Diagonal Patterns

The triangle has diagonal patterns that include ones, counting numbers, and triangular numbers.

Powers of 2

If you add

horizontally,

they are all powers of 2.

Rules

Ones always go along the outsides of the triangle

Continue by adding the numbers above to get the next number

**Blaise Pascal**

**Pascal's triangle**

One toy that is used is this counting ring toy.

How pascal's

triangle is used today?

Learning!

Infants and young children are learning with Pascal's Triangle all the time.

This toy helps by exposing the child to numbers, colors, and patterns. Also, the number of rings get smaller just like the triangle.

This toy is most like Pascal's Triangle because it is smallest at the top and it gets bigger and bigger as you go down. This toy exposes the child to size, shapes, colors, and patterns.

Probability is an other way that Pascal's Triangle is used today.

Blaise Pascal was born on June 19, 1623. He was born in Auvergne, France, now Clermont-Ferrand. Pascal's father was a mathematician. As a child Pascal was a math prodigy. He did not go to school, his father taught him. In 1642, he invented the Pascaline. This machine was the first calculator. It has dials that look like gears. You turn the dials clockwise and numbers appear on the output dial. He made this machine for his father, a tax collector, to make calculating numbers easier for him. In the late 1640s, Pascal wanted to follow in Evangelista Torricelli’s steps. So he focused on physical science. He experimented with atmospheric pressure. Pascal proved Torricelli's theory involving the cause of barometrical variations. In 1665, Pascal accidentally invented his roulette machine when he was trying to make a "perpetual motion machine" . While he was working on his roulette machine, Pascal started communicating with Pierre de Fermat. While he was talking with de Fermat, he was experimenting with the likelihood of outcomes on rolls of a die. He found that these events did not occur randomly. Pascal died on August 19, 1662.

Another toy is the stackable rings.

Work Cited

http://www.mathsisfun.com/pascals-triangle.ht

http://www-history.mcs.st-andrews.ac.uk/Biographies/Pascal.html

http://www.maths.tcd.ie/pub/HistMath/People/Pascal/RouseBall/RB_Pascal.html

http://www.credomag.com/2012/10/05/pascal-and-skepticism

http://www.math.rutgers.edu/~erowland/pascalssimplices.html

http://www.educationaltoysplanet.com/1-to-5-ring-counter.html

www.pistachioproject.com/2012_12_01_archive.html

http://www.biography.com/people/blaise-pascal-9434176

http://www.britannica.com/EBchecked/topic/725527/Pascaline

http://onlinemathcircle.com/wiki/index.php?title=Pascals_Triangle

Exponents of 11

If you take the numbers from each row, they form exponents of 11, but there is a trick.

11^5