Pascal's triangle
Pascal's triangle is a beautiful part of the mathematics with many exciting patterns and properties.
One of the mesmerizing properties is the following:
The value of a row, if each entry is considered a decimal place (and numbers larger than 9 carried over accordingly), is a power of 11 (11^{n}, for row n).
Let us examine and visualize this.
- We configure the number of rows, n (counting from row 0).
- We display the corresponding triangle.
- Below the triangle, we sum up the entries from the last row in the triangle.
- Finally, we calculate 11^{n} and compare that value to the last row in the triangle and more importantly to the sum of the entries from the last row.