Math is a language that translates throughout the world.Blaise Pascal (1623-1662), a French mathematician, created what we today call, Pascal's Triangle. With his triangle, containing many mathetmatical patterns, the language of math helps us to better recognize mathematical sequences, and problem solving strategies.
Some Patterns found in Pascal's triangle
(outlined in red) we can see the outside diagional of the triangle, all the numbers are 1's.
outlined in light blue) we notice an arthmatic sequence: numbers 1-13.
outlined in light blue) we notice an arthmatic sequence: numbers 1-13.
Next, we have a pattern often called the "hockey stick pattern". As you can see with the numbers outlined in a pattern that looks to be the shape of a hickey stick; when a diagonal of numbers are selected starting with any of the 1's bordering the sides of the triangle and ending on any number inside the triangle on that same diagonal, the sum of the numbers inside the selection is equal to the number below the last number in the selection that is not on the same diagonal itself.
With this pattern of row sequence, we can follow the pattern of the powers of the number 2, all the way through 2^13th.
The next pattern is found by taking the sum of the rows, as seen in this diagram.
Just from the short lesson we have done in class, I have found that Pascal's Triangle is very interesting. I would have never guessed that there were so many patterns. I think looking at all the different patterns and sequences strengthens our learning strategies. It makes us look into things a little more than we might normally have. When I first thought of all the patterns in this triangle, I would have never thought of the "hockey stick" pattern. I thought that was very interesting.
ReplyDeleteI know that Pascal's Triangle was a little difficult for me to understand at first. In class we looked at a number of different patterns, which made it a little easier, as does this blog post. I agree with Ashley, I would have never seen the hockey stick pattern as well, but it is kind of cool. This is a good activity for people to search for patterns because there are so many of them.
ReplyDeleteThis was very interesting for me to learn. I had a hard time seeing the patterns at first but once it came to me, it was as if they didn't stop coming. I agree, the hockey stick pattern is quite difficult to find, but this would be an excellent project in the classroom to get the students thinking!
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