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You can't uniquely identify each point on its surface using only two dimensions Yes you can. Run a sharpie along the bottom edge of the paper so that it bleeds
by dfranke 15y ago
You can't uniquely identify each point on its surface using only two dimensions
Yes you can. Run a sharpie along the bottom edge of the paper so that it bleeds onto both sides of the paper. Now tape the ends of the strip together with a half twist to make a Möbius strip. Place a point anywhere on the strip. Draw a line through that point such that the line meets both edges of the strip at a right angle. Measure the distance along that line between your point and the darkened edge; call this x. Now, hold the Möbius strip in your left hand so that you're pinching it by the tape. With your right hand, run your finger along the strip, starting from the tape and moving to the right. Measure how far you have to move your finger in order to reach the line you drew; this could require up to two loops around the strip. Call this distance y. The tuple (x,y) uniquely identifies your point.
- grannyg00se 15y agoWow. It took me a while to figure out what you were saying, but it was well said and I eventually got it. Thanks.
- kd0amg 15y agoFor the record, we use a similar trick on sphere-like surfaces, as latitude and longitude.
- dfranke 15y agoOh dear, I just realized I dropped a sentence while I was composing this comment and now it's too late to edit. The beginning of it should read, "Yes you can. Cut out a long rectangular strip of paper. Run a sharpie..."
- bmm6o 15y agoAlternately, just realize that the rectangular strip of paper has a natural set of coordinates, and nothing is lost by twisting and taping. You get a discontinuity at the tape, but that's not a problem.