Euler's Alchemy

                              e^iπ + 1 = 0 


Nice Lee Simmons piece today for Wired, rhapsodizing on "Euler's identity":

http://www.wired.com/2014/11/eulers-identity/

Love this wormhole analogy toward the end:

"But the weirdest thing about Euler’s formula—given that it relies on imaginary numbers—is that it’s so immensely useful in the real world. By translating one type of motion into another, it lets engineers convert messy trig problems (you know, sines, secants, and so on) into more tractable algebra—like a wormhole between separate branches of math. It’s the secret sauce in Fourier transforms used to digitize music, and it tames all manner of wavy things in quantum mechanics, electronics, and signal processing; without it, computers might not exist."

Give it a read....

Euler... Thinker Extraordinaire

1) Probably any mathematician would rank Leonhard Euler as one of the greatest mathematicians of all time (he pretty much shows up on anyone's top five list). And Professor William Dunham reveres Euler as the very top of the heap. In this video he entertainingly makes the convincing case for Euler -- Dunham talks for about an hour, followed by 30 mins. of question-answers -- for such a long presentation it maintains interest well:

You'll learn what i^i equals (and how Euler computed it), as well as Euler's better-known contributions, all accomplished in an era long before computers and calculators.
One odd, quirky side-note: it turns out that of the top 5 mathematical formulas/results (as voted on somewhere) 3 come from Euler and the other 2 from Euclid... just an interesting twist that mathematicians with 2-syllable names beginning with "Eu" are responsible for so much powerful math! (...uhh, in the future, please just call me Eushek).




2) No promises that it'll get you thinking as sharply as Euler, but the below post offers a nice primer on mathematical thinking/proof (based on logic and abstract reasoning), which I think may be similar to the approach Keith Devlin takes in his Coursera MOOC course on the same subject (but someone feel free to correct me if the comparison is off-base).

http://amininima.wordpress.com/2013/07/25/how-to-prove-somethin/

Beautiful Math!

Interestingly, this "business" site is listing "the 11 most beautiful math equations" (you have to click through them one-by-one):

http://www.businessinsider.com/the-11-most-beautiful-math-equations-2013-1#general-relativity-1

EXXXXXCEPT that it DOESN'T include Euler's most famous identity (even though it includes another Euler formula). How is that possible??? Is the below not THE MOST beautiful equation in mathematics by near-unanimous decree!?:

Anyway, if you've practiced enough with Vi Hart, you may be able to follow along with this fellow!:

==> AFTER composing the above post I discovered Keith Devlin, writing on Twitter, saying he had indeed submitted Euler's Identity for the above article but somehow it didn't make the cut... UNbelievable!!

"Dr. Euler's Fabulous Formula"

Nice recent post on possibly mathematics' most famous or awe-inducing equation, e^iπ+1=0 :

http://tetrahedral.blogspot.com/2012/02/euler.html

e^i(π) + 1 = 0

Astrophysicist Adam Frank waxes poetic (almost) over Euler's "incomparable and glorious" Identity, involving "five magic numbers," and "beauty" (...with Justin Bieber thrown in for good measure):

http://www.npr.org/blogs/13.7/2010/09/02/129610905/best-equation-ever?ft=1&f=114424647

Frank asks, "Why are so many mathematically inclined folks sent into paroxysms of delight over this string of symbols which seem like gibberish to others," and then he proceeds to answer the question for the reader.