My latest posts can be found here:
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Additionally, some earlier writings:
Thanks in advance ...
For some of my readers, this will all be completely mysterious. But for others, part way through they will go "I recognise this!"
So I'd really like to hear from you ... if you recognise this, at which point did the penny drop? I'd also really like to know if you think this is obvious, and possibly even if you've seen it before.
Note: I don't need it explained to me - I know how it works! But if you'd like to show that you know how it works, then I'd be happy to hear that too.
Consider the following algorithm. I'll work through an example. I'll divide 450 by 23. We start by creating this table:
The middle row is doubling 23 until the answer is strictly larger than 450. Now suppose we have two columns, using a, b, c for quantities we know, and x and y for quantities we don't (yet) know, we complete the table by working leftwards:
Since 368 < 450, the next column is:
Since 184 >= 82, the next column is:
Since 92 >= 82, the next column is:
Since 46 < 82, the next column is:
Since 23 < 36, the next column is:
So I claim that 450 divided by 23 is 19 with remainder 13.
As I said, for some of you this will feel very familiar. At what stage did you get the connection (with the thing I'm carefully not mentioning)?
Have you seen this before?
Have you thought about this before?
Let me know.
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