• Dinesh Lahoti

Pascal’s triangle

We have been talking about finding patterns everywhere and in continuation of that series here is a number triangle, commonly known as Pascal's Triangle.

Figure 1

Can you spot the patterns inside this triangle? How many of them can you spot?

Here are a few of the patterns in the pictures below.

Figure 2

Figure 3

Pascal's Triangle is formed by adding two adjacent numbers to form the next number in the series below as shown in figure 1 above. It is a triangular arrangement of numbers. There are different patterns that emerge out of this series. Some of the uses of the emerging patterns out of this triangle are - algebra - expanding binomials, combinatorics, probability - binomial mass function. While these are some serious applications, one can also find some fun patterns like Sierpinski’s triangle, Fibonacci series.

Looking through the history of this pattern, even though it is now known as Pascal's triangle, it was discovered long back in ancient India by Pingala. The same way it was discovered by Amir Khusrao in Persia (now Iran), and its mention is found in Chinese and German texts.

There are a number of such patterns hidden within this triangle. Try finding out more patterns now!

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