I should plot the reduced denominators and graph it. Copy/paste as text, split by “/”

I should plot the reduced denominators and graph it.
Copy/paste as text, split by “/”

Oh that’s cool. A periodic pattern.
1
2
0.5
2

1
2
0.5
2

 

60008228_10100140548606488_7211299082675945472_n

So: By fours: 1/4, 3/8, 5/12, 7/16 to approach 1/2…

59897179_10100140549260178_7521867716878139392_n

—-

Also by fours but shifted by +1 gives you:
1/3, 2/5, 3/7, 4/9, 5/11, 6/13

 

60087799_10100140550637418_1241518472240824320_n

 

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Also by fours but shifted by -1 gives you:
3/6, 5/10, 7/14, 9/18 – cool.

60014262_10100140550722248_1441769703214153728_n

 

Ok, so there’s a formula hiding in here to generate lowest denominators for a given integer of any size.

What is it? It is probably very simple as it’s periodic.

——————————–

Does it have to be a good music video? Math is easy.

—-

 

Why is 1, 2,0.5, 2
So familiar?
 
Circles? Gotta be circles.
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 Yeah, JUST as you wrote that I ‘got it’.
Why 1/2=0.5 and 1/5=0.2
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 Still though… I like that periodic multiplier for creating the perfect denominator in base 10 for any base 10 integer. Handy.
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Lets see if I can do pseudo code for it:
x=base 10 integer
y=lowest denominator for x (1/x)
If x/4=1, y=1*x.
If (x-2)/4=1, y=0.5*x
if (x+1)/4=1, y=2*x
if (x-1)/4=1, y=2*xOk, all 4 cases accounted for. Sloppy but functional
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 How fractions reduce nicely into a pattern.I don’t ‘get it’ enough to explain it.But I saw a pattern as you try to get as close to 1/2 cleanly as your denominator got bigger
====
 Hardest thing for me to put my brain around though is how are fractions base-10? I still don’t think they are but I’m missing something.
====
 I know our # systems is column based. 0s place, 10s place, etc. An odometer is how our representation works.

But what’s the gear ratios? :)

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