Math EE - Euler's Number (mathematical constant)

[beth0525]

Topic: Euler's Number

Question: What is the definition of "e" and what are its applications?

I have already begun research on my question, but I am wondering whether I should change its wording. My moderator seems okay with it but I am still unsure. So far, in terms of applications I have:

- Euler's Formula

- Proof that pi is transcendental

- Bernoulli number

- Hyperbolic Functions

Right now, I have been trying to work through each application on my own, so that I am doing my own mathematics which I am told is impressive. However, it has been difficult to find sources of research. I recently came upon some sections of a book written by Euler, but it is in Latin.

My question is, will interpreting the explanations in Euler's book (originally in Latin) when he works through the definition of e and Euler's formula by way of mathematics be appropriate for my essay? I have already begun this process and it makes it easier to do my own original work because I do not understand Latin so I work through Euler's steps mathematically rather than through his explanations. The problem is that my moderator is afraid it will make the essay into an English EE, rather than a Math EE.

Any comments on my topic and question are appreciated as well. Thank you for just reading this! I know this is a difficult topic, but I sincerely love mathematics and any ideas on my essay or just in general are fantastic! Hope everyone has an amazing day!

[citizenoftheuniverse]

Well I at least am very impressed with your EE topic and methodology I don't think your paper will turn into an English EE at all, working through Euler's mathematics seems very much related to math. Indeed, since you don't speak Latin, you cannot analyze the language at all, making it virtually impossible for this to turn out like an English EE. To me, it sounds kind of like a math IA to be honest .

I do think your question could be more focused though. It seems very general compared to your research, maybe you could key in on your focus more?

In the EE guide, for 2/2 in criterion A, it says:

"The research question is clearly stated in either the introduction or on the title page and is

sharply focused, making effective treatment possible within the word limit."

I don't know if your question has "sharp focus", even though I feel like your actual research does.

The EE guide has a section on mathematics and appropriate titles:

http://www.dominics-int.org/files/Extended_Essay_Guide_from_2013.pdf

[beth0525]

Thank you so much! I will definitely continue with my research and interpreting Euler's work, since I think it may be a strong point in my essay.

Since I have more focused research, I will take your advice and make my question have more of a "sharp focus" as you have stated. I will talk it over with my moderator and definitely review the EE guide again. Thanks again!