How to fit three circles into a ball?
June 21, 2017 7:29 PM Subscribe
How do you cut notches into three discs and fit them together so they describe a sphere? Can they remain intact, or must one of them be cut in half?
The artist Robert Wechsler cut notches in coins and made them into larger geometric forms, as shown here in his portfolio. Some of them are simple, while other contain dozens and dozens of coins.
I am mostly curious about one form where he combines three coins -- here, three pound coins -- into a sphere.
I understand how to notch two flat circles so they fit together at a right angle, but can a third one be added without actually cutting out its entire middle (and then, presumably, soldering them all together)?
HOW DID HE DO IT?!
The artist Robert Wechsler cut notches in coins and made them into larger geometric forms, as shown here in his portfolio. Some of them are simple, while other contain dozens and dozens of coins.
I am mostly curious about one form where he combines three coins -- here, three pound coins -- into a sphere.
I understand how to notch two flat circles so they fit together at a right angle, but can a third one be added without actually cutting out its entire middle (and then, presumably, soldering them all together)?
HOW DID HE DO IT?!
Best answer: It appears that the coin facing us in the linked image is in fact cut in half, horizontally.
posted by so fucking future at 7:40 PM on June 21, 2017 [1 favorite]
posted by so fucking future at 7:40 PM on June 21, 2017 [1 favorite]
You can't see all sides of the sphere. I imagine that that is important. Look at the coin with "TAMEN" on the rim. Imagine sliding that up and away from you and think about how the coins must be cut to make that happen. It should be a simple matter to cut the remaining two coins to fit. IOW - don't assume symmetry where none is required.
posted by It's Never Lurgi at 7:41 PM on June 21, 2017 [1 favorite]
posted by It's Never Lurgi at 7:41 PM on June 21, 2017 [1 favorite]
Best answer: To my eye, it's a little easier to see what's going on in this image, where the same thing is done with quarters. At least one of the edges doesn't line up so well, suggesting that one is actually in two pieces.
posted by supercres at 8:28 PM on June 21, 2017 [4 favorites]
posted by supercres at 8:28 PM on June 21, 2017 [4 favorites]
Best answer: Yeah, apologies for the crummy sketch, but this is how I think the quarters are fit together: http://imgur.com/a/7B3u8
I can't think of a way to do it without cutting one.
posted by traveler_ at 8:49 PM on June 21, 2017 [3 favorites]
I can't think of a way to do it without cutting one.
posted by traveler_ at 8:49 PM on June 21, 2017 [3 favorites]
I am pretty sure the following cuts will work. Think of the first one as the equator, and then slide the other two in, one from the top, one from the bottom. It won't hold itself together, thus the glue. (No guarantees this is the pattern the artist used.)
http://imgur.com/a/4AwIn
posted by ktkt at 8:59 PM on June 21, 2017 [3 favorites]
http://imgur.com/a/4AwIn
posted by ktkt at 8:59 PM on June 21, 2017 [3 favorites]
On second look, it is definitely not how the artist in the OP did it.
posted by ktkt at 9:00 PM on June 21, 2017 [2 favorites]
posted by ktkt at 9:00 PM on June 21, 2017 [2 favorites]
To my eye, it's a little easier to see what's going on in this image, where the same thing is done with quarters. At least one of the edges doesn't line up so well, suggesting that one is actually in two pieces.
The construction on that one isn't obviously the same, though. On the pound-coin one, none of the visible ridges on the outside go more than 180° around; but on the quarter one, the "equator" quarter goes at least 270° around. (Of course, as noted by It's Never Lurgi , the back of the pound-coin linkage might look different from the front.)
posted by Johnny Assay at 4:26 AM on June 22, 2017 [1 favorite]
The construction on that one isn't obviously the same, though. On the pound-coin one, none of the visible ridges on the outside go more than 180° around; but on the quarter one, the "equator" quarter goes at least 270° around. (Of course, as noted by It's Never Lurgi , the back of the pound-coin linkage might look different from the front.)
posted by Johnny Assay at 4:26 AM on June 22, 2017 [1 favorite]
I think this will work:
On one disk, cut slots along a diameter 1/3 down from the top, 1/3 up from the bottom.
On the other two, cut slots 2/3 of the diameter. Fit these on the first disk, one down from the top, one up from the bottom.
I'll leave it to you to figure how wide the slots have to be, and what bevels they have to have, to fit snugly and stay at the preferred angle.
posted by SemiSalt at 6:39 AM on June 22, 2017
On one disk, cut slots along a diameter 1/3 down from the top, 1/3 up from the bottom.
On the other two, cut slots 2/3 of the diameter. Fit these on the first disk, one down from the top, one up from the bottom.
I'll leave it to you to figure how wide the slots have to be, and what bevels they have to have, to fit snugly and stay at the preferred angle.
posted by SemiSalt at 6:39 AM on June 22, 2017
Pictures.
Discs with cuts emphasized in ink here.
"Sphere" here. It would fall down flat if I tried to put it on a flat surface. Hence the glass. Hard to photograph, too. I should have used different colors of paper.
posted by SemiSalt at 8:51 AM on June 22, 2017
Discs with cuts emphasized in ink here.
"Sphere" here. It would fall down flat if I tried to put it on a flat surface. Hence the glass. Hard to photograph, too. I should have used different colors of paper.
posted by SemiSalt at 8:51 AM on June 22, 2017
And on third thought, I retract my answer. On my first piece, you can't make the four cuts all the way into the middle cube, or it all falls apart. But you also can't make them a bit shorter, as that forces wider cuts on the other two (wider than the width of the coin, that is), which will leave gaps when you try to put it all together. No more 3-d geometry late at night for me.
I am mostly convinced it can't be done without some extreme cleverness. We need to cut out 6 "radial segments" total (four along the equator, one pointing to the north pole and one pointing to the south pole, if you think of Earth for visualizing), not including the middle cube (with side length the width of the coin). We also need the middle cube cut out on two of the coins. This is all because that's how much overlap we have, so we need to get rid of the excess for everything to fit.
But this appears impossible. On the coins with the middle cube cut out, we can only cut the radial strip in one of the compass directions, or the coin will fall into two or more pieces. This leaves four radial strips to cut from the third coin, but this again falls apart because the center cube doesn't stay attached to anything when you cut in all four compass directions. (Here's my sketch from before -- http://imgur.com/a/4AwIn. Due to lack of sleep, I didn't notice the first coin falls apart.)
Plausibly there is some way to cut the radial segments out partly from one coin and partly from another, but I am not seeing a path to the end result.
posted by ktkt at 2:51 PM on June 22, 2017 [1 favorite]
I am mostly convinced it can't be done without some extreme cleverness. We need to cut out 6 "radial segments" total (four along the equator, one pointing to the north pole and one pointing to the south pole, if you think of Earth for visualizing), not including the middle cube (with side length the width of the coin). We also need the middle cube cut out on two of the coins. This is all because that's how much overlap we have, so we need to get rid of the excess for everything to fit.
But this appears impossible. On the coins with the middle cube cut out, we can only cut the radial strip in one of the compass directions, or the coin will fall into two or more pieces. This leaves four radial strips to cut from the third coin, but this again falls apart because the center cube doesn't stay attached to anything when you cut in all four compass directions. (Here's my sketch from before -- http://imgur.com/a/4AwIn. Due to lack of sleep, I didn't notice the first coin falls apart.)
Plausibly there is some way to cut the radial segments out partly from one coin and partly from another, but I am not seeing a path to the end result.
posted by ktkt at 2:51 PM on June 22, 2017 [1 favorite]
That doesn't replicate the one shown in the question, though, SemiSalt – basically yours are all running longitudinally, while the example has two longitudinal and one equatorial.
posted by Lexica at 3:25 PM on June 22, 2017
posted by Lexica at 3:25 PM on June 22, 2017
Best answer: Ok, on further thought I think it's possible. Here's one way to do it:
http://imgur.com/a/BfDsH
It really takes advantage of the coins' thicknesses and some tricky precision cutting.
posted by traveler_ at 7:44 PM on June 22, 2017 [13 favorites]
http://imgur.com/a/BfDsH
It really takes advantage of the coins' thicknesses and some tricky precision cutting.
posted by traveler_ at 7:44 PM on June 22, 2017 [13 favorites]
Traveler's description is how I thought it would work from the original image.
posted by blurker at 12:47 PM on June 23, 2017
posted by blurker at 12:47 PM on June 23, 2017
Response by poster: The artist himself answered my email, and very cheerfully said that he'd cut one of the coins clean through. So supercres, traveler_, and so fucking future -- you were all right -- and traveler_, it looks like you have done the artist himself one better!
As a bonus factoid, he told me that "I don’t solder the coins. they are all press-fit together. I find that glues and solder all alter the color of the coins, and the unique patina and wear of each coin is something I try to preserve." Not sure how that would work with the one coin that's cut clean in half, but now I have some ideas to play with.
Thanks, everyone!
posted by wenestvedt at 8:12 AM on June 28, 2017 [1 favorite]
As a bonus factoid, he told me that "I don’t solder the coins. they are all press-fit together. I find that glues and solder all alter the color of the coins, and the unique patina and wear of each coin is something I try to preserve." Not sure how that would work with the one coin that's cut clean in half, but now I have some ideas to play with.
Thanks, everyone!
posted by wenestvedt at 8:12 AM on June 28, 2017 [1 favorite]
This thread is closed to new comments.
posted by wenestvedt at 7:30 PM on June 21, 2017