### Long, LOOONG overdue

Apr. 10th, 2007 05:30 pm**canijustbejanet**

So rather than actually buying a digital camera myself, or borrowing my mom's, or something sensible like that, 26 months after finishing the afghan based on my userpic, here's an actual post of an actual picture of the actual afghan.

Because I had to marry a guy who had a digital camera in order to have use of one available enough that when I thought "hey, let's get a picture of that" I could. Silly me.

So there it is: SOLS(10). I finished it on January 30, 2005, here's a picture finally.

is a Latin square of order 3.

And then

is a Latin square of order 3 orthogonal to the one above. Orthogonality goes both ways in a pair of Latin squares.

A self-orthogonal Latin square is a Latin square whose entries, when transposed across the diagonal, form a Latin square orthogonal to the original. And that's what we have here.

For about the longest time, the world lived pretty content in the knowledge that there is no pair of orthogonal Latin squares of order 10. But the world was wrong, and they do so exist. So do self-orthogonal Latin squares of order 10. And this afghan is a representation of just such a thing. The inner and outer parts of the squares correspond across the diagonal, and each color represents a value from 1 to 10.

If you want more info about such things, feel free to look up Latin Squares in Wikipedia and Mathworld, or check out the text I learnt from, a good zero-fearing book.

This was done entirely in Red Heart Super Saver acrylic worsted, in White, Black, Cherry Red, Amethyst, Blue, Paddy Green, Bright Yellow, (these are guesses) Vibrant Orange, Chocolate, and Mexicana is the variegated. I used a size I Susan Bates aluminum crochet hook. Actually, I probably used several, as I tend to lose hooks and now I have quite a few I hooks.

The squares are whipstitched together, and there is a border of two rounds of single crochet around the edges.

And so if you ever wondered what my default userpic was all about, there it is. :)

Because I had to marry a guy who had a digital camera in order to have use of one available enough that when I thought "hey, let's get a picture of that" I could. Silly me.

So there it is: SOLS(10). I finished it on January 30, 2005, here's a picture finally.

**Math Details:**A Latin Square is an nxn square or matrix where each number from 1 to n (or 0 to n-1, if you don't have zero fear) appears exactly once in each row and each column. A pair of Latin squares are orthogonal if the entries, when put in ordered pairs, create all the n x n ordered pairs. An example:1 | 3 | 2 |

3 | 2 | 1 |

2 | 1 | 3 |

And then

1 | 3 | 2 |

2 | 1 | 3 |

3 | 2 | 1 |

A self-orthogonal Latin square is a Latin square whose entries, when transposed across the diagonal, form a Latin square orthogonal to the original. And that's what we have here.

For about the longest time, the world lived pretty content in the knowledge that there is no pair of orthogonal Latin squares of order 10. But the world was wrong, and they do so exist. So do self-orthogonal Latin squares of order 10. And this afghan is a representation of just such a thing. The inner and outer parts of the squares correspond across the diagonal, and each color represents a value from 1 to 10.

If you want more info about such things, feel free to look up Latin Squares in Wikipedia and Mathworld, or check out the text I learnt from, a good zero-fearing book.

**Craft Details:**This is a simple granny square, four rounds of sets of 3 double crochets arranged to form squares, and then bordered with one round of single crochet. The inner two rounds were one color, the outer rounds were different on 90 of the 100 squares, that is, all but the diagonal. Every square is unique.This was done entirely in Red Heart Super Saver acrylic worsted, in White, Black, Cherry Red, Amethyst, Blue, Paddy Green, Bright Yellow, (these are guesses) Vibrant Orange, Chocolate, and Mexicana is the variegated. I used a size I Susan Bates aluminum crochet hook. Actually, I probably used several, as I tend to lose hooks and now I have quite a few I hooks.

The squares are whipstitched together, and there is a border of two rounds of single crochet around the edges.

And so if you ever wondered what my default userpic was all about, there it is. :)