INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More

Every week we dedicate an hour to Beautiful Mathematics - the Mathematics that shows us how Beautiful is our Intellect. Today we are going to discuss the Fermat's Little Theorem.

This week, I decided to do three beautiful proofs in this one-hour session...

**Proof of Fermat's Little Theorem**( via Combinatorics )

It uses elementary counting principles. Here is a Wikipedia resource to learn it.

**Fibonacci Tilling**

This is about how we will prove that the number of ways we can cover a 2xn board with a 2x1 dominoes is the same as - the n-th Fibonacci Number.

We will also discuss some identities related to the Fibonacci Numbers using this idea of the Tiling.

For eg: .

**Sylvester - Gallai Theorem**and**Extremal Principle**

Here, we will show the proof of the theorem which states that

The **Sylvesterâ€“Gallai theorem** in geometry states that, given a finite number of points in the Euclidean plane, either

- all the points lie on a single line; or
- there is at least one line which contains exactly two of the points

This will introduce the students to the idea of the Extremal Principle and the Well Ordering Principle.

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

JOIN TRIAL
Google