Should I have been a mathematician?

Many, many years ago I noticed that the square of a number consisting of all sixes had a particular pattern.

With pretensions to be a mathematician I set out to prove why this was so! Every ten years or so I would re-visit the previous solution and attempt to improve on it. Now I have decided to publish it on my blog, for posterity.

If you understand it, comments are welcome. See image files below or a PDF file here

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