History
Which mathematician is Pascal’s Triangle named after?
Blaise Pascal
What number appears at the top of Pascal’s Triangle?
1
Which row gives the coefficients for expanding ((a+b)^2)?
Row 2, (1,2,1), when counting the top as row 0.
What shape does Pascal’s Triangle form?
A triangle
Was Blaise Pascal the first person in history to discover this triangle?
No. It was studied by mathematicians in other cultures before Pascal, including China, India, and Persia.
How do you find the numbers inside each new row?
Add the two numbers directly above each position. Each row also begins and ends with 1.
Expand ((x+1)^2).
(x^2+2x+1).
What is the sum of the numbers in row 4, (1,4,6,4,1)?
16, which equals (2^4)
Around which century did Blaise Pascal publish an important work about the triangle?
The 17th century, in 1654.
What is the sum of the numbers in the row (1,4,6,4,1)?
16, because (1+4+6+4+1=16).
Expand ((x+y)^3) using Pascal’s Triangle.
(x^3+3x^2y+3xy^2+y^3).
What are the first five numbers in the diagonal pattern that gives the natural numbers?
(1,2,3,4,5), found in the second diagonal when counting the outer 1s as the first diagonal.
What is one historical reason Pascal’s Triangle became important
It helped mathematicians study probability, combinations, and binomial coefficients.
What is special about the numbers on each side of Pascal’s Triangle?
The numbers on both sides are always 1, so every row starts and ends with 1.
Expand ((x+2)^3)
(x^3+6x^2+12x+8)
Name two applications of Pascal’s Triangle besides expanding binomials.
Probability and combinations. It can also help count possible selections.