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Tagged As Education
and Tagged As Maths
None of this is new, you can find it on the internet
with the appropriate search. I know that.
But having said that, I've never seen it laid out like this,
and several people I've shown it to have been surprised by
it and found it quite exciting. |
I'm revisiting this, so I'd be interested to know where people
"fall off the perch" and give up. I have my theories, but I'd
like to get actual feedback.
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.
So ...
Consider the following algorithm. I'll work through an example.
I'll divide 450 by 23. We start by creating this table:
|
A:
|
.
|
.
|
.
|
.
|
.
|
0
|
|
B:
|
23
|
46
|
92
|
184
|
368
|
736
|
|
C:
|
.
|
.
|
.
|
.
|
.
|
450
|
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:
Given this
situation:
|
|
If b >= c then
|
If b < c then
|
Since 368 < 450, the next column is:
| | | | | 2*0+1 |
|
A:
|
.
|
.
|
.
|
.
|
1
|
0
|
|
B:
|
23
|
46
|
92
|
184
|
368
|
736
|
|
C:
|
.
|
.
|
.
|
.
|
82
|
450
|
| | | | | 450-368 |
Since 184 >= 82, the next column is:
| | | | 2*1 |
|
A:
|
.
|
.
|
.
|
2
|
1
|
0
|
|
B:
|
23
|
46
|
92
|
184
|
368
|
736
|
|
C:
|
.
|
.
|
.
|
82
|
82
|
450
|
| | | | Copied |
Since 92 >= 82, the next column is:
| | | 2*2 |
|
A:
|
.
|
.
|
4
|
2
|
1
|
0
|
|
B:
|
23
|
46
|
92
|
184
|
368
|
736
|
|
C:
|
.
|
.
|
82
|
82
|
82
|
450
|
| | | Copied |
Since 46 < 82, the next column is:
| | 2*4+1 |
|
A:
|
.
|
9
|
4
|
2
|
1
|
0
|
|
B:
|
23
|
46
|
92
|
184
|
368
|
736
|
|
C:
|
.
|
36
|
82
|
82
|
82
|
450
|
| | 82-46 |
Since 23 < 36, the next column is:
| 2*9+1 |
|
A:
|
19
|
9
|
4
|
2
|
1
|
0
|
|
B:
|
23
|
46
|
92
|
184
|
368
|
736
|
|
C:
|
13
|
36
|
82
|
82
|
82
|
450
|
| 36-23 |
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.
Send us a comment ...
| 
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