# Pascal's Triangle

n = + 1 rows

Numbers
Binomial Coefficients

## Using the Applet

Choose the number of rows to display (capped at 30+1) and whether you'd like the cells to be labeled with binomial coefficients or the integer value of the coefficient. Then, choose which property to explore:
• Play Sums
Watch the triangle's construction by sums. The outer cells of the triangle are labeled 1. Each interior cell is the sum of the two cells immediately above it.
• Play Hockey
Click on an outer cell. The possible interior entries to choose from on the associated diagonal will be highlighted. Click on any of these interior entries to see the hockey stick property.
• Play Sierpinski
See the entries of the triangle shaded by parity. In the applet, the odd valued cells will be darkened and even valued cells will remain white. The effect is particularly striking when at least 20 rows are displayed.
• Play Triangular
Highlight the sequence of triangular numbers, found on the third diagonals of Pascal's triangle.
• Play Squares
Reveal the sequence of square numbers hidden in the triangle, formed by the sum of adjacent triangular numbers on the third diagonal.
• Play Primes
Highlight the primes found on the second diagonals. Note that if a prime is found, every interior cell's value in that row will be divisible by the prime.
• Reset
Clear the triangle.