Prison Magic Square | The Magic Square that was born in the Prison using only PRIME NUMBERS
Channel: Magic Square Puzzles
Date: 31/08/2020

• Numbers can be broadly divided into two categories, Prime Numbers and Composite numbers. Any number that can be divided by 1 and itself is called the Prime number.
• Example of a Prime number is 2,3,5,7,11 etc.
• 2 is a really odd prime number in the sense that it is the only even prime number.
• Any even number cannot be a prime number because it will be instantly divisible by 2.
• Composite numbers are those numbers that can be divided by 1 and themselves apart from some other number.
• For example 15 is divisible by 1, 15, and also by 3 and 5. 9 is divisible by 1 and 9 apart from 3.
• There is a theorem that any positive integer could be expressed as a product of a prime number.
• Why is a day divided into 24 hours and why is a circle divided into 360 degrees. of course, there are other types of expressions to denote a circle
• We can say that a circle has 360 degrees or we can say a circle has 400 gradians. Both mean the same but are expressed in different ways.
• Both the systems are in use.
• but reverting back to the original question as to why a circle is divided into 360 degrees or 360 equal parts or equal angles in that 360 is a composite number divisible by 2, 3, 4, 8, etc.
• Hardy differentiated between pure mathematics and applied mathematics.
• He scorned applied mathematics on how the science could be put to destructive purposes also.
• He would say in his mathematician's apology ‘I have never done anything "useful". No discovery of mine has made or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world’
• Hence he said I have never done anything "useful". No discovery of mine has made or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world
• He did work in collaboration with Weinberg and came out with the hardy-Weinberg principle in population genetics.
• He also joined hands with Ramanujan to form the Hardy – Ramanujan asymptomatic formula in integer partitions.
• Both of these works of his he thought were of no use to humanity. but they are now widely used in frontier research.
• He at the time of discovery thought that these are pure mathematics and have no capacity to be useful to the general population for either good or bad particularly in a war.
• but he was proved wrong. The hardy-Ramanujan asymptomatic formula was used to investigate atomic nuclei by Neils Bohr and they were also used in the Bose-Einstein condensate systems.
• My mother Indira Narasinga Rao once asked P.K. Srinivasan a renowned Mathematics teaher who was also the Director of the Ramanujan museum in Chennai, about what was the use in her discovery a method of creation of a magic square.
To this Shri P.K. Srinivasan said that your work is pure mathematics and applied mathematics is different. Great Mathematicians do not look at finding solutions to the day to day problems. They take upon some work, maybe inspired by Nature, and find some patterns and put them into equations. They do not bother beyond that. They do their research work for quenching their own thirst for knowledge or the love of the subject.
• The application part comes later.
• Many of Euler’s work is useful now in the era of computers when the concept of computers was not even there in his lifetime.
• As said Hardy also worked in the Prime Numbers and their distribution in the number system.
• He was happy that his work would be of no military use.
• But today Prime Numbers are useful, nay indispensable in cryptography, internet security, etc.
• We will see more of that in the coming sections.
• today we would see about prime number magic square or a prison magic square
• Euler did his Konigsberg bridge problem to address the problem of the people residing in Konigsberg. Apart from that theoretical question, there was not much of use to anybody living in the Konigsberg. prior to Euler giving out a solution to the bridge problem also people were using all the bridges to go into the island in Konigsberg and after that also people were using all the bridges to go in and out of the island.
• But today it is useful in optimizing the circuits or any systems. So when Euler worked on the problem it had no practical applications and the people would have said why he is working on such an insane and useless question. His solution was then in the realm of Pure Mathematics but today it has come into the realm of Applied mathematics.
• They lived in their own world.
• Let us take a peep at their wonderful world.
• Today we will look into a wonderful magic square called the prison magic square. The author of this magic square is not known. But it is a very intriguing square.
• It is said that it was constructed by a prison inmate sentenced to life inside a prison.
• He used the Prime numbers entirely to create this Prison Magic Square.
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