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.
