 Leonhard Euler's math discoveries extend to astronomy, ballistics, optics, music theory, fluid dynamics, mapmaking, shipbuilding — and Sudoku. |
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Posted on 04/17/2007 11:17:48 AM PDT by Incorrigible
By AMY ELLIS NUTT
| Leonhard Euler's math discoveries extend to astronomy, ballistics, optics, music theory, fluid dynamics, mapmaking, shipbuilding — and Sudoku. |
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In the spring of 1727, two weeks after the body of Isaac Newton was laid to rest in London's Westminster Abbey, an obscure 19-year-old mathematician by the name of Leonhard Euler left his home in Basel, Switzerland, to take up an academic position in St. Petersburg, Russia.
When he died there in 1783 at the age of 76, Euler (pronounced "oiler'') had become the most prolific scientific writer in history and the greatest mathematician of the Enlightenment.
This week marks the 300th anniversary of Euler's birth, and, while hardly a household name, Euler is ranked by many alongside the ancient Greek Archimedes and the 19thcentury German John Friedrich Gauss as one of the most brilliant mathematicians of any era.
Euler contributed to a wide range of mathematical disciplines and invented several new ones, including graph theory, number theory, higher algebra and the calculus of variations. In the year of his death he also invented a diabolical 81-square puzzle that today is called Sudoku.
At least 50 different mathematical terms and formulas bear the name Euler, and his ideas have been applied to everything from astronomy to ballistics, optics, music theory, fluid dynamics, mapmaking and shipbuilding.
No object or physical phenomenon escaped Euler's imaginative curiosity. His observations of the way a column or beam buckled led to his discovery of fundamental principles in building and bridge design.
His desire to find the optimal shape and pattern of teeth in a cogwheel led to the design of the first paddle-wheel boat and later to the construction of the first machines of the Industrial Age.
One of Euler's greatest contributions to current mathematics arose out of his unique approach to an old puzzle concerning the geography of the Prussian city of Konigsburg (now Kaliningrad, Russia). A medieval town founded by Teutonic knights, Konigsburg is bisected by the river Pregel. Before it was flattened by bombing raids in World War II, the city's two islands were connected by seven bridges. The citizens of Konigsburg, so the story goes, always wondered whether it was possible to walk through the city by crossing each bridge once and only once.
In 1739, Euler solved the problem. By replacing the land masses and the bridges with points or vertices and connecting arcs, he proved it was not possible, and at the same time laid the groundwork for what would become graph theory.
Today graph theory underlies the science of networks that is being applied to such practical and real-world problems as computer chip design, traffic flow, pharmaceutical discovery and the interruption of terrorist cells.
Among mathematicians Euler may best be known as the creator of one of the world's most beautiful equations, as a poll determined several years ago. Praised both for its astonishing simplicity and its daring breadth, the formula, known as Euler's Identity, joins the study of space or geometry with that of algebra or quantity, essentially simplifying the mathematics of both engineering and physics. And it does so by using the three most common constants (e, pi and i) and the two most basic counting numbers (0 and 1) in all of mathematics.
In the equation — e, raised to the power of i x pi, 1 = 0 — the letter "e'' denotes the infinite number 2.71828 ... , pi is the infinite number 3.14159 ... , multiplied by the square root of minus one, which is the imaginary number "i.'' Add those numbers to 1 and you get exactly zero.
Published in 1748, Euler's Identity is perhaps the most improbable formula in all of mathematics. Essentially it says that the result of raising an irrational number to a power that is an irrational number, results in a natural number. Linking the most basic counting numbers 1 and 0 with the irrational numbers "i'' and pi, is like saying the music of Bach is in the same class as the Beastie Boys.
In the 19th century, Harvard mathematician Benjamin Peirce tried to explain the equation to his students this way: "Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore, we know it must be the truth.''
Euler's extraordinary gifts included not only a lively intuition, but a prodigious ability to calculate and a near-photographic memory. His friends and family often remarked on his ability to quote from any page in Virgil's Aeneid — in Latin — and his uncanny ability to resurrect, verbatim, the minutes of an academic meeting held years earlier.
During his lifetime, the peripatetic polymath published some 866 scientific papers, only a fraction of which have yet been translated from the original German, Latin and French.
But perhaps the most astonishing aspect of Euler's life is that while it was so prodigious, it was also so normal. He was friendly, outgoing and generous and, unlike Albert Einstein's turbulent family relations, Euler relished his home life. Of his 13 children, only five survived infancy, and he often took them to the zoo. He wrote in his memoirs that he was never more content than when he was at home: "I made some of my most important discoveries while holding a baby in my arms with other children playing around my feet.''
Despite being blind for the last dozen years of his life, Euler continued to produce. Shortly before his death in September 1783, Euler was calculating the orbit of the recently discovered planet Uranus, studying the mechanics of balloon motion, and at the same time teaching mathematics to his grandchildren.
Perhaps the highest praise of the mild-mannered savant was rendered recently by Edward Sandifer, a professor at Western Connecticut State University.
''A lot of people polish the happiness out of math,'' he said, "but Euler left the happiness in.''
(Amy Ellis Nutt, a staff writer for The Star-Ledger of Newark, N.J., studied the philosophy of mathematics at the Massachusetts Institute of Technology. She can be contacted at anutt(at)starledger.com.)
Not for commercial use. For education and discussion purposes only.
I wonder was he of the Houston Eulers.
1=0........Happens every payday............
Man, sometimes I can’t help but get angry that there were guys two hundred years ago that know calculus and analytic geometry better than I ever will. These were guys who were crapping into jars, but they’re way smarter than me. That galls me to no end.
Euler?......Euler?.....
No, but he was a TITAN of his age............
No relation to Ferris B. Euler
And the tv show NUMB3RS
One of my Calc profs was fond of using Newton’s expression:
“The reason we can see so far is because we stand on the shoulders of giants.”
Though I heard it’s older than Newton.
The old English program “Connections” where the links between discoveries and inventions over time are documented was a great program and always left me thinking how depended these geniuses were on the postal service of their time!
Thanks for posting.
Amy Ellis Nutt = A. Nutt ???
I love threads such as this. Thanks for posting.
Oddly enough, I found that I did better in my mathematics courses when I read up some of the history of the mathematicians whose equations were being discussed. Unfortunately, I was flailing about in Sophomore year Differential Equations when I started looking in to the history and somehow it all clicked better.
Thanks for posting this.
The author left out a plus sign in Euler’s Identity
(it’s e to the i pi power + 1 = 0).
But a great read.
But they didn’t have toilet tissue, therefore, I am sure their end was more galled than is yours.
I keep hearing about this game “sudoku” all the time, but have no idea what it is; can anyone describe/explain it in a sentence or two?
Anyone?
I loved that series! Used to have it on tape but it's long gone. I wonder if it's out on DVD somewhere. Forget the name of the leisure suit guy but he was a riot.
(Click the pic. There's a t-shirt for everyone in this world!)
Anyone?
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