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Euler's Equation

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Flash
155707.  Sun Mar 11, 2007 5:44 pm Reply with quote



Quote:
A reader poll conducted by Mathematical Intelligencer named the identity as the most beautiful theorem in mathematics. Another reader poll conducted by Physics World in 2004 named Euler's identity the "greatest equation ever", together with Maxwell's equations.

The book Dr. Euler's Fabulous Formula [2006], by Paul Nahin (Professor Emeritus at the University of New Hampshire), is devoted to Euler's identity; it is 400 pages long. The book states that the identity sets "the gold standard for mathematical beauty."

Constance Reid claimed that Euler's identity was "the most famous formula in all mathematics."

Gauss is reported to have commented that if this formula was not immediately apparent to a student on being told it, the student would never be a first-class mathematician.

After proving the identity in a lecture, Benjamin Peirce, a noted nineteenth century mathematician and Harvard professor, said, "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."

Stanford mathematics professor Keith Devlin says, "Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."


wiki

I will never be a first-class mathematician, it turns out. Those of you who are: is this any use to us?

 
MatC
155764.  Mon Mar 12, 2007 5:10 am Reply with quote

[color=yellow]"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." [/color]

If a statement like that is of no use to us, then we are of no use.


Last edited by MatC on Mon Mar 12, 2007 4:05 pm; edited 1 time in total

 
Jenny
155899.  Mon Mar 12, 2007 2:01 pm Reply with quote

My husband has a cousin who is a high-flying mathematician. Would anybody like me to ask him if he can elucidate that sentence about Euler's equation or are you lot (include me out here) equipped to do it yourselves?

 
eggshaped
155902.  Mon Mar 12, 2007 2:04 pm Reply with quote

We are equipped I think, but we decided that its practical uses were such that 99% would never use it in the real world. As such it would be hard for panellists to empathise with its importance. Let alone its beauty.

 
Flash
155917.  Mon Mar 12, 2007 3:45 pm Reply with quote

What eggshaped is alluding to is that he and Gray had a fight about its meaning this morning which looked like turning very ugly indeed until it turned out that they were agreeing with each other, though neither of them knew it.

 
MatC
155921.  Mon Mar 12, 2007 4:07 pm Reply with quote

That's no excuse not to hit each other, though, is it?

 
Gray
155988.  Tue Mar 13, 2007 5:34 am Reply with quote

That's what we thought.

The question was something like 'is there any way that this equation can be identified with any concept, picture or effect with which people might be familiar?' and I said emphatically not.

Although you can show on the Argand plane (where real and imaginary numbers 'meet') what 'shape' the equation delineates, you can't relate it to anything 'in real life' that could mean anything to anyone. It doesn't have 'meaning' in any direct sense (and it was the word 'meaning' which, as always, caused trouble!)

With Einstein's equation, you can 'grasp it' to a certain extent because everyone is familiar with the concepts of mass and energy and nuclear bombs, but with Euler's equation, you're starting off raising a trancendental number to the power of an imaginary number multiplied by another trancendental number - way off the map as far as conceptualising it as any kind of image which people could relate to...

...or be amusing about.

 
MatC
155990.  Tue Mar 13, 2007 5:37 am Reply with quote

The quote itself is funny - and profound, and very qi. You’ve got to find a way to use that: come on, boffins!

 
Vitali
155993.  Tue Mar 13, 2007 5:48 am Reply with quote

Lenin came up with a rather idiotic equation that read as follows:

Communism = Soviet power + electrification.

By the rules of simple arithmetics, it means that:

Soviet power = Communism - electrification
and
Electrification = Communism - Soviet power!!!

 
Frederick The Monk
156737.  Thu Mar 15, 2007 7:01 am Reply with quote

E is for Equations and I think we could have a bit of fun here, even including Euler's identity. I particularly like the communist equation rewritten. There must be lots of stupid business jargon style equations we could rewrite to prove they are complete nonsense. For instance:

According to these people

A Good Business Model Plus Marketing Equals Success

This rather suggests that marketing is as waste of time as idea as a good business model would be Success minus Marketing.

According to these people
Jesus plus a Web page equals a lot of thriving businesses

Which gives us a definition of Jesus as 'a lot of thriving businessses minus a web page'.

According to these people
Compliance plus governance equals long-term gains

Which is an equation I'm sure a lot of corporate boardmembers would appreciate as it suggests that good governeance is simply long term gains with the compliance removed.

 
Jenny
156793.  Thu Mar 15, 2007 9:45 am Reply with quote

Those are gems Fred - I love 'em.

 
MatC
157285.  Sat Mar 17, 2007 7:00 am Reply with quote

March 14th (3.14, in American) is Annual Pi Day.
Here http://www.exploratorium.edu/pi/pidaysched.html you can find details of the day’s events, including “An introduction to Pi and a special rap performance by none other than Albert Einstein (in puppet form...)”


“This year we will have on-hand TWO forms of pie - pizza and fruit. The pizza pies will be provided by the fine pizzerias of San Francisco, and the fruit pies are being donated by some of our local bakeries. Please feel free to bring your own to add to the festivities! What better way to ponder pi than eating pies?”


Link to Einstein.

 
Flash
157291.  Sat Mar 17, 2007 8:03 am Reply with quote

Quote:
Apu: I can recite pi to 40,000 places. The last digit is 1.

Homer: Mmm... pie.

 
DELETED
158017.  Tue Mar 20, 2007 1:40 pm Reply with quote

DELETED

 
MatC
159322.  Fri Mar 23, 2007 10:15 am Reply with quote



This is a picture of the triumphant solution to a famous maths problem, “so complicated it would cover the island of Manhattan if written out.”

S: Western Daily Press, 22 March 07
http://www.aimath.org/E8/
http://edition.cnn.com/2007/TECH/science/03/21/math.puzzle.solved.ap/index.html

 

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