ratio simplifier

ruby-talk
1

given a ratio (ex. 374:266 or 724.36292:740.37872) how do I get the smallest ratio? 187:133 for the first ex. Now for the second ex, that is a tricker answer. Do I convert to integer and then calculate the smallest ratio? I think I am leaning that way.

Also, 187:133 seems a bit large. Next question is how to identify a smaller ratio that is "close"? say within 2 or 3 decimal places? this example ratio is about 1.4060:1 or I guess I could say 14.06:10 then about 7:5? Not sure if I'm even close to the right track on this.

Be nice if there were already a gem that did this calculation. But I can write a method once I find a correct algorithm. I've tried google searching, but keep getting either web pages that do a Ratio Simplifier or things about gem stone ratios.

NOTE: this is not for Rails. It is for a process that I'm writing. Will be ran on my mac locally only.

$ ruby -v
ruby 3.0.0p0 (2020-12-25 revision 95aff21468) [x86_64-darwin20]

$ uname -a
Darwin far-wa.local 20.3.0 Darwin Kernel Version 20.3.0: Thu Jan 21 00:07:06 PST 2021; root:xnu-7195.81.3~1/RELEASE_X86_64 x86_64

def ratio_simplifier( x, y )

  return nil if x.nil? or y.nil?
  x = x.round
  y = y.round
  
  # do math magic here
  # ...

  return "#{x}:#{y}"

end # ratio_simplifier

puts ratio_simplifier 374, 266

Thanks for any insight

Eric
ruby-talk@far.tips

2

Quick answer, the Rational class does that for integers. That's a first
step, the rest depends on how you define approximatiins.

3

Sometimes the hardest part is finding the right terms to search for.
The numerator and denominator of an irreducible fraction are relatively
coprime.
Down the wikipedia rabbithole:

Xavier's reply saved my evening.
After relearning that Floats and Rationals don't mix well. Fixed decimal to
the rescue...

$ pry
[1] pry(main)> require 'bigdecimal'
=> true
[2] pry(main)> require 'bigdecimal/util'
=> true
[3] pry(main)> ratio = Rational(374,266)
=> (187/133)
[4] pry(main)> Rational ratio.to_d(1)
=> (1/1)
[5] pry(main)> Rational ratio.to_d(2)
=> (7/5)
[6] pry(main)> Rational ratio.to_d(3)
=> (141/100)
[7] pry(main)> Rational ratio.to_d(4)
=> (703/500)

-gf-

···

On Mon, Feb 1, 2021 at 6:45 PM Xavier Noria <fxn@hashref.com> wrote:

Quick answer, the Rational class does that for integers. That's a first
step, the rest depends on how you define approximatiins.
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4

look up continued fraction convergents.

martin

···

On Mon, Feb 1, 2021 at 4:33 PM Gerard Fowley <gerard.fowley@iqeo.net> wrote:

Sometimes the hardest part is finding the right terms to search for.
The numerator and denominator of an irreducible fraction are relatively
coprime.
Down the wikipedia rabbithole:
Coprime integers - Wikipedia
Irreducible fraction - Wikipedia
Euclidean algorithm - Wikipedia
Xavier's reply saved my evening.
After relearning that Floats and Rationals don't mix well. Fixed decimal
to the rescue...

$ pry
[1] pry(main)> require 'bigdecimal'
=> true
[2] pry(main)> require 'bigdecimal/util'
=> true
[3] pry(main)> ratio = Rational(374,266)
=> (187/133)
[4] pry(main)> Rational ratio.to_d(1)
=> (1/1)
[5] pry(main)> Rational ratio.to_d(2)
=> (7/5)
[6] pry(main)> Rational ratio.to_d(3)
=> (141/100)
[7] pry(main)> Rational ratio.to_d(4)
=> (703/500)

-gf-

On Mon, Feb 1, 2021 at 6:45 PM Xavier Noria <fxn@hashref.com> wrote:

Quick answer, the Rational class does that for integers. That's a first
step, the rest depends on how you define approximatiins.
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<http://lists.ruby-lang.org/cgi-bin/mailman/options/ruby-talk>

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