Sunday, 24 February 2013

SUNDAY, 24 FEBRUARY 2013

Today is the $55^{th}$ day of the year.

$55 = 5 \times 11$

$55$ is a member of the Fibonacci Sequence, is a Triangular Number and is in Pascal's Triangle. Actually, the fact that it is a triangular number implies that it is in Pascal's triangle. This is because, from the third row of the triangle down, the third number in each row is the next member of the triangular number sequence, see here for an illustration.

Slightly less trivially, $55$ is a member of the Toothpick Sequence which is nicely illustrated here or there is an animated version here. To use this animation, leave everything as it is and just click the Next button. When you see the value 10 in the field labelled N: then there are 55 toothpicks in the diagram.