Secrets of Mental Math by Arthur Benjamin and Michael Shermer

So it's time for another "Book of the Week" review. This time let's look at something fun and simple - a great guide on magic of maths and mental math.

About the Authors:

Arthur Benjamin is a professor of mathematics at Harvey Mudd College in Claremont, California. In addition, he is also a professional magician and performs his mixture of math and magic all around the world. Besides that Michael Shermer is host of the Caltech public lecture series and a contributing editor at Scientific American.

Michael Shermer is an American science writer, historian and the found of The Sceptics’ Society. He is also the chief editor of his magazines Skeptic and a columnist at Scientific American.

 Source

Short Review:

Secrets of Mental Math is a great book for those who enjoy maths magic. It will teach amazing math tricks which will surprise yourself and amaze your friends. But it’s not only about magic of mathematics, it’s a great guide to mental mathematics. It covers a  variety of techniques which will not only increase your arithmetic abilities and speed, but will also teach you to do operations on huge numbers in your head. So if you’re a fan of mental mathematics be sure to check this one out.

You can find the book here:

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So You Want to Study Physics?

What sorts of things get physicists (or wannabe physicists, like the teacher of this class) excited? Is it the dream of building grand intellectual edifices capable of describing the Universe with amazing accuracy and elegance? Or, perhaps, discovering something so unexpected that it totally blows your mind? Maybe it's simply the act of doing physics! Whatever the case, there are certainly many things in physics to get excited about, and this great video explores them.




You might be interested in:

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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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Fermat's Last Theorem

I present you another BBC Horizon jewel called the "Fermat's Last theorem". All of you math lovers are gonna love it.

Thanks for checking this out!

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Maths Can Be Fun

So as you might have noticed I've been lately watching a lot of documentaries and lectures about physics, maths and all that stuff. I presented you the Ted Talks channel a while ago, and I still think it's one of the best channels on youtube so feel free to check it out. However, I also found some great docummentaries from BBC a while ago. One if them I would like to share with you. It's called The History of Mathematics.

Now when it comes to maths, I guess I'm like most of you - I don't enjoy spending countless hours solving the same problems and writing everything all over again after making a silly mistake. Yet, at the same time, I realise that there is another side of mathematics. It's like the dark side of the moon, that we never see, yet it's so mysterious and cool. The beauty of maths is all around us, after all, even Galileo once said - maths is the languange of our universe. The ability to use simple equations to understand our universe, calculate amazing things, like distances to stars or mass of the sun using simple techniques that were invented thousands of years ago soung fantastic to me. Unfortunatelly, most of the teachers and school systems simply hide this beautiful side of mathematics under tons of boring homework and bad explanations.

But let's get back to the subject. I found this great documentary, which tells the story of mathematics. It's narated in a very interesting way. Also it shows the more interesting side of mathematics, and how it evolved since the ancient times. I really enjoyed this BBC documentary and I hope you will too. So here's the link (you will find later parts on youtube).

History of Mathematics Part 1

Thanks for reading!


Also check this out if you're interested:

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So You Want to Learn Physics?

So you want to learn physics? Good choice! But can you really learn it if you're bad at maths or too old for for college? The answer is yes.

For more than 3 years I've been studying various subjects of physics on my free time and I found many good books and free lectures. The hardest part about self-studying is finding suitable books and lectures. Most of the time you just simply find books that are too hard or too easy, thus it's important to know good authors and lecturers.

So a couple of months ago I stumbled upon a great video lecture of physics from Yale university. Basically it's a part of a project in which universities from all around the world share video lectures with people on the web. This is a general course on physics - it contains a variety of subjects, such as mechanics, special relativity, waves and other classical stuff. For most of the part, maths is fairly straightforward (as much as maths for physics can get).

So here's the link with the free lectures (there is a variety of other free lectures on this website covering astronomy, economics, chemistry and so on):

Free Yale Courses

Just for a taste - first lecture:

PS. if you find maths during the video lectures overwhelming you can always check out some great books on maths from the For Dummies series. You can find them here:

Maths for Dummies

Thanks for reading!

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