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Reducing Scales - Recurring numbers & Patterns
tomos:
I work with scaled drawings.
Sometimes I have to produce various versions of a drawing at differnet scales.
I can do it fine, but to be honest I find it hard to get my head around some of the concepts.
Here's an example - the reason I even thought of posting it is the numbers with the recurring numbers after the decimal point.
I reduce a drawing/figure @ 1:00 to 70% of original size.
1:100 * 70% =
7:1000 =
1:142.857142857142∞
The 857142 bit is repeating so I added the infinity symbol ∞ (not sure if that's correct)
Later, I need to reduce the new modified version to 1:50 (which would be 50% of the first figure).
i.e. I want to reduce (1:100 * 70%) to 1:50 i.e. to (1:100 * 50%)
100 * 70% = 70
100 * 50% = 50
70 * X = 50
X = 50/70 = 0.7142857142857142∞
which would be 71.42857142857142∞%
which number is exactly half of the number for the first 70% reduction (1:100 * 70%) = 1:142.857142857142∞
I cannot explain that - I possibly could figure it out, but I'll just enjoy it and move on.
Re the recurring number - if I divide or multiply by two, the result seems to be always recurring at some stage after the decimal point.
BTW is that the correct name - simply "recurring digit" ?
PS thank god I dont work with imperial scales :p
tomos:
You can get the first recurring digit there by dividing 1000 by 7.
(If possible I show a 10 metre scale - that's partly why I look at what 1000 is:
7cm on drawing is 1000cm =10m)
Here a bit of experimenting with halving the recurring number:
TaoPhoenix:
Heh I used to like this stuff as a young'un 30 years ago! ( :tellme: )
Notice you stopped just before the pattern broke! Last I knew of these kinds of patterns as a kid, it matters whether the front whole number is odd or even, which determines if the decimal "can divide by 2 all by itself" or else a flow-over 0.5 amount is given/taken back and forth from it.
The whole Casting-Out-Nines series of tricks might be involved here too, but I'm not sure.
Renegade:
That's a funky little pattern there. :) (I love number magic and the like.)
tomos:
As said, what got me is the way the number cropped up again.
Let's see:
To reduce from 70% to 50% I must multiply the 70% version by half the scaled-value (? terminology again) of one [1] at that scale (70%)
Just seems freaky to me - might try to look closer at it when I have time.
Might be something to do with area - 50% of something from the scale POV is 25% of the area.
If I figured that out for 70% ...
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