Euler appreciation

In the past few years, I started to hear the name Euler pop up in multiple math and mechanical science classes, and I decided to learn a bit more about the man behind all of the math. After researching Euler to write this blog and studying the results of what we can do with Euler’s discoveries, I feel that the post is going to be a bit less of a biography and a little bit more of a Euler appreciation post.  

From a background perspective, one of the many things I learned about Euler is that his last name is pronounced “oiler,” which means that I have been butchering the pronunciation for several years now. He was born in Basel, Switzerland, in 1707, spent a good amount of his time in Saint Petersburg teaching at the Imperial Russian Academy of Sciences, and eventually spent some time teaching at the Berlin Academy. If you’d like to know a bit more about his life and personal detail, this biography has some nice information. For the rest of this, I’d like to dive into some of his work that means a lot to me personally. 

Called by many mathematicians the most beautiful of all equations, one of Euler’s greatest contributions to the world is Euler’s Identity:

You’ll often see a j in the place of that i in engineering applications. Here is a Khan Academy video that walks through how Euler’s Identity can be found from special cases of Taylor series for sine and cosine. You don’t have to understand all of the math behind this to appreciate this amazing discovery. Different sources will give you their interpretation of what makes Euler’s formula so incredible. For us in mechanical engineering, Euler’s identity allows us to model moving systems. It allows us to solve circuits. It helps us mathematically describe things about the world around us. It’s kind of huge.

Euler did a great amount of work for fluid dynamics. In addition to the great body of work he wrote within fluid dynamics, he created equations for the motion of inviscid (no viscosity) fluids. They allow us to relate the change in velocity along a streamline to change in pressure along that same streamline.

Euler wrote a great amount about many topics. Some estimates say he wrote more than 500 books during his life. Some of these works were the Letters to a German Princess which were a series of actual letters he wrote to a real German Princess as a means to tutor her. In these letters, he explained a range of topics from math to physics to religion, all in a way that was understandable to the public. He began by explaining the concept of size by defining a foot and working his way up to the distances between planets. It was a great way to get not only the princess but the general public excited about science. 

Euler also applied his talent in mathematics to other fields. He wrote a few hundred pages on music. One of which was this idea of calculating how good any two notes will sound together. Here’s a video that explains the concept in a bit more depth. It’s not a perfect system, but the way the intervals are ranked in terms of pleasing sound seems about right to my ear. 

 

My dad sat me down one day to tell me a bit about Euler’s work in graph theory because that meant a lot to him, and I’m sure you would get a different perspective on Euler’s work if he or anyone else wrote this blog. We could go into great depth talking about the numerous fields he touched; the man even has a Wikipedia page about things named after him.