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Joel Young

What is the coolest and most practical math equation?

November 5, 2009

I know that many of you will look at the topic of the blog and give a big “ick” or some other guttural sound that I don’t know how to spell. To you I offer my sympathy. Of course, for the rest of you that choose to read on, you may be wondering what in the world this topic has to do with a wireless blog. For you I confess that my mind has been rejuvenated by what I will term cool math thoughts and the direct tie to wireless will need to be made clear in a future blog due to the length limitations placed upon me by the curators of the blog. For you, I request your patience.

Recently the eldest of my four sons went off to college. As a freshman at Arizona State, he has declared a major in math and psychology. I discovered that one of the coolest things about having a kid in college is that I get the most amazing flow of text messages. These messages offer up opinions, pose questions and also include the occasional challenge. They cover topics ranging from social justice, to ancient philosophy, to integration using trigonometric substitution, intertwined with the proverbial need for more snack food. During one of these text conversations, I learned that my son’s favorite number is e (not the letter, but the root of the natural log) and that his professor had promised to prove that

where i is the imaginary number representing the square root of -1.

I didn’t remember having a favorite number or a favorite equation for that matter, but after hearing my son’s explanation as to why e is his favorite number, I thought I should probably find favorites of my own. Then it hit me and I realized that I had a favorite equation, it had just been forgotten, lost in the sea of power point slides and ROI calculations over 25 years; embedded in that equation is my favorite number. My favorite equation is Euler’s Formula:

Most of math, electrical engineers and physicists would agree that Euler’s formula is a work of art, defining a relationship between and exponential function and trigonometric functions using complex numbers, enabling us to do such cool things as high speed modulation of digital signals. Of course, by some manipulation and plugging in π/2 for x, and raising both sides to the i^th power, you also get…

How cool is that, if you raise the imaginary number i, to the imaginary power of i, you get a real number, Hence, metaphorically letting your imagination go can result in something real, no matter how irrational it may be. My favorite number is i. Let your imagination run wild!

Posted by Joel Young on November 5, 2009 | Comments (13)

November 21, 2009

In response to: What is the coolest and most practical math equation?
Casual observer commented:

"non-conclusion jumper" made a statement of (apparent religious) belief, "I believe that their simplicity and logic demonstrates that there is no need for a God, as long as there are set rules in the Universe." If there is a set of rules, who's the author? This question was answered by the greatest mind in all of modern humanity, who was also the discoverer of the relationship between mass and energy, when he said, "God does not play dice with the universe.", ... Albert mc^2instein.

November 13, 2009

In response to: What is the coolest and most practical math equation?
Wondering in Roanoke commented:

Another area of interest would be contour integration and the theory of residues. This is the basis for the inverse of the Laplace Xform and heavily utilizes the properies of the natural log. 2(pi)*i is the residue of 1/s at the origin. This plays heavily into the importance of "e" and the backround of Euler's Identity. I find this one of the most interesting facets of mathmatics. I am half kidding about the proof of the existence of God, though as is mentioned in another posting, "something is going on here" ...

November 13, 2009

In response to: What is the coolest and most practical math equation?
non-conclusion jumper commented:

There is nothing close to a proof of the existence of God here. What you should consider is how this could NOT be the case in a logical, sustainable Universe. To do this, look at the axioms that are used to produce whatever equation you consider to be God-prooving. If you believe that these axioms demonstrate the existence of God, then we are on a different level altogether. Rather, I believe that their simplicity and logic demonstrates that there is no need for a God, as long as there are set rules in the Universe.

November 13, 2009

In response to: What is the coolest and most practical math equation?
Alex Knox commented:

Mathematics is such a great subject.
My favorite is the exponential form of a complex number: e^jθ=Cosθ+jsinθ

November 13, 2009

In response to: What is the coolest and most practical math equation?
I Heart Trig commented:

The Pythagorean Theorem (a^2 + b^2 = c^2) is definitely both simple to remember and very useful... But my favorite is the quadratic: x=[-b +- the square root of (b^2 - 4ac)]/2a
Pi for the win!!!

November 13, 2009

In response to: What is the coolest and most practical math equation?
just me commented:

how about this one
L R
- = -
l E
L = length of effort arm
l = length of resistance arm
R = resitance weight or force
E = effort force
Something much simpler and that is a part of everyone's life, even if they don't know it.
Pretty good, Huh?
Theres another simple equation you mite know.
2
E=MC
Energy = Mass x speed of light squared
E = energy
M = Mass
C = speed of light (otherwise refered to as constant)
Another pretty nifty math equation, don't ya think?

November 13, 2009

In response to: What is the coolest and most practical math equation?
kirt blattenberger commented:

dork

November 13, 2009

In response to: What is the coolest and most practical math equation?
GE commented:

For practicality, its hard to beat C^2=A^2+B^2 ...

November 13, 2009

In response to: What is the coolest and most practical math equation?
Curt commented:

It can't hurt to ask: WHY should Euler's equation hold in an otherwise chaotic cosmos?
I don't know about God, but SOMETHING's going on to make this so.

November 13, 2009

In response to: What is the coolest and most practical math equation?
Wondering in Roanoke... commented:

Somewhere here may be close proximity to the proof of the existence of God.

November 13, 2009

In response to: What is the coolest and most practical math equation?
WaltP commented:

I know a mathematician who lives in California at the junction of el Camino Real and el Camino Imaginary.

November 13, 2009

In response to: What is the coolest and most practical math equation?
David Pinsky commented:

My favorite form of this equation is:
e^2(pi)i-1=0
All of teh most usefull and therefore coolest numbers; 0,1,2,e,i,and pi all appear exactly once in the expression, which neatly relates them all!

November 13, 2009

In response to: What is the coolest and most practical math equation?
charliew commented:

And I thought I was alone! Agree on my favorite being Euler, resulting in:
e^(i*pi) = -1

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