Google honors Fermat!

Kudos to Google!

Anyone who loves math knows how rare it is for mainstream society to be exposed to mathematics of any kind.  However, yesterday, Google exposed tens of millions of people to one of the most famous mathematicians of all time, Pierre Fermat.  To honor his 4o1st birthday on August 17, Google created the Doodle seen above.  What is the Doodle about?  Well, written on the chalkboard is what is known as Fermat’s Last Theorem.  Simply put, the theorem states that the equation x^n+y^n=z^n has no integer solutions for n>2 and x,y,z ≠ 0.

However, what has become more famous than the actual theorem is the mystery Fermat left behind.  The theorem, discovered after his death and written in the margin of his copy of Arithmetica, included the note  “I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.”

For the next three centuries, legendary mathematicians tried hopelessly to recreate the proof that Fermat claimed he had discovered.  Finally, in 1993, the mathematician Andrew Wiles (with a little help from others to fill in some gaps) found a proof.  Beyond putting the mystery to rest, Wiles put to rest the idea that Fermat ever had a legitimate proof of the theorem as the mathematics he used had only been developed in the 20th century.

So, if Fermat never left a proof, then why call it a theorem?  Any high school geometry student will tell you that a theorem requires a proof.  It all has to do with the fame of the person making the claim.  Fermat was about as famous as any mathematician could be and was, therefore, given the benefit of the doubt.  Unfortunately, for us mere mortals it would have been called a conjecture and, more importantly, lost to the sands of time.

A perfect sphere?

Beauty … perfection … words many non-math people don’t expect to hear when it comes to mathematics.  But talk to any math person and, sooner or later, one of these words will be used to describe the subject.  As the legendary number theorist G.H. Hardy once described it, “Beauty is the first test: there is no permanent place in the world for ugly mathematics.”

For most people, their first opportunity to see such beauty and perfection comes with a course in high school geometry.  Studying the properties of polygons or learning that the ratio of a circle’s circumference to its diameter is exactly pi are opportunities to witness first hand the elegance of the subject.

Unfortunately, as math people know too well, the perfection of geometry exists only in our minds.  Thanks to the laws of physics, in the “real world”, the perfect forms of geometry just do not exist.  A rhombus is never quite a rhombus.  The ratio of a circle’s circumference to its diameter is close to pi but never exactly pi.

However, before we all run into the woods to hide from the hideous and ugly real world of imperfection, TAKE A DEEP BREATH!  It turns out that there is new hope for us!

According to recent research from Imperial College in London, we need not look farther than the electron to see geometric perfection – well, almost perfection.   Previously thought to be a distorted sphere (aspheric), scientists were surprised when they discovered just how spherical an election is.  According to their research, the electron differs from a perfect sphere by only 1×10^-27 cm or, if you are a more visual person, .000000000000000000000000001 cm.  To understand this in more practical terms, if the electron were blown up to the size of our solar system, it would differ from a perfect sphere by the width of a human hair!  (Thanks to sciencedaily.com for the example.)

So, lovers of beauty and perfection, fear not – maybe mathematics in the real world isn’t that ugly after all.

If you are interested in reading more about this on sciencedaily.com, click here:  http://www.sciencedaily.com/releases/2011/05/110525131707.htm

If you would like to read the official abstract for the paper, click here: http://www.nature.com/nature/journal/v473/n7348/full/nature10104.html

Need Help with Parallel Parking?

Are you 16 and learning how to drive?  Are you afraid of the torturous task of parallel parking?  Fear no more!  Now, Simon Blackburn, mathematics professor from the University of London has investigated the task of parallel parking.  And, thanks to him, you can now have a more complete understanding of the ‘joy’ of parallel parking, hopefully helping you to pass the test.

Read the paper here:  Perfect Parking

You are all very welcome!

111,111,111 times 111,111,111 = ?

Any answers?  Any guesses?  Want a hint?  The answer is a Palindromic number – a number that is the same written forwards or backwards.  (For example, 12321  and 1432341 are Palindromic numbers.)

So, try it and see what you get.  Enjoy!

The perfect cup of coffee

There is an old Hungarian mathematics quote that I love to recite, “A mathematician is a device which turns coffee into theorems.”  Well, on Christmas morning, I received the perfect gift from my daughters to complement the quote. (To my fellow geometry fans, notice the choice of word ‘complement’.)

Let’s face it, this is my dream coffee cup … a cup containing 20 of the greatest achievements of human thought. Now each morning when I drag myself out of bed at 4:30, I will have a little inspiration to go along with the first cup, and the second, the third, and, of course, the fourth … you get the idea.

For those of you looking to order your own, please click here.