The Euler Archive(eulerarchive.maa.org)

52 pointsby jacquesm8 lat temu6 comments

eulerarchive.maa.org

http://eulerarchive.maa.org/

6 comments

I read a bit of original Euler material on the elastica and Euler spiral for my PhD thesis [0] on interactive curve design, devoting two chapters to such history. I personally found it fascinating and beautiful.

[0] http://levien.com/phd/phd.html

enriquto8 lat temu

So it's you! I read your thesis a few years ago, and recommended it to many people. I enjoyed the figures of elastica solutions with varying parameter, and I spend my time playing with spiro paths in inkscape; sometimes you get really wicked curves. Thank you so much, I love your work!

sf018 lat temu

Anyone has suggestions on good papers in English translation from the archive? Here's one that is the first published proof of Fermat’s Little Theorem (link to translation at bottom of page):

http://eulerarchive.maa.org//pages/E054.html

svat8 lat temu

Euler's first major work, the one that brought him fame, was his solution to the Basel problem (https://en.wikipedia.org/wiki/Basel_problem), when he was 28. Namely, he found the sum of the reciprocals of the squares of the integer, i.e. the value of the series (1 + 1/4 + 1/9 + 1/16 + ...), to be π²/6.

According to https://faculty.math.illinois.edu/~reznick/sandifer.pdf Euler gave three solutions in his 1736 paper now numbered E41: http://eulerarchive.maa.org/pages/E041.html ("De summis serierum reciprocarum" = "On the sums of series of reciprocals")

Here is Jordan Bell's translation: https://arxiv.org/abs/math/0506415

mathnmusic8 lat temu

3Blue1Brown has a beautiful explanation of the Basel problem: https://www.youtube.com/watch?v=d-o3eB9sfls

sf018 lat temu

very great, thanks for the reply!

btw, for anyone interested in Euler, these two books (kind of pricey) are worth seeking out:

Introduction to Analysis of the Infinite - Book I and II