Give some interesting facts about Pascal's Triangle.
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The numbers on each row are binomial coefficients. The numbers on the second diagonal form counting numbers. The numbers on the third diagonal are triangular numbers. The sum of the numbers on each row are powers of 2. A series of diagonals form the Fibonacci Sequence.The numbers on each row are binomial coefficients.
The numbers on the second diagonal form counting numbers.
The numbers on the third diagonal are triangular numbers.
The sum of the numbers on each row are powers of 2.
A series of diagonals form the Fibonacci Sequence.
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Answer:
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra
Explanation:
Top 3 Secrets of Pascal’s Triangle
But First…How to Build Pascal’s Triangle
At the top center of your paper write the number “1.”
On the next row write two 1’s, forming a triangle.
On each subsequent row start and end with 1’s and compute each interior term by summing the two numbers above it.
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Secret #1: Hidden Sequences
The first two columns aren’t too interesting, they’re just the ones and the natural numbers.
The next column is the triangular numbers. You can think of the triangular numbers as the number of dots it takes to make various sized triangles.
Similarly the fourth column is the tetrahedral numbers, or triangular pyramidal numbers. As their name suggests they represent the number of dots needed to make pyramids with triangle bases.
The columns continue in this way, describing the “simplices” which are just extrapolations of this triangle/tetrahedron idea to arbitrary dimensions. The next column is the 5-simplex numbers, followed by the 6-simplex numbers and so on.
Secret #2: Powers of Two
If we sum each row, we obtain powers of base 2, beginning with 2⁰=1.
Secret #3: Powers of Eleven
The triangle also reveals powers of base 11. All you have to do is squish the numbers in each row together. Which is easy enough for the first 5 rows, but what about when we get to double-digit entries?
Turns out all you have to do is carry the tens place over to the number on its left