﻿ Mere Bagatelle
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There are lots of nice mathematical activities for children that generate the pattern of numbers known as Pascal’s Triangle. The numbers are usually represented in a triangle which gets wider and wider. We wanted to put them onto an afghan so our triangle gets wider for seven rows but after that the side bits have been missed off and it tapers back again to form a square. The sequence of numbers is the same but ours just has some missing.

One activity asks how many ways you could go to reach a particular block. Using this afghan that would mean starting at the cream coloured brick in the top left corner and always moving forward towards the dark brown brick in the bottom right corner.

The answer for each brick is found by adding the numbers in the two bricks immediately above it.  If there were two ways of getting to a particular brick and only one way of getting to the brick next to it there would be a total of three possible ways to get to the brick that lies in front of them. The third row has bricks with the numbers 1, 2, 1, so the following row has numbers 1, 3, 3, 1. The numbers start to increase dramatically after a few rows. There are 924 ways of getting to the last brick on this afghan.

The bricks are filet crochet grids with holes filled in to make the shape of the numbers. I had recently been making a piece of filet crochet and, not being a crochet expert, this suddenly struck me as a way of being able to add a written message to an afghan. ‘Writing’ the numbers of Pascal’s Triangle on the bricks seemed an obvious thing to do. It is not always easy to read the numbers, particularly if you get the afghan the wrong way round, but that helps to stop the answers being too obvious.

Mere Bagatelle is a nice way to use up 49 oddments of yarn. Making all the bricks the same colour would not change the mathematics but it might make the afghan look less interesting.

The name, Mere Bagatelle, has a variety of connotations. It can be thought of as something insignificant as this might be if you were taking 49 oddments of yarn with little or no value. It also reminded us of the old-fashioned bagatelle games where balls were fired with a spring and came to rest in various numbered homes. Theoretically, these balls will follow the same pattern if rolling through a regular grid. For some reason, Steve has never liked this afghan. It isn’t one of my favourites though I have a feeling it is not going to fade away. There are aspects of this concept that keep popping back into my head. Also, the pattern of regular pins or spots, like the five on a dice repeated lots of times, is known as a quincunx. I love that word and I am sure that one day it will all re-emerge as something else.

MERE BAGATELLE