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Ancient Puzzle Gets New Lease on 'Geomagical' Life

timothy posted more than 3 years ago | from the what-do-you-call-the-part-above-the-subtext dept.

Math 73

techbeat writes "An ancient mathematical puzzle has found a new lease on life, reports New Scientist. The magic square is the basis for Sudoku, pops up on the back of a turtle in Chinese legend and provides a playful way to introduce children to arithmetic. But all this time it has been concealing a more complex geometrical form, says recreational mathematician Lee Sallows. He recently released dozens of examples of his 'geomagic squares' online. 'To come up with this after thousands of years of study of magic squares is pretty amazing,' blogged author Alex Bellos. Magic squares are used to help create codes for transmitting information and in the design of drug trials so geomagic ones may have real-world uses, says mathematician Peter Cameron. New Scientist has also put up a gallery of the geomagic squares."

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73 comments

I like turtles... (-1)

Anonymous Coward | more than 3 years ago | (#35006368)

comment is in the subject.

Re:I like turtles... (0)

Anonymous Coward | more than 3 years ago | (#35006414)

Especially sea turtles! they stay alive for weeks stored on their backs and provide a supply of fresh meat for yer crew!

Arrr.

Re:I like turtles... (1)

derGoldstein (1494129) | more than 3 years ago | (#35006528)

Someone's going to say it, so it might as well be me: It's turtles all the way down!

Oh, and I was going to use Italic instead of bold text, but the <i> doesn't seem to work in the new design... or maybe it's just me.

Not exactly a turtle (4, Informative)

jsse (254124) | more than 3 years ago | (#35006372)

It was no ordinary turtle. It is called a dragon turtle which is huge in size with a dragon head: http://www.kunde.org.tw/image3/01-book-032.jpg [kunde.org.tw]

Legend said that it carried strange messages on its shell. The messages looked simple (as you can see in the picture above) but people later found the complex meanings behind them.

This messages are the building blocks of most numerologies in ancient China, including Fengshui and I-Ching.

This is one of the most famous OPA (Out of Place Artifact) in China history.

Re:Not exactly a turtle (1)

Sulphur (1548251) | more than 3 years ago | (#35006432)

It was no ordinary turtle. It is called a dragon turtle which is huge in size with a dragon head: http://www.kunde.org.tw/image3/01-book-032.jpg [kunde.org.tw]

Legend said that it carried strange messages on its shell. The messages looked simple (as you can see in the picture above) but people later found the complex meanings behind them.

This is one of the most famous OPA (Out of Place Artifact) in China history.

If it were a mock turtle, would the messages be wrong mockingly?

Re:Not exactly a turtle (1)

derGoldstein (1494129) | more than 3 years ago | (#35006492)

It was no ordinary turtle. It is called a dragon turtle which is huge in size with a dragon head

Well there's a fat bald guy riding this one [kateysgarden.com], so I can't read what its shell says. Damn it, there's always a fat guy in the way.

Re:Not exactly a turtle (0)

Anonymous Coward | more than 3 years ago | (#35007822)

I don't want to get snappy about this, but Real Men ride the shark

Re:Not exactly a turtle (0)

Anonymous Coward | more than 3 years ago | (#35008672)

Legend said that it carried strange messages on its shell. The messages looked simple (as you can see in the picture above) but people later found the complex meanings behind them.

After spending some time in the bathroom with the message, I cracked it:
"Be sure to drink your Ovaltine."

This layout sucks (-1)

justleavealonemmmkay (1207142) | more than 3 years ago | (#35006422)

the sidebar is hiding the frickin' text. GO BACK to FUCKING BETA

Re:This layout sucks (1)

burisch_research (1095299) | more than 3 years ago | (#35006678)

This is a bug caused by having a long slashdot username. The long username means that the left menubar is extra-wide, and covers the main content pane. I have reported this issue, so maybe we'll get a fix one day.

Re:This layout sucks (0)

Anonymous Coward | more than 3 years ago | (#35006782)

Not just that, you also have to click the link, instead of the entire title bar like we were used to, when we want to expand posts.

Also, what happened to position:fixed on that little expansion bar? That was really useful.
Now we have to [home] if we want to hide / show posts.

Didn't we see this last week? (-1)

Anonymous Coward | more than 3 years ago | (#35006424)

Calling Mr Ono... time to have sex with Mr Swallows.

His writing style is atrocious. (1)

lxs (131946) | more than 3 years ago | (#35006468)

I went to the site to find out what geomagic squares are, but by the time I reached the end of the summary I completely lost interest.

Re:His writing style is atrocious. (2, Insightful)

Anonymous Coward | more than 3 years ago | (#35006876)

I went to the site to find out what geomagic squares are, but by the time I reached the end of the summary I completely lost interest.

Oh no, not his writing style. Fucking idiot - look at his gallery, its actually very clever and not everyone can afford a writing staff to get past the crap filter on morons like you (which I assume is a self-feeding mechanism, as you keep getting spoon fed BS by such filters throughout your life you will only ever know such). Swearing for your benefit in hopes to publicly degrade you while making you stop reading at the first line.

Re:His writing style is atrocious. (1)

mr_gorkajuice (1347383) | more than 3 years ago | (#35008168)

Improving slashdot, step one: disable anonymous comments.

ACs can have great comments (2)

tkprit (8581) | more than 3 years ago | (#35010134)

Some of the best comments I've ever read on /. were by ACs. Just sayin' :)

Re:ACs can have great comments (0)

Anonymous Coward | more than 3 years ago | (#35013700)

It would have been funny if you had posted that anonymously.

Re:His writing style is atrocious. (1)

Ironchew (1069966) | more than 3 years ago | (#35015008)

Improving slashdot, step one: disable anonymous comments.

You know you can set modifiers on AC comments in your preferences, right? -3 is a good setting.

Re:His writing style is atrocious. (0)

Anonymous Coward | more than 3 years ago | (#35016652)

AC's are a very important part of /. There ar emany times a person may wish to comment on a subject but for legal, social, political, employment, sexual reasons may NEED to remain anonymous. I myself am anonymous here as I am a gay, friendless, lawyer who is currently running fro Parliament.

Re:His writing style is atrocious. (1)

2.7182 (819680) | more than 3 years ago | (#35010800)

I read the whole article and found it entirely not terribly original or interesting. Sure, maybe you can make a code from it. I can generate tons of weird combinatorial/geometric widgets that do the same thing.

Re:His writing style is atrocious. (0)

Anonymous Coward | more than 3 years ago | (#35007274)

I found the intro [geomagicsquares.com] quite easy to understand.

It's really a neat idea. I bet there is going to be a Flash/iPhone/Android game using it anytime soon.

Re:His writing style is atrocious. (1)

tkprit (8581) | more than 3 years ago | (#35010256)

Easy to understand, but not exactly... enthusiastic?

A similar site (and they're also promoting a book), prime curios [utm.edu], exudes enthusiasm imo, encourages user input, and I think promotes interest in math. I think the 'geomagical' site could use some editors (which prime curios probably utilizes).

Re:His writing style is atrocious. (0)

Anonymous Coward | more than 3 years ago | (#35011328)

Really? Seemed fine to me; a bit wordy perhaps, but it *is* an excerpt from a book that is likely intended to have a bit of a "popular" feel to it. I found it to be quite readable.

Recreational Mathematician? (2)

jellyfrog (1645619) | more than 3 years ago | (#35006484)

Sounds suspicious. Oh I bet it's 'perfectly safe', but you start out on math and who knows where you'll end up? Smoking crack out of rolled up nonstandard analysis theorems in a gutter in cambridge? It's a gateway drug, I tell ya.

Re:Recreational Mathematician? (1)

derGoldstein (1494129) | more than 3 years ago | (#35006568)

Recreational Mathematics is a form of masochism. It's no different then those guys that whip their own backs or who go to those clubs where everyone wears black leather. It's sick and twisted, but there's nothing we can do about it, since they're technically only hurting themselves.

Re:Recreational Mathematician? (2)

Yvanhoe (564877) | more than 3 years ago | (#35006616)

Yep. On the other hand, programming for fun is a lot more sane.

Recreational Mathematician! (1)

tkprit (8581) | more than 3 years ago | (#35010356)

LOL, thank you! I do the occasional diffy Q just to relax, as well as code 'for fun' (well, I don't get paid anyway).

(Well, I also do diffy Qs keep up skills so I can make sure I stay ahead of my kids, who apparently aren't overly fond of mathematics. If you don't use it, ya LOSE it :D )

New Scientist = odd number fail (1)

wickerprints (1094741) | more than 3 years ago | (#35006522)

Check it out on page 5 of the New Scientist link [newscientist.com]. Apparently, they think 8 is an odd number, and 9 and 11 are not. So much for the "new math."

Re:New Scientist = odd number fail (0)

Anonymous Coward | more than 3 years ago | (#35006558)

Check it out on page 5 of the New Scientist link [newscientist.com]. Apparently, they think 8 is an odd number, and 9 and 11 are not. So much for the "new math."

QFT

Geomagic squares go 3D

In this square, the target is a 3 × 3 × 3 cube. Note that the polyomino size forms the consecutive series of odd numbers "1, 3, 5, 7, 8, 13, 15, 17" while their shapes are derived from a formula for creating magic squares devised by the 19th-century French mathematician Édouard Lucas.

Re:New Scientist = odd number fail (0)

Anonymous Coward | more than 3 years ago | (#35006758)

they let this slide because...well.... the other numbers will tell you, there's something severely weird about 8

Re:New Scientist = odd number fail (0)

Anonymous Coward | more than 3 years ago | (#35007244)

I think it has been that way since seven eight nine.
(or seven ate nine for those who didn't read it outloud)

Re:New Scientist = odd number fail (0)

Anonymous Coward | more than 3 years ago | (#35006584)

If you look at the picture they're right... the shapes are 1, 3, 5, 7, 9, 11, 13, 15, and 17... if only they didn't try to type it out

Re:New Scientist = odd number fail (1)

DarthJohn (1160097) | more than 3 years ago | (#35006620)

Also on that page: 1 + 3 + 5 + ... + 15 + 17 = 3.3^3
wtf?
if I do 1+3+5+7+9+11+13+15+17 I get 81 which is 3^4

Re:New Scientist = odd number fail (2)

wickerprints (1094741) | more than 3 years ago | (#35006792)

By 3.3^3, they mean 3 x 3^3, not (3.3)^3. It's an unfortunate use of the period symbol to denote multiplication because standard keyboards do not have the centered dot symbol.

Re:New Scientist = odd number fail (0)

Anonymous Coward | more than 3 years ago | (#35007158)

Why, then, do they write "3.3^3" when they should be consistent and write either "3^4" or "3.3.3.3"? Seems pretty silly to me. Disclaimer: I did not read TFA.

Re:New Scientist = odd number fail (2)

wickerprints (1094741) | more than 3 years ago | (#35008170)

Ah, because they want to emphasize the fact that the "sum" of the figures in a given row, column, or diagonal is a 3x3x3 cube, and thus the total number of cubic units is three times the sum of a single row/column, or 3 x 3^3, which in turn is the sum of the nine consecutive odd integers from 1 to 17, which form the individual entries of the geomagical square.

Re:New Scientist = odd number fail (1)

tkprit (8581) | more than 3 years ago | (#35010960)

&#183 (and I think even &middot) has worked fine in HTML for years (albeit not on /. for some reason). I use parentheses, dots, and carets myself, (or enter it in http://www.wolframalpha.com/ [wolframalpha.com] and copy the pretty mathematically-correct image), but I'm not New Scientist.

Re:New Scientist = odd number fail (2)

eyeoftheidol (651095) | more than 3 years ago | (#35006816)

Yes, but they want to express it as 3.3^3 to bring out the relationship with a 3.3 shape (ie, a square). (You are reading "3.3" as "3 multiplied by 3", aren't you?)

Re:New Scientist = odd number fail (1)

DarthJohn (1160097) | more than 3 years ago | (#35007222)

I read it as "three and three tenths," didn't know there was another way to read that. Thanks for the tip.

Re:New Scientist = odd number fail (1)

techbeat (714650) | more than 3 years ago | (#35019648)

Thanks very much for pointing this out. I edited the story for New Scientist and it's fixed now.

Searl Effect Generator (0)

Anonymous Coward | more than 3 years ago | (#35006796)

Prof. John Searl also quotes the "Law of the squares" as fundamental in the science behind his invention.

Magic Squares in n dimensions (0)

Anonymous Coward | more than 3 years ago | (#35006910)

For a more complete treatment of this in "n dimensions", check out my friend, Charlie Kelly's work on this: http://www.charleskelly.com/interests.htm. He has a magic square generator there as well which is pretty cool.

Re:Magic Squares in n dimensions (1)

gilleain (1310105) | more than 3 years ago | (#35007922)

Interesting, but these 'geomagic squares' of Lee Swallows are generalised in a different way. It is the dimension of the elements of the square, not the square itself. So, in his formalism, numerical magic squares (of any dimension) are just 1-D geomagic squares, where the numbers could represent line segments or arcs of a circle.

Re:Magic Squares in n dimensions (1)

AshtangiMan (684031) | more than 3 years ago | (#35009464)

Hmmm . . . the 2x2 square at the end is represented by arcs in circles, which I am not at all understanding. But maybe there were the appropriate number of arcs to represent the line segments . . . I still don't see how that relates to the 3x3 and 4x4 squares.

If only I could also live for a thousand years... (0)

Anonymous Coward | more than 3 years ago | (#35007164)

.. then I coud do magic too!

(See I made the 'l' disappear.)

Call bullshit (0)

eyenot (102141) | more than 3 years ago | (#35007378)

This isn't "new". The conceptual diagrams he's talking about have been part of IQ tests for ages. Obviously, he's never taken one.

Nice work, but incomplete? (1)

degeneratemonkey (1405019) | more than 3 years ago | (#35009886)

I think this guy's work can be abstracted even further.

I'm no mathematician, but I see no reason to stop at geometric shapes. It seems to me that any arbitrary set T with an addition operator defined over it has the potential to be a space in which magic squares can be found. In the case of this guy's work, that set happens to be the set of n-dimensional geometric shapes with the addition operator defined as a geometric union. In traditional magic squares, that set is simply {x : 0 x 10}.

Re:Nice work, but incomplete? (1)

Natlaw (626413) | more than 3 years ago | (#35010552)

He does give that in the more formal definition in the appendix: http://www.geomagicsquares.com/appendix.php [geomagicsquares.com]

Re:Nice work, but incomplete? (1)

degeneratemonkey (1405019) | more than 3 years ago | (#35012118)

Thanks, totally missed that. This is great, and I would actually be interested to see it generalized over n-dimensional "magic" structures (i.e. magic hybercubes). At some point it feels like mental masturbation, but interesting no less.

Re:Nice work, but incomplete? (0)

Anonymous Coward | more than 3 years ago | (#35016416)

He does give that in the more formal definition in the appendix: http://www.geomagicsquares.com/appendix.php [geomagicsquares.com]

Somewhat more formal at least. I found it to be too relaxed and the definitions formulated such that working with the objects is overly complicated for no good purpose. Also, I fail to see need for some of his constraints other than he was think in terms of groups. In particular, what would require commutivity or an identity element?

Re:Nice work, but incomplete? (0)

Anonymous Coward | more than 3 years ago | (#35011452)

Observations: I just looked at a couple of these, and it seemed that in each case, in every "sum" X to which a fragment/"polymino" x belongs, x is in the same spot (modulo symmetries of the square/object).

Abstract: Take a set S with a (necessarily commutative?) concatenation operation (+):SxS -> S, and associate to each x in S a partition set P(x) in the power set of S consisting of all sets {p1,p2,...,pn} that sum up to x in some fashion?

Questions: For geometric shapes, is there a well defined addition operation? The pieces have to be shuffled around somewhat . . . Is it possible that modulo symmetries of the square/other shape, this addition is well defined in some fashion? i.e. equivalence classes modulo symmetry add up correctly?

Re:Nice work, but incomplete? (1)

degeneratemonkey (1405019) | more than 3 years ago | (#35012070)

I'm not sure about the technical definition of "well-defined" if there is a specific one in the case of an addition operation. I assume that for n-dimensional volumes, it is sufficient to define addition as a union of two volumes (a volume being a bounded infinite set in R^n).

Re:Nice work, but incomplete? (1)

degeneratemonkey (1405019) | more than 3 years ago | (#35012090)

I really hate not being able to edit /. posts. On second thought, I would more succinctly define an n-dimensional volume as any subset of R^n. Addition would still be a simple set union.

Incomplete definition (0)

Anonymous Coward | more than 3 years ago | (#35010006)

While a magic square is indeed a mathematical game, Soduko is not. Sudoku could just as easily be played with letters substituted for the numbers 1-9, or even with colors. It is somewhat annoying to hear people say Sudoku is a 'math game' or that if you're good at it, you must have a propensity for mathematics. This is simply not true. While mathematics is ultimately about pattern recognition, I wouldn't go so far to say that Sudoku is a mathematical game.

Old civilizations numerologies (0)

Anonymous Coward | more than 3 years ago | (#35011034)

I was just wondering, how much currently we dont know yet, of ancient mathematics; after having found this link http://hardware.slashdot.org/comments.pl?sid=208132&cid=16971732 to comments about numerologie based mayan astronomy (in the discussion about the new slashdot format)

Re:Old civilizations numerologies (0)

Anonymous Coward | more than 3 years ago | (#35011540)

The comment you are talking about must be this one http://meta.slashdot.org/comments.pl?sid=1965970&cid=35010612 (on classic bookmark) from your linked posts the maya astronomy its explained as practice based on numerical systems with some numerological (cultural explanation) on top and not the inverse

pentalobular containment (1)

epine (68316) | more than 3 years ago | (#35012980)

Not much excitement in this thread.

Last week I spent nearly a full day on Knuth's Dancing Links algorithm in relation to a combinatorial problem in coding theory (it's not a strong fit, but I thought there might be a stray intuition).

This little divertimento lead me to discover some clever tricks in how to set up the Dancing Links matrix for a certain class of problems to avoid traversing symmetric solutions. Considering the apathy level on this story, it would be a waste of breath to spell it out here.

It's cute, but the guy is trying to make a bit too much of it. For me it's just a toy problem in simultaneous exact cover that lends itself to visual aphorisms.

Maybe he could do a 4x4x4x4 grid of Wang tiles (I'm thinking 4D cubes with coloured faces) where every 1x1x4x4 subslice of 16 Wang cubes can be assembled into a 2x2x2x2 hypercubelet with every 2x2 face of the target cubelets conforming to some property, such as colours all same, or colours all different, and the 24 assembled cubelets (if my math is right, and it always is--in cartoon world) form some interesting tour of the 24 palladium quasi-crystals oscillation nodes.

Anyone? It's the key to pentalobular Arc reactor containment, for anyone with a giant pile of mil-scrap.

Re:pentalobular containment (1)

lennier (44736) | more than 3 years ago | (#35014004)

the 24 palladium quasi-crystals oscillation nodes.

Anyone? It's the key to pentalobular Arc reactor containment, for anyone with a giant pile of mil-scrap.

Tony Stark, is that you?

Re:pentalobular containment (0)

Anonymous Coward | more than 3 years ago | (#35017238)

Wang tiles ... Wang cubes ...

haaaa hahahaha you said wang.

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