Conclusion

You should now have a better understanding of the intricacies of Pascal's Triangle.  It is an amazing mathematical tool that has seemingly unlimited patterns and applications throughout various mathematical topics.  Just when we think we've found all it can possibly be used for, someone discovers another pattern and/or application.  I hope you have developed a greater appreciation for its usefulness, even if you don't understand all of those uses.  If you are interested in exploring more about this topic there are thousands of websites about Pascal's Triangle that can be found by typing in key words such as "Pascal's Triangle" into a search engine like Google.  Sources range from extremely elementary to extremely complex.  Here are a couple more good sites not included in the "Research Phase":

Pascal's Triangle and Fibonacci Numbers:

http://goldennumber.net/pascal.htm

All About Pascal's Triangle and Related Topics:

http://milan.milanovic.org/math/english/contents.html

Happy exploring!