### Draw some triangles

Try this. With 3 straight lines, construct 9 non-overlapping triangles on an alphabet M. This appears in The Simpsons’s 26th season finale “Mathlete’s Feat”!

### When sinx, cosx and e^x goes to a party

$cosx$, $sinx$ and $e^x$ go to a party. $sinx$ and $cosx$ are partying away but $e^x$ is miserable and anti social. $cosx$ and $sinx$ go up to $e^x$ and say ‘what’s wrong, why don’t you integrate?’

$e^x$ replied, It doesn’t make any difference does it?

This little joke should remind students about integrating the three terms. And a side note, they are really related, for instance in Complex Numbers.

### Mathemagic!

Arthur Benjamin is a brilliant mathematician and calls himself the mathemagician. Yes, he performs magic with mathematics. Magic or not, you decide!

This is an interesting probability problem (paradox). And no, this isn’t about the Cheryl’s Birthday Problem.

In probability theory, the birthday problem or birthday paradox[1] concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. -Wikipedia

The above graph shows how many people you need to approach to find someone who has the same birthday with you!

This shows how counter-intuitive probability is! And like what I always tell my students, don’t use intuition for probability but formulas.

### Why is it all triangles in 3D

We see objects all the time and our brains decode the 3D shapes, but how do computers model these shapes and why break it all down to triangles?

### Why is 0! = 1?

This question is probably very baffling to several students. Many students will exclaim $0!=0$ to me, but this is incorrect. To understand why $0!=1$, we need to first look at what $n!$ means; $n!$ is the number of ways to arrange $n$ objects in a row. And we all know that $n!=1 \times 2 \times 3 \ ... \times n$. So shouldn’t $0!=0$?

Think about this, the number of ways to arrange 1 object is 1, that is, put the object there by itself. However, the number of ways to arrange $0$ object is one! Cos there is nothing to arrange so we still have one way to do it.

Give it some thought and feel free to discuss with me!

Related video by Dr James Grime

### Patterns in prime numbers

So you still think prime numbers are random?

Take a look at this really cool project, it kinda reminds me of the sieve of Eratosthenes: El Patrón de los Números Primos: Prime Number Patterns – Jason Davies

You can examine more on divisor plot as well.

Prime numbers has mystified mathematicians for centuries, there seems to be a pattern but mathematicians aren’t able to find a method to predict the next sequence or understand what exact cause prime numbers to be the sequence it currently is.