# INTRODUCTION

This is a different post from my usual style – there will be no pictures, and just the one link which I feel must be shared and which will feature at the end of the post.

# FORTY

It is inevitable when writing about the number 40 that there will be considerable overlap with the detail contained in Derrick Niedermann’s wonderful book Number Freak but I hope that some of the stuff I come with is new. One of the things Niedermann talks about is the use of forty in ancient times to denote ‘a large number’ in which he context he mentions various biblical references and the tale of Ali Baba and the Forty Thieves – which reference particularly appeals as I am the proud owner of both a four volume boxed set of the complete 1,001 nights and a Folio Society edition of the highlights.

## SOME OF THE PROPERTIES OF THE NUMBER 40

It can be expressed as the sum of a square and a triangle in two different ways: Two squared added to the eighth triangle number or five squared added to the fifth triangle number (note 8+2 = 10 and 5+5 = 10).

It is both double and quadruple a tetrahedral number (10= 1+3+6 = the sum of the first three triangle numbers and 20 + 1+3+6+10 = the sum of the first four triangle numbers).

It is the sum of the fourth triangle and the fourth pyramid number (10 = 1+2=3+4 and 30 = 1+4+9+16) and it is also thus the sum of third tetrahedral number and the fourth pyramid number.

Another connection of two fours and forty is that four squared plus 4 factorial = 16 + 24 = 40.

## WHY THE NUMBER 40?

I have written about the number 40 because today is my 40th birthday and I thought this would be a fun way to commemorate the landmark for followers of my blog.