Playtime

What if I told you that one of the top mathematicians of today makes discoveries in his field through valuable playtime?  It’s true!  And he is not the only one.  Just think about why children play.  For a child, playtime is work.  It is their way of figuring out how the world works as they grow up.  But why does it have to stop at adulthood?  It doesn’t, and it shouldn’t.  For someone such as number theorist Manjul Bhargava, playtime is his way of figuring out how the world works.  And he is very good at it!  In fact, he won a Fields Medal in 2014.  (A Fields Medal is only one of the highest honors a mathematician can receive, akin to a Nobel Prize.)

And how does he play?  For one, he is an artist.  He studies Sanskrit poetry and is an accomplished musician.  Both of these pursuits are rich in mathematics.  Did you know that Sanskrit poetry has the Fibonacci numbers?  I talked about Fibonacci numbers in the previous posts Flowers and Fibonacci and Fibonacci Fun.  Except, in India, the numbers in the famous sequence are called the Hemachandra numbers.

How else does he play?  His office at Princeton University is littered with mathematical toys such as Rubik’s Cubes, Zometools, and puzzles.  And what studies about Fibonacci/Hemachandra numbers would be complete without a collection of pine cones?  These toys are not fun and games.  But, maybe they really are?  Either way, Rubik’s cubes helped Bhargava to solve a 200-year-old number theory problem while he was still a graduate student at Princeton.  Talk about the power of play!

If you want to read more about this accomplished mathematician, check out the following article in Quanta magazine:   2014 Fields Medal and Nevanlinna Prize Winners Announced

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NOVA “The Great Math Mystery”

“Mathematics is the alphabet with which God wrote the universe.” – Galileo Galilei

This NOVA special is an entertaining exploration of whether mathematics is a product of human discovery or invention.  An attempt to find an answer goes through history and spotlights the contributions of names such as Fibonacci, Pythagoras, Plato, Galileo, Newton, Maxwell, Marconi, Englert, and Higgs.

The Great Math Mystery

Fibonacci Fun

The Fibonacci sequence has been mentioned in a previous post, but let’s look at one of the many cool patterns hidden in the numbers.

Just to refresh your memory about the Fibonacci sequence, it appears as follows:  1, 1, 2, 3, 5, 8, 13, 21, …  Each new term in the sequence is found by adding the last two terms.

Now that you have the sequence in your mind, let’s look at a pattern.  Find a number and multiply it with the number following the next.  For instance, if you take 3, multiply it with 8.  The result will always be 1 more or 1 less than the square of the number in between.  So, 3 x 8 = 24 while 5 squared is 25, a difference of 1.  The product is 1 less than the square.  How about we take 5 with 13.  The 8 squared is 64 while 5 x 13 = 65.  Again, there’s a difference of 1.  The product is 1 more than the square.  Whether the result is 1 more or 1 less will alternate down the sequence.  Pretty cool, huh?

The alternating pattern is made all the cooler when you stop to realize that the ratios of successive numbers alternate higher and lower, always approaching phi (the Golden Ratio).

Flowers and Fibonacci

Count the spirals.  How many do you see?

Photo: Cynthia Scofield
Location: Bok Tower Gardens, Lake Wales, Florida

The number of spirals in this camellia is a Fibonacci number.  The Fibonacci sequence starts with 1,1 and then adds the previous two terms to get the next.

1, 1, 2, 3, 5, 8, 13, 21, 34, …

Fibonacci numbers pop up in many areas of the natural world.  Start counting the spirals in pine cones or seed heads or the petals in flowers.  You will be amazed at how often a Fibonacci number turns up!

 Photo: Cynthia Scofield        Location:  Back Yard, Central  Florida