Describe some of the patterns that emerge in Pascal\'s triangle. Give some examp

ID: 2986489 • Letter: D

Question

Describe some of the patterns that emerge in Pascal's triangle.
Give some examples of how Pascal's triangle is connected to various other parts of mathematics.
Describe some of the practical applications that involve Pascal's triangle.
Explore the history of Pascal's triangle.
- In what places, times and cultures has it been known?
- How did it become known in Europe? Why is it named after Pascal?
- Who was Blaise Pascal anyway? When and where did he live? What else did he do?
- Has credit for this knowledge been unjustly appropriated by Europe?
If you are studying to become a K-12 teacher, share some ideas for lesson plans involving Pascal's triangle. (If you find teaching resources online, be sure to properly cite them.)
Be sure to provide some examples.

Explanation / Answer

1)Hockey Stick Pattern,Fibonacci Numbers,the star of dravid,Parallelogram Pattern,Pascal's Triangle is symmetric .

2)number theorey,Pascal's triangle determines the coefficients which arise in binomial expressions,Pascal's triangle is in the calculation of combinations,central limit theorem.

3)If you just look at the coefficients of the polynomials that you get, you'll see Pascal's Triangle! Because of this connection, the entries in Pascal's Triangle are called thebinomial coefficients.

4)a)2nd century India,1oth century on chandra shastra,1653 greeks study.,10th century chinese

b)Petrus Apianus (1495%u20131552) published the triangle on the frontispice of his book on business calculations in the

16th century. This is the first record of the triangle in Europe,ascal collected several results then known about the triangle, and employed them to solve problems inprobability theory. The triangle was later named after Pascal by Pierre Raymond de Montmort (1708) who called it "Table de M. Pascal pour les combinaisons"

c)Blaise Pascal ( 19 June 1623 %u2013 19 August 1662) was a French mathematician, physicist, inventor, writer and Christian philosopher,described a convenient tabular presentation for binomial coefficients,he contributed much to hydrodynamics hydrostatics.

d)yes

5)https://en.wikipedia.org/wiki/Pascal's_triangle

https://en.wikipedia.org/wiki/Blaise_Pascal

http://mathforum.org/dr.math/faq/faq.pascal.triangle.html

http://wiki.answers.com/Q/What_are_some_practical_applications_of_pascals_triangle