Pascals Triangle Math 100.docx

Pascals Triangle Ramirez,Joyce Nicka G. W,sat (7:30-9:30)

One of the most interesting Number Patterns is the Pascal's Triangle but what really is the Pascals triangle? According Peter Fox (1998) it is a triangular array of the binomial coefficients. The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top (the 0th row). The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. The triangle may be constructed in the following manner: In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as 0. For example, the initial number in the first (or any other) row is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row. According to Hosh (2019) It is named for the 17th-century French mathematician Blaise Pascal, but it is far older. Chinese mathematician Jia Xian devised a triangular representation for the coefficients in the 11th century. His triangle was further studied and popularized by Chinese mathematician Yang Hui in the 13th century, for which reason in China it is often called the Yanghui triangle ,but according to Coomal(2015) it has been studied throughout the world for thousands of years, particularly in ancient India and medieval China, and during the Golden Age of Islam and the Renaissance, which began in Italy before spreading across EuropeThe pascals triangle can also be a fun way of learning patterns and numbers as said by Lemay (2009) Pascal's triangle shows many important mathematical concepts like the counting numbers and the binomial coefficients.

References: Peter Fox (1998). Cambridge University Library: the great collections. Cambridge University Press. p. 13. ISBN 978-0-521-626477. William Hosh (2019). Pascal's triangle,https://www.britannica.com/science/Pas cals-triangle Gerald Lemay (2009). The Relationship Between Pascal's Triangle & Combinations, https://study.com/academy/lesson/therelationship-between-pascals-trianglecombinations.html Robert Coomal (2015).Properties of Pascal’s Triangle, https://www.livescience.com/51238-propertiesof-pascals-triangle.html