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I have a construction to say a ratio. I think of or and would be the correct prepositions.

So, If I give you my practice case

  1. The ratio of minimum rectangle’s floor area to enclosed circle area is tested with a defined threshold and a candidate, given a low ratio, is taken as natural object assuming that natural object has a more irregular boundary.

  2. The ratio between floor area of enclosed minimum rectangle and enclosed circle area is tested with a defined threshold and a candidate, given a low ratio, is taken as natural object assuming that natural object has a more irregular boundary.

As I cannot figure out the best preposition with the grammatically correct construction, I would like to ask what would be given a grammatically correct sentence?

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    As written, this is more like a writing critique, which would be either too localized or off-topic. If you wanted to reword it as a broader question about the correct preposition to use with "ratio", you might have better results here.
    – Lynn
    Mar 23, 2013 at 15:56
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    The ratio of Google hits for "ratio of A to B" to hits for "ratio between A and B" is 6710 : 4230 at my space-time coordinates. (I actually entered the letters.) Substituting X for A and Y for B, the ratio becomes 1240 : 475. Substituting (in the original) B for A and Q for B, the figures are unsurprisingly low, the ratio being 1 : 0 (and virtually meaningless as a statistic). Both are permitted, but we wouldn't usually say the ratio between P and Q is 7 : 5 (ie we usually use of / to if we're giving the value of the ratio).
    – Edwin Ashworth
    Mar 23, 2013 at 16:07
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    I think you need more work on articles (a, an, the) than on of or between.
    – GEdgar
    Mar 23, 2013 at 16:08
  • @GEdgar: yes. i am not native english speaker... could you please show me my errors in the sentence
    – gnp
    Mar 23, 2013 at 18:53
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    And is not a preposition. It's a conjunction.
    – RegDwigнt
    Mar 23, 2013 at 20:06

2 Answers 2

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I'm currently studying a Phd in mathematics. I would write:

The ratio between the floor areas of an enclosed minimum rectangle and an enclosed circle is tested with a defined threshold. A candidate, given a low ratio, ...

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Either combination is fine. If it helps any, in mathematics, when the colon is used to denote a ratio, it is customarily read as to or is to. From Wikipedia's colon:

The colon is used in mathematics, cartography, model building and other fields to denote a ratio or a scale, as in 3:1 (pronounced “three to one”). When a ratio is reduced to a simpler form, such as 10:15 to 2:3, this may be expressed with a double colon as 10:15::2:3; this would be read "10 is to 15 as 2 is to 3". Unicode provides a distinct character U+2236 ∶ ratio for mathematical usage.

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