At the convention this year in both my Masters With the Master and Afternoons With Larry sessions, the question “What does e(iπ) mean?” came up. This document [1] explores this question in greater depth.
As a bonus, I also answer the question “What happens to a number when you multiply it by i?”
Feedback and lively mathematical banter are encouraged and appreciated.
6 Comments To "Zeroing in on Curriculum and Instruction: What Does e(iπ) Mean?"
#1 Comment By John Van Horn On September 17, 2015 @ 10:29 am
can’t access the document
#2 Comment By Ewan Barr On September 17, 2015 @ 11:30 am
The link to the document is not active
#3 Comment By Mathnasium Matters On September 17, 2015 @ 11:40 am
Thanks for letting us know, John and Ewan. I fixed the link and it’s working on my end. If you continue to experience issues with it, please let us know.
Best,
Damaris
#4 Comment By Luke Sciberras On September 17, 2015 @ 12:43 pm
Cool topic! Another great addition to ‘The Larry Files’!
#5 Comment By James Pinato On September 17, 2015 @ 3:33 pm
Hi All,
This is why using polar coordinates is amazing because they can be used with the complex plane!
Another way we can show that e^(i*pi)=-1 is through the usage of some heavy linear algebra/calculus via a proof using a couple of power series. Specifically, why e^(i*x)=cos(x)+i*sin(x) for all x. In most pre-calc books, you would see this represented as cis(x).
As long as we know the basics for what the Maclaurin series for sin(x) and cos(x) look like, the proof is quite elegant and clever.
Best,
James Pinato
Mathnasium of Poway
#6 Comment By Joshua Klarmann On March 10, 2016 @ 3:12 pm
I wish we could comment in LaTeX, would love to supply that proof.