An Implementation of Magic
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(5) The implementation is extensible. Our implementation demonstrates the feasibility of the magic-sets transformation for commercial relational systems, and . Read a free sample or buy An Implementation of Magic by Kim J Cowie. You can read this book with Apple Books on your iPhone, iPad, iPod.
Left, a geomagic 3x3 square where each element is a decomino — a polyomino made up of 10 square units. The decominoes in each row, column and diagonal can be fitted together to form a 5x6 rectangle. They can be assembled in two different ways, which are drawn on either side of each row, column and diagonal. This is one of only two geomagic squares possible when the pieces are all decominoes - making this type of geomagic square much rarer than when all the pentominoes from one to nine are used. Right, a geomagic 3x3 square where each element is a polyomino, ranging in size from one to nine.
The squares around the periphery show how the polyominoes from the corresponding rows, columns and diagonals can be pieced together to form the same shape, in this case a 4x4 square with one internal cell removed.
Implementation of Magic-sets in a Relational Database System
Sallows found 4, squares like this, consisting of the polyominoes from one to nine, and making the same target shape - many more than he expected. Peter Cameron, professor of mathematics at Queen Mary, University of London, calls geomagic squares "a wonderful new piece of recreational maths, which will delight non-mathematicians and give mathematicians food for thought". Despite the inherent whimsy of the field, he said: Perhaps no other area of non-practical mathematics has been so popular for so long as magic squares.
Their story begins 4, years ago in China, where, according to legend, a turtle crept out of the Yellow River.
The reptile is said to have had dots on its underside positioned in such a way as to make the 3x3 square described above. The Chinese called this square the lo shu , and gave it spiritual importance, believing that it encapsulated the harmonies of the universe. Feng shui, the Chinese system of arranging objects, such as furniture in homes, is in part based on the lo shu.
But veneration of magic squares was not confined to the Chinese. In India amulets with magic squares were worn as protective charms, in Turkey virgins embroidered magic squares on the shirts of warriors and in western Europe Renaissance astrologers equated them with planets. This square is particularly amazing. Not only do the rows, lines and diagonals add up to 34, but the four corners, the four digits in the central square, and the four digits in the top left, top right, bottom left and bottom right quarters do too.
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There are many other combinations of four numbers in the square that add up to 34, and it is fun looking for them. The most notable aficionado was United States founding father Benjamin Franklin, who liked to spend his spare time constructing particularly innovative variations. In one evening in his 40s he composed a 16x16 square that he claimed was "the most magically magical of any magic square ever made by any magician".
Sallows, aged 66, is very much an enthusiastic amateur. He left school at 17 with no qualifications and his mathematics is entirely self-taught.
He was an electronics engineer in the non-academic staff at the University of Nijmegen until he retired two years ago. While it is certainly remarkable that a non-mathematician has given this established field a new lease of life, it is perhaps only to be expected, since most academic mathematicians would now consider magic squares as too frivolous to occupy their time. So, as above, the 3x3 has every number from one to nine and the 4x4 every number from one to Sallows says he was instantly "turned on by the symmetries" of magic squares, and once he had got the bug he began to invent new rules and modifications.
He is celebrated for inventing the "alphamagic square", which is doubly magic:. The rows, columns and diagonals add up to 45 when considering the meaning of the words. But when considering the number of letters in each word — so five is 4 and twenty-two is 9 — this also generates a magic square, whose rows, columns and diagonals add up to Sallows gained a certain amount of fame in the recreational maths world for his alphamagic square, but dismisses it as "zany, a bit silly".
He was more excited by looking at the algebra behind magic squares. Sallows was playing around with the Lucas formula: The software features a component framework, enabling developers to rapidly build new application components and other business processes. Parmalat has its own team of five developers, and speed and efficiency is crucial for their needs," he says. The software also allows user-friendly transparent integration with third-party Web authoring tools. Business logic can be assigned to control on Web pages with no need for special scripting. MGX is a JSE Securities Exchange-listed, new economy company that represents world-class products and services and delivers measurable business outcomes for customers across business-critical areas of the information economy.
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