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Joshua Quinn
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I have this strange fascination with impossible objects: 2-D pictures that seem to represent 3-D objects, but that couldn't actually exist in three dimensions. The sort of thing found in optical illusion books and usually associated with M.C. Escher.

I'm even more fascinated by the idea of taking these objects and, against all alleged possibility, actually constructing them in three dimensions. I've seen a number of such models over the years, but almost all of them suffered from the same problem: they only looked "right" when viewed from one specific angle, while standing perfectly still, with one eye closed to eliminate depth perception. (This is usually because of some surface, X, that appears to be in front of some other surface, Y, but is actually behind it, with a section of Y cut away to make it look like X is in front.)

Even the ones built by Jerry Andrus, the acknowledged master of impossible object construction, exhibits this property, which almost negates the point of building the things in 3-D in the first place.

So a couple years ago I sat down and designed and built one that overcame that problem. It's a 3-D realization of the figure known as the Penrose Square, pictured below. It's really 3-D, and really looks like it should from any angle, with both eyes open. I can't explain in words how it works, but if anyone would like to make their own out of cardboard and scotch tape, let me know and I'll send you a PDF file with the "plans."

Is anyone else into this bizarre area of illusion/math/art/strangeness?


Click here to view attached image.
Every problem contains the seeds of its own solution. Unfortunately every problem also contains the seeds of an infinite number of non-solutions, so that first part really isn't super helpful.
John Smetana
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I love this sort of thing Quinn and would certainly appreciate a copy of your file. Thanks for your generosity.

Best thoughts,
John Smetana
Jonathan Townsend
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Hello Quinn,

me too please... Smile

Jonathan all the coins I've dropped here
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Quinn, I'd also be interested in your generous offer.

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You may find the following very interesting.
It's a link from Bangor University's (Wales, UK) infomatics department.
Examples from the sculptor John Robinson. These are 3d representations of optical illusions that actually exist and have been built by the entrance to the department.
It is very weird walking around them and trying to figure out how they've been built. Fascinating. The link is:

James Peters
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Yes, please!
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Profile of robsigns
Check out Ian Rowland's website.
He's got a whole host of impossible objects he created with cards, etc.
G. LaBarre
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This PDF of a Penrose Square sounds like something that would make a great picture frame. Please send me a copy.
Glen Alan - "The HOW in your Magic should be Secondary to the WOW in your Magic."
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Michael Miller
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As a kid, I loved mathematics, and got interested in topology - the study of surfaces. I recall reading about a Kline Bottle, which is a 3 dimensional version of a moebius strip. The old Time-Life series of books on sciences had a beautiful photograph of a model of a Kline Bottle, in the volume on mathematics.
a/k/a Mike Miller
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Michael Miller
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IAN ROWLAND does a fantastic linking square in front od the public, if anyones has tips on it that would be very helpful.
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That looks pretty cool.....
"Everything should be made as simple as possible, but no simpler." (Einstein)...
Parson Smith
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As a kid, I too got interested in topology.
one of the interesting things that I learned was how to remove your vest without removing your coat.
Here kitty, kitty,kitty. Smile
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I like to use moebius strips with kids. if you cut it in half on its length you will get one long loop twice the size. I take a meobius and give them a normal circle and go from there.

(I would suggest not really little kids)

We go through life backwards. The past is visible and the future is cloudy, it seems we are walking backwards.-- Terry Pratchet
Parson Smith
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It has been a long time since I played with moebius strips.
Thanks for reminding me.
Here kitty, kitty,kitty. Smile
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Profile of GarySumpter - id love to see the file Smile
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