Welcome again to the wonderful but sometimes weird world of wireless comms, written by Joel Young, CTO of Digi International.
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 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 favourite 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 favourite number or a favourite equation for that matter, but after hearing my son's explanation as to why e is his favourite number, I thought I should probably find favourites of my own.
Then it hit me and I realized that I had a favourite 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 favourite number. My favourite 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 favourite number is i. Let your imagination run wild!
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 favourite 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 favourite number or a favourite equation for that matter, but after hearing my son's explanation as to why e is his favourite number, I thought I should probably find favourites of my own.
Then it hit me and I realized that I had a favourite 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 favourite number. My favourite 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 favourite number is i. Let your imagination run wild!
Comments (2)
Surely the best equation is
e^j.pi +1 = 0
Yes, it is only a point aspect of the general case you give above (ie x = pi) but it so elegant: five of the most important numbers in one equation.
Electrical engineerrs would disagree with your above: we use 'j' not 'i' (which is current)
Posted by El Rupester | February 19, 2010 10:41 AM
Posted on February 19, 2010 10:41
In terms of practicality, how about Ohm's law? I = V/R
Posted by Alun Williams - Electronics Weekly.com | February 23, 2010 7:05 PM
Posted on February 23, 2010 19:05