one in half,
For it stays in one piece when divided.
When the strip is dissected off-center instead, the result may seem even stranger:
Let's use the CLI to verify what we've just seen!
Let L and W denote the initial length and width of the strip, respecitively.
Enter the number of initial half-twists (or 'q' to quit) : 1
Enter D>=2 to mark the line 1/D along which the strip will be dissected (or 'q' to quit) : 2
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When dissecting a strip with 1 half-twist 1/2 way across its width, you get a single connected strip which is 2 times longer than the original one:
Length: 2L
Width: W/2
Number of half-twists: 4
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Let L and W denote the initial length and width of the strip, respecitively.
Enter the number of initial half-twists (or 'q' to quit) : 1
Enter D>=2 to mark the line 1/D along which the strip will be dissected (or 'q' to quit) : 3
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When dissecting a strip with 1 half-twist 1/3 way across its width, you get two linked strips, one of which is 2 times longer than the other:
Strip #1
Length: 2L
Width: W/3
Number of half-twists: 4
Strip #2
Length: L
Width: W/3
Number of half-twists: 1
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Let L and W denote the initial length and width of the strip, respecitively.
Enter the number of initial half-twists (or 'q' to quit) : q
Goodbye!
Basic santity check:
Enter the number of initial half-twists (or 'q' to quit) : 0
Enter D>=2 to mark the line 1/D along which the strip will be dissected (or 'q' to quit) : 2
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When dissecting an untwisted strip 1/2 way across its width, you get two disconnected strips of the same length:
Strip #1
Length: L
Width: W/2
Number of half-twists: 0
Strip #2
Length: L
Width: W/2
Number of half-twists: 0
Basic insanity check:
Enter the number of initial half-twists (or 'q' to quit) : 101
Enter D>=2 to mark the line 1/D along which the strip will be dissected (or 'q' to quit) : 7
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When dissecting a strip with 101 half-twists 1/7 way across its width, you get two linked strips, one of which is 2 times longer than the other:
Strip #1
Length: 2L
Width: W/7
Number of half-twists: 204
Strip #2
Length: L
Width: 5W/7
Number of half-twists: 101
Original image sources:
Compile and run with CHICKEN Scheme:
csc main.scm
./mainOr interpret without compilation:
csi main.scm