Basics
What is the value at the very top of Pascal’s Triangle?
1
What number appears at both outer edges of every row in Pascal’s Triangle?
1
Pascal’s Triangle is used to find coefficients in which type of algebraic expansion?
The binomial expansion
What was the nationality of the mathematician Blaise Pascal?
French
What kind of symmetry does Pascal’s Triangle have across its vertical axis?
Mirror symmetry (left and right sides are symmetrical)
In Pascal’s Triangle, each number is the sum of which two numbers?
The two numbers directly above it to the left and right
The sum of the numbers in each row of Pascal’s Triangle equals what mathematical pattern?
Powers of 2 (1, 2, 4, 8, 16...)
What are the coefficients of the expansion (x+y)³ according to Pascal’s Triangle?
1, 3, 3, 1
Who is the triangle named after?
Blaise Pascal
What famous fractal appears when you shade all the odd numbers in Pascal’s Triangle?
The Sierpinski Triangle
What shape is formed when you write out Pascal’s Triangle?
A Triangle
What sequence appears in the second diagonal of Pascal’s Triangle (1, 2, 3, 4...)?
The Natural Numbers
Which number in Pascal’s Triangle represents “5 choose 2”?
10
Which ancient civilization studied Pascal’s Triangle centuries before Pascal’s time?
The Chinese Civilization
What kind of pattern is created when you color Pascal’s Triangle using only odd and even numbers?
A repeating fractal or checkerboard-like pattern
What numbers appear in the 4th row of Pascal’s Triangle?
1, 3, 3, 1
Which famous sequence appears when you add the shallow diagonals of Pascal’s Triangle?
The Fibonacci sequence
In probability, Pascal’s Triangle is most often used to calculate what?
Combinations
What is Pascal’s Triangle called in Chinese mathematics?
Yang Hui’s Triangle
In binary form, the number of odd numbers in row 2ⁿ is always equal to what?
A power of 2
How many numbers are there in the 6th row of Pascal’s Triangle?
7
What pattern is formed by the third diagonal of Pascal’s Triangle (1, 3, 6, 10...)?
The triangular numbers
What does each entry in Pascal’s Triangle represent in combinatorics?
The number of ways to choose k items from a set of n (combinations)
Which Persian mathematician described Pascal’s Triangle in the 11th century?
Omar Khayyam
What is the name of the identity in Pascal’s Triangle where a diagonal set of numbers adds up to the number just below and to the right of the last in the set?
The Hockey Stick Identity