Pascal's triangle

But this is also the formula for a cell of Pascal's triangle.

This gives a way of reading the coefficients from Pascal's triangle as shown on the right.

This is indeed the simple rule for constructing Pascal's triangle row-by-row.

Pascal's Triangle can be extended to negative row numbers.

This recursive formula then allows the construction of Pascal's triangle.

The set of numbers that form Pascal's triangle were known before Pascal.

Pascal's triangle has many properties and contains many patterns of numbers.

The numbers of vertices follow the numbers in Pascal's triangle.

These coefficients for varying n and b can be arranged to form Pascal's triangle.

These figures are obtained from the binomial expansion illustrated by Pascal's triangle.

Some of the results mentioned above can be derived from properties of Pascal's triangle.

Pascal's triangle helps explain why the favored team often loses the World Series.

Writing only dimensions, one obtains a row of Pascal's triangle:

Tetrahedral numbers can therefore be found in the fourth position either from left or right in Pascal's triangle.

He wrote on the binomial theorem and Pascal's triangle.

That is, choose a pair of numbers according to the rules of Pascal's triangle, but double the one on the left before adding.

A second useful application of Pascal's triangle is in the calculation of combinations.

Rule 90 is also interesting because it creates Pascal's Triangle modulo 2.

This is equivalent to saying that the elements in one row of Pascal's triangle always add up to two raised to an integer power.

Overlaying Pascal's triangle onto the pins shows the number of different paths that can be taken to get to each bin.

Pascal's triangle can be made as follows.

These numbers are simple combinatorial numbers that come from Pascal's Triangle.

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

Place these dots in a manner analogous to the placement of numbers in Pascal's triangle.

Today, this triangle is known as Pascal's triangle.