Pascal's Triangle Calculator
Generate Pascal's Triangle and explore its fascinating mathematical properties.
Triangle Size
Find Specific Value
C(5, 3) =
10
Pascal's Triangle
1
11
121
1331
14641
15101051
1615201561
172135352171
Selected Value
10
Row 5, Position 3
Row 5 Properties
Sum2^5 = 32
Alternating Sum0
Values[1, 5, 10, 10, 5, 1]
Fibonacci Diagonals
Diagonal sums form Fibonacci sequence:
1123581321
Key Properties
- Each row is symmetric
- Sum of row n = 2^n
- Entry (n,k) = C(n,k) = n!/(k!(n-k)!)
- Each number = sum of two above it
- Contains triangular, tetrahedral numbers
- Diagonal sums give Fibonacci sequence
Applications
- Binomial expansion coefficients
- Probability calculations
- Combinatorics problems
- Number theory patterns