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Ancient Puzzle Gets New Lease on 'Geomagical' Life
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."
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
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.
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.
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.
Check it out on page 5 of the New Scientist link. Apparently, they think 8 is an odd number, and 9 and 11 are not. So much for the "new math."
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.
Entomologically speaking, the spider is not a bug, it's a feature.
Yeah, get a goat!
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.
char*f="char*f=%c%s%c;main(){printf(f,34,f,34);}";main(){printf(f,34,f,34);}
So he hasn't found the Time Cube yet...
This is not the sig you're looking for.
Looks fine in Firefox.
That said, I think it could be argued that sites are getting too complex, causing them to take too long to load and very prone to misrendering.
www.wavefront-av.com
Looks fine in Firefox.
That's because your username is short
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.
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.
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}.
Some of the best comments I've ever read on /. were by ACs. Just sayin' :)
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 )
What the hell? I RTFA and have no idea what this is about. What is a polymino? Guess what? I still think it's a horse.
You're thinking of "Palomino". See "Piece" on Hard Drop.
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.