The triangle works like this: On the first row, you only write the number 1. Then to make the next rows you add the number above and to the left with the number above and to the right to find the new value. Lastly, if there isn't a number to the right or left, then you put a zero in its place.
The numbers used in the triangle were originally from studies of binomial numbers combinatorics (how cool)! from India and the Greek studies of figurate numbers. His triangle was already discovered in China in the early 11th century due to a Chinese mathematician Jia Xian, who lived from 1010 to 1070. Next, Yang Hui in the 13th century formally presented the triangle and how it's still called Yang Hui's triangle in China. I think this brings up a really interesting point because all around the world during earlier times people were constantly making discoveries but in today's world only a few people are actually credited. I think in the US, for instance, we never mention Yang Hui because the education system puts such an emphasis on Western ideals. Back then it would be totally understandable due to a lack of communication systems but at the same time I believe that education overall would be more valuable if American students could learn more about histories of concepts and ideas from other places in the world to be better informed people. I also just find facts like this to be really neat!
Here are visual representations of the
Ancient Chinese patterns:
Number patterns in the triangle:
Odd and even numbers:
Exponents of 11:
Horizontal sums (they double each time!):
.http://en.wikipedia.org/wiki/Pascal%27s_triangle
http://www.mathsisfun.com/pascals-triangle.html
