Binary Representation of Pascal's Triangle

487 Views Asked by At

When I recently searched Pascal's triangle on Wolfram Mathworld, the following image appeared. enter image description here

Wolfram Mathworld states that this is the binary representation of Pascal's triangle. I am not very familiar with binary representation, and I am not sure how it is generated.

Could any of you provide some explanation or resources to help me understand this beautiful binary representation?

1

There are 1 best solutions below

0
On BEST ANSWER

In this representation, each "hump" represents one row of Pascal's triangle, and the columns in each hump are binary representations of the numbers in the corresponding row of the triangle, left-to-right, least significant bit at bottom.

For example, the row $1,4,6,4,1$ corresponds to

 111
  1
1   1

and the row $1,6,15,20,15,6,1$ to

   1
  1 1
 11111
 11 11
1 1 1 1