I prefer that point of view if you want to understand Euler's identity, and I find John Baez does it even better:
http://math.ucr.edu/home/baez/trig.html
The Baez article does leave it to the reader to convince himself that exp(i*theta) is good notation for a point on a unit circle.
I have problems with the attitude of the article you linked, though. Especially
"Therefore, I’d like to complain to the thousands of people who find Euler’s identity stunning and beautiful."
followed by a snide list of reasons why someone might find it beautiful. It's very common when doing math that something amazing is obvious an hour later. I believe that we are better served by reminding ourselves that (a) nobody knows everything, and (b) the basics facts are actually very beautiful.
I totally agree on the attitude on the blog, the author is clearly working through non-mathematical issues on their own (if you read some of the other entries you can see how those challenges affect their writing). That said, I tend to see it as a counterpoint to mathematics blogs that are bit too gushing the other way. And its amusing the path that is taken as well.
Comments
I prefer that point of view if you want to understand Euler's identity, and I find John Baez does it even better: http://math.ucr.edu/home/baez/trig.html The Baez article does leave it to the reader to convince himself that exp(i*theta) is good notation for a point on a unit circle.
I have problems with the attitude of the article you linked, though. Especially "Therefore, I’d like to complain to the thousands of people who find Euler’s identity stunning and beautiful." followed by a snide list of reasons why someone might find it beautiful. It's very common when doing math that something amazing is obvious an hour later. I believe that we are better served by reminding ourselves that (a) nobody knows everything, and (b) the basics facts are actually very beautiful.
I totally agree on the attitude on the blog, the author is clearly working through non-mathematical issues on their own (if you read some of the other entries you can see how those challenges affect their writing). That said, I tend to see it as a counterpoint to mathematics blogs that are bit too gushing the other way. And its amusing the path that is taken as well.