Scientific American* presents *Math Dude* by Quick & Dirty Tips. *Scientific American *and Quick & Dirty Tips are both Macmillan companies.*

Now that we’ve learned how to draw Pascal’s famous triangle and use the numbers in its rows to easily calculate probabilities when tossing coins, it’s time to dig a bit deeper and investigate the properties of the triangle itself. Why is that an interesting thing to do? Because it turns out that Pascal’s triangle is not a one trick pony—it’s useful for a surprising number of things.

And not only is it useful, if you look closely enough, you’ll also discover that Pascal’s triangle contains a bunch of amazing patterns—including, kind of strangely, the famous Fibonacci sequence. Where is it? And what other patterns are hidden in the triangle? Stay tuned because that’s exactly what we’re talking about today.

**Did Pascal Discover Pascal’s Triangle?**

Before looking for patterns in Pascal’s triangle, let’s take a minute to talk about what it is and how it came to be. As you’ll recall, this triangle of numbers has a 1 in the top row and 1s along both edges, and each subsequent row is built by adding pairs of numbers from the previous. So the first row is just 1; the second row is 1, 1; the third row is 1, 2, 1; the fourth row is 1, 3, 3, 1; then 1, 4, 6, 4, 1; and so on.

We keep calling this pattern “Pascal’s triangle,” but who is that? And was he actually the first person to study this pattern? Well, Pascal was a French mathematician who lived in the 17th century. And, no, he was not the first person to study this triangle…not by a long shot. It turns out that people around the world had been looking into this pattern for centuries. So why is it named after him? It’s probably partly due to cultural biases, and partly because his investigations were the most extensive and well organized. Which meant that soon after publishing his 1653 book on the subject, “Pascal’s triangle” was born!