Pascal’s Triangle Triangles

Pascal's Triangle

Ahh, a sad day – this is the last of my planned Pascal’s Triangle posts. Let’s all take a moment to ponder the wonders we have found… Relationships between networks, probability, sequences of counting numbers, triangular numbers, square numbers, powers of 2, powers of 11 and the Fibonacci numbers. What better place to finish our tour of a wonderful maths concept than with colouring in?

You may be thinking “she’s lost her mind! What does colouring in have to do with maths?!”

But even if you’re not, I’m going to answer the question anyway! Do you remember colouring in a 100-square when you were at school? If you colour in all of the multiples of 2 you find a pattern, and it’s the same for the other multiples too. You could also colour in multiples of numbers to find the prime numbers and that was pretty too.

So today I have done some colouring in for all of us! And mostly for me. But for you too. Here is a Pascal’s Triangle you can use for this purpose, do print them if you would like to.

Pascal's triangle filled

So to start off our colouring, let’s do the multiples of two. This means colour in anything in the two-times table, a.k.a. all the even numbers:

Multiples of 2

How pretty is that?

If you imagined that the lone coloured hexagons were triangles (and the bigger triangles-of-hexagons had straight sides)  what we see is called the Sierpinski Triangle and it is a type of fractal pattern. And it is also pretty 🙂 If you were teaching this in a lesson you could ask students to predict what the next line would look like based on the line above (without doing any adding first!). Would there be triangles with sides of length 1, or 2, or 3; which row will be coloured all the way across the triangle like 8 is and so forth.

Think about the 100-square you coloured in when you were small. Do you remember how the different multiples produced different patterns? I have the triangles coloured for the multiples of 3, 4, 5 and 6 here. You could ask students to predict what the different patterns might be for different multiples, then colour them in and find out if they were right.

I hope you’ve had as much fun with Pascal’s Triangle as I have (you might need to colour some in to have that much fun though), I think it is just amazing how many areas of maths link together through this one concept! Thank you for joining me for Pascal’s Triangle and I look forward to talking more with you next week about one of the things I’ve already shared in relation to Pascal’s Triangle. See if you can guess which one it will be!

NumberJacqui

Posts in the Pascal’s Triangle series:

Pascal’s triangle with routes

Pascal’s Triangle with Probability

Pascal’s Triangle Sequences part 1

Pascal’s Triangle Sequences Part 2

Pascal’s Triangle Triangles

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s