Order Nine Magic Square Puzzle
Painting - Digital Oil
This interactive painting is a jumbled order-9 square, or a semimagic square, meaning the rows and columns add to the same number but the diagonals do not. Jumbling the magic square into a semimagic square actually makes it more challenging to solve as the pattern is more difficult. However, to make it a bit easier, only prime numbers have been omitted. Buy this piece on canvas and solve it with a paint writer or a paint pen to make it truly interactive. Difficulty level: Intermediate.
Recreational mathematics includes logic puzzles and other puzzles that require deductive reasoning, the aesthetics of mathematics, and peculiar or amusing stories and coincidences about mathematics and mathematicians. Some of the more well-known topics in recreational mathematics are magic squares and fractals. Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study of mathematics.
In recreational mathematics, a magic square of order n is an arrangement of n-squared numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n-squared. The term "magic square" is also sometimes used to refer to any of various types of word square.
Magic squares have fascinated humanity throughout the ages, and have been around for over 4,120 years. They are found in a number of cultures, including Egypt and India, engraved on stone or metal and worn as talismans, the belief being that magic squares had astrological and divinatory qualities, their usage ensuring longevity and prevention of diseases.
Magic squares were known to Chinese mathematicians, as early as 650 BCE and Arab mathematicians, possibly as early as the 7th century, when the Arabs conquered northwestern parts of the Indian subcontinent and learned Indian mathematics and astronomy, including other aspects of combinatorial mathematics. The first magic squares of order 5 and 6 appear in an encyclopedia from Baghdad circa 983 CE, the Encyclopedia of the Brethren of Purity (Rasa'il Ihkwan al-Safa); simpler magic squares were known to several earlier Arab mathematicians. Some of these squares were later used in conjunction with magic letters as in (Shams Al-ma'arif) to assist Arab illusionists and magicians.
Chinese literature dating from as early as 650 BC tells the legend of Lo Shu or "scroll of the river Lo". In ancient China there was a huge flood. The great king Yu tried to channel the water out to sea where then emerged from the water a turtle with a curious figure/pattern on its shell; circular dots of numbers which were arranged in a three by three grid pattern such that the sum of the numbers in each row, column and diagonal was the same: 15, which is also the number of days in each of the 24 cycles of the Chinese solar year. This pattern, in a certain way, was used by the people in controlling the river.
The Lo Shu Square, as the magic square on the turtle shell is called, is the unique normal magic square of order three in which 1 is at the bottom and 2 is in the upper right corner. Every normal magic square of order three is obtained from the Lo Shu by rotation or reflection.
The Square of Lo Shu is also referred to as the Magic Square of Saturn or Chronos.
The order-4 magic square in Albrecht Dürer's engraving Melencolia I is believed to be the first seen in European art. It is very similar to Yang Hui's square, which was created in China about 250 years before Dürer's time. The sum 34 can be found in the rows, columns, diagonals, each of the quadrants, the center four squares, and the corner squares(of the 4x4 as well as the four contained 3x3 grids).
(Primary Source: Wikipedia)
January 5th, 2012
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