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I am a sophomore in college and currently enrolled in a Upper Division Problem Solving class.

I was assigned a final project in which I need to come up with some sort of mathematical investigation problem, which needs to be challenging but doable.

I this class we were exposed to problems which sought to shift our way of reasoning. In other words, it allowed us to view problems from different angles and tackle them.

I will be presenting the problem to my class and it should take them approximately 10-15 minutes to solve.

Everyone in the class has been exposed to at least Calculus 2.

The course covered topics on The Multiplicative Structure of the Number System; Big ideas, Strategies and Models; Functions and Covariation; Proportional Reasoning; and Algebra and the Cartesian Connection.

Big Ideas was described as "central organizing ideas of mathematics…(and are) characteristic of shifts in learners’ reasoning—shifts in perspective, in logic, and the mathematical relationships they set up".

Any brilliant ideas ?

Marco Neves
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  • I don't know how "original" you need to be but this MO post http://mathoverflow.net/questions/48771/proofs-that-require-fundamentally-new-ways-of-thinking seems to be related. Some of the proofs are a little above Calc 2, but you may be able to understand the first example: Euler's (not Euclid's) proof that their are infinitely primes. – Dair May 03 '16 at 08:25

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In the Big Ideas direction, I could suggest providing a mathematical formalisation of the intuitive idea that the period of small oscillations of the pendulum is independent of the amplitude, along the lines of this article.

Mikhail Katz
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