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 ith 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!