3x3 Magic Square

Last time we looked at magic squares in general and found out that the most simple magic square is of order 3x3.

There is beautiful legend about the discovery of this popular magic square.

As the story goes, in ancient China there was a huge deluge: the people offered sacrifices to the god of one of the flooding rivers, the Lo river (洛水), to try to calm his anger. A magical turtle emerged from the water with the curious and decidedly unnatural (for a turtle shell) Lo Shu pattern on its shell, which contained the numbers in an aray of a magic square. As the legend says, these numbers showed the people how often and how many sacrificies should be given to calm the Lo river.

The Lo Shu square containing the numbers on the turtle's back:

 

Image Credit

So what are these magic numbers?

It appears that all magic squares obey some rules. For instance all normal magic squares of un-even order (of  n x n order, where n = 3,5,7...) have a special number at the centre called the magic constant.

So for a 3x3 magic square you have 1+2+3+4+5+6+7+8+9=45. In a magic square you have to add 3 numbers again and again. Therefore the average sum of three numbers is 45:3=15. The number 15 is called the magic number of the 3x3 square.

You can also achieve 15, if you add the middle number 5 three times.  You can reduce 15 in a sum of three sums eight times: 15= 1+5+9;  15= 2+4+9;  15= 2+6+7;  15= 3+5+7
15=1+6+8;  15=2+5+8;  15=3+4+8 ; 15=4+5+6

The odd numbers 1,3,7, and 9 occur twice in the reductions, the even numbers 2,4,6,8 three times and the number 5 four times. Therefore you have to place number 5 in the middle of the magic 3x3 square.

The remaining odd numbers have to be in the middles of a side and the even numbers at the corners. 

*The formula to find other magic constants is:

M= [n(n^2 +1)]/2

So by using the information above we can see that there exists only 1 magic 3x3 square (of numbers 1-9). Of course you can rotate the magic square in total of 8 ways, which gives all the possible distributions of the numbers in a 3x3 magic square.

Thanks for reading!

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Wonders Of Mathematics - Magic Squares

So one of the books that I really enjoyed recently is the famous Dan Brown's "The Lost Symbol". If you read the book (and you should) you might have noticed that it has many interesting maths references. One of which is hidden in the famous Albrecht Dürer's 1514 engraving Melencolia. It's a very special magic square.

But what are these magic squares? Magic squares are very interesting square arrangements of numbers. The numbers are arranged in such a way, that the sum of all columns, rows and diagonals is equal to the same number.

Magic squares come in different sizes that are called orders, for instance 3x3, 4x4 and so on (it's just a number of rows and columns). As for the sum that is constant for columns, rows and diagonals it's called the magic constant.

 

 

Image Source

The most simple magic square is of order 3x3 (it's easy to see that 2x2 squares are not possible). But how do you construct such a magic square, without relying to guess work? There are various rules, which can help you construct the square faster, however some guess work is still essential.

So when stumbled across these magic squares, I decide it would be fun to found a 3x3 magic square without any help. It's quite fun, well at least much more fun than sudoku, so I encourage you to try it.

Thanks for reading. Next time we're gonna look at all possible 3x3 magic squares and at the mysterious Melancolia engraving.

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Mind Blowing Facts About Nuclear Bombs + Chernobyl Disaster

While surfing around the web I found many interesting stories and urban myths about science. One of them is about a blind girl who sees a flash on an atom bomb.

A Blind Girl Sees a Flash of an Atomic Bomb

The first story is about an atomic bomb. As the story goes, during a testing of an atomic bomb in 1945 a blind Mexican girl saw the explosion. The interesting part about this story is that it's true. Now, it's quite clear that there are many ways to feel an atomic explosion without actually seeing it in some way. Thus it's not clear how the girl felt the explosion. Still it's an amazing story.



Now I like this story, because it's about atom bombs. I mean there are many subjects, which both scare and fascinate people these days. Ghosts, evil spirits, ufos and other paranormal phenomena - all of these subjects are always popular in the modern myths and legends. However, there is another group of subjects, which are even more fascinating. It's the real stuff. And by that I mean serial killers, unexplained scientific phenomena, terrorist attacks, nuclear explosions and so on. All of these things are even scarier, because they might just happen to you...

Atom bombs fascinated people ever since the first tests and explosions at Hiroshima and Nagasaki in 1945. After all, what can be more fascinating and horrifying at the same time than the most deadliest weapon, which can kill thousands in a matter of seconds. Thus I dug up some interesting facts about nuclear bombs and explosions. Enjoy!

1. There are still some 26,000 nuclear warheads in the world, enough to destroy civilization many times

over and destroy most life on earth. Nuclear weapons make humans an endangered species.

2. More than 95% of all nuclear weapons are in the arsenals of the US and Russia.

3. The average nuclear weapon in the US arsenal is approximately eight times more powerful than the
nuclear bomb that destroyed Hiroshima, immediately killing some 90,000 people.

4. There are currently nine countries with nuclear weapons (US, Russia, UK, France, China, Israel, India,

Pakistan and North Korea).

5) In the aftermath of the Cold War, a variety of

new nuclear threats have emerged. Among these are the following dangers:

• Increased chances of nuclear weapons falling into the hands of terrorists willing to use them;

• Policies of the US government to make nuclear weapons smaller and more usable;

• Use of nuclear weapons by accident, particularly because of decaying Russian infrastructure; and

• Spread of nuclear weapons to other states that may perceive them to be an “equalizer” against a more
powerful state.

6) The cost of US nuclear weapons research,

development, testing, deployment and maintenance has exceeded $7.5 trillion.

7) Cost of the Manhattan Project (through August 1945): $20,000,000,000


8) In ten minutes, a hurricane releases more energy than all the world's nuclear weapons combined!


9) Belarus received 70% of the contamination from Chernobyl.

Neighboring regions are often hit hardest in the event of a nuclear disaster, and that’s been especially true in the case of Belarus. Located just 10 miles away from the Chernobyl Nuclear Power Plant, scientists estimate that this landlocked country was hit by 70% of the radioactive outburst.

10) Nuclear rain from the Chernobyl disaster fell as far away as Ireland.

11) Chernobyl disaster remains the only Level 7 incident on the International Nuclear Event Scale. That is, it's the biggest man-made disaster in human history.


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Real Ghost Hunters and So Much More...

When it comes to paranormal phenomena, most of the scientists are sceptical right from the start, that is why I was amazed to find out that there is such a thing as a Society for Psychical Research.

Society for Psychical Research is a non-profit UK based organization seeking to understand and explain paranormal phenomena in a scientific manner. The SPR was founded in 1882 in London by a group of eminent thinkers including Edmund Gurney, Frederic William Henry Myers, William Fletcher Barrett, Henry Sidgwick, and Edmund Dawson Rogers. Initially six committees were established in order to research Thought-Transference, Mesmerism and similar phenomena, Mediumship, Reichenbach Phenomena (Odic Force), Apparitions and Haunted Houses, physical phenomena associated with séances, and the Literary Committee which studied the history of these phenomena.

 Source

 Today the society is run by a president and a council of twenty members. The organization is based at 49 Marloes Road, Kensington, London, with a library and office open to members. Also the society publishes quarterly Journal of the Society for Psychical Research (JSPR), the irregular Proceedings and the magazine Paranormal Review.

The greatest thing about this organization is that it is open for public. By paying for the membership you get access to the libraries, subscription to the Journal of The Society and invitations to the meetings of the society.

I also happen to find a Journal of the society, which was really interesting to read. Here's the link:

Journal of the Society for Psychical Research

Website of the Society for Psychical Research

Thanks for reading!

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Science or Science Fiction?

What is science? A rather philosophical question I have to say. Well if you're a student then chances are science will associate with tons of homework. And if you are a simple statistical person, than science is actually nothing more than some magical thing which is the cause of your Ipod or computer. If you're a geek like me, than science is like magic to you, after all what can be more magical than flying to the Moon or having all the knowledge of thousands of libraries just one click away from you on the internet. These all definitions are all great, but what is science more precisely? Maybe we should check the vocabulary?

"The word science comes from the Latin "scientia," meaning knowledge." More precisely, science is knowledge attained through study or practice. That's all fine but you must be wondering why I'm talking about all of these definitions. Well the answer is simple, because we life in a time when it's not clear what is the difference between science and science fiction. 


A few days ago I watched a very nice movie back from the 50s, you know the golden age of horror movies about monsters, aliens and space travel. The special effects looked kind of silly after all of these years, but the movie was still kind of interesting and funny in same way. However, after watching the movie, where some crazy astronauts flew to Mars, I asked myself a very simple but a truly interesting question - is this movie a Sci-fi movie? The reason for this question is of course the famous president Obama announcement during which he revealed the new plans to travel to Mars in a course of 20 - 30 years. So if we are going to Mars, then the crazy Sci-fi movie that I've seen, is not so unrealistic. As a matter of fact if we were to look at various Sci-fi works from the early 1900s and even earlier, we would realise, that almost everything that was science fiction now is real science.For instance, some months the world was shaken when some crazy scientists discovered that some materials can bend light rays in some ways to make the material invisible. Wouldn't you like to have an invisible coat, huh?


Every time, every decade, every era is famous for something, for instance the 60s are famous for rock music and hippies, the 20th century is famous for wars and scientific inventions and so on. So what is our century famous for? I truly believe that our century is the golden age of science.
The fact that science fiction is no longer just fairy tails, means that we are truly living in a very unique time. We can travel to space, use mobile phones, the internet, travel between continents in a matter of hours and live long healthy lives. What  science fiction was in the past is now science. And the fact that we are living in the world where it is no longer clear what is science fiction and what is science, truly means that we are living in a magical world indeed.

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Time Measuring Devices Throughout The History

Time Measuring Devices Throughout The History

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