I am to give a mathematics talk in a couple of weeks and I am writing to request suggestions for possible topics of the talk. The relevant information is as follows:
(1) The audience for the talk consists of first and second year students in science; some of the students might be first or second year students in mathematics. In particular, I cannot expect that any member of the audience is particularly knowledgeable in mathematics; I think at a minimum I can assume a knowledge of the elements of calculus. However, I would prefer the talk to not be directly based on calculus.
(2) The audience consists of very intelligent students. Nevertheless, I probably should not expect the audience to have to do a great deal of thinking while listening to the talk.
(3) The talk is to be 15 minutes in length. In particular, I probably have to focus on one theme during the talk.
I would like to talk about a mathematics topic that fits the following description:
(a) The talk appeals to an intelligent person who is not particularly knowledgeable in mathematics but is not too trivial that it does not appeal to a mathematics student.
(b) The talk illustrates a beautiful piece of mathematics.
(c) The talk is solely based on mathematics.
Thank you very much in advance for all suggestions for the topic of the talk! I will certainly acknowledge you in the talk if I use your suggestion for the topic of the talk.