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I am a math teacher in Asia. In one math question there are two triangles, A and B. I want to ask which has the larger area. Should I ask:

"Which area of triangle a or triangle b is larger"?

or

"Which triangle, a or b, has a larger area"?

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The second one would be more correct: "Which triangle, A or B, has a larger area?"

However, a better way (in my opinion) to phrase it would be simply "Which triangle has a larger area?", if there are only the triangles A and B to choose from.

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The second choice you present is correct as you present it. The first choice would be improved if you eliminate the "of" and enclose "triangle a or trianble b" with commas. The "of" in the first choice as you present it implies that triangle a has more than one area.

  • The first sentence is not corrected by saying "Which area, triangle a or triangle b, is larger?" Triangle a is not an area. It is a geometrical construction that has area as one of its properties. You could ask "Of triangle a and triangle b, which has the larger area?" – aeismail Sep 7 '14 at 7:13
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@tchrist is correct, for two triangles one has a larger area (we are assuming they don't have the same area). Hence Erik Kowal's, larger vs. largest is most definitely not pedantic.

Although using the word largest and most of the responses here would likely be understood by the hearer/reader. The phrase:

Which triangle has the larger area, triangle a or triangle b?"

is excellent grammar, leaves no room for misunderstanding and more importantly, demonstrates good understanding of English.

  • Your answer consists of a series of assertions with no underpinning logic or rationale. – Erik Kowal Sep 7 '14 at 10:39
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"Which triangle, a or b, has the largest area?" unambiguously means what it says. (Note the slight modification of your wording.)

"Which area of triangle a or triangle b is larger?" makes it sound as though triangles a and b have been subdivided into smaller areas, and you are asking which of those areas in each triangle is the largest.

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    Um, no. With two triangles, one has the larger area and one the smaller. Only with three or more is it possible to use largest. – tchrist Sep 7 '14 at 2:12
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    @tchrist - I'm sorry, but the distinction you have drawn is pure scholastic pedantry that ought to have died out before you were even born. – Erik Kowal Sep 7 '14 at 2:15
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    @ErikKowal: tchrist is correct. Moreover, mathematics demands more precision in usage than other contexts. "Larger than" is a binary operation in mathematics: you check whether a is a greater quantity than b or not. "Largest" implies a series of binary operations, which you do not have. – aeismail Sep 7 '14 at 7:20
  • @aeismail - We're comparing two areas here, not a series of numbers. My suggested formulation is perfectly apt in this context, and impossible to misinterpret -- though 'larger' would also work, of course, since there are only two triangles. Tchrist's objection to 'largest' is based not on mathematical grounds, but on linguistic pedantry. – Erik Kowal Sep 7 '14 at 9:04
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    @ErikKowal: Because when you have two numbers a and b, a is either smaller than b, equal to b, or larger than b. These are all uniquely representable mathematically, and is what the question is formally asking: ("Is area(a) > area(b)?") "Largest" doesn't have the same simple mathematical interpretation, and therefore complicates the mathematics, in exchange for marginal linguistic simplification. – aeismail Sep 7 '14 at 11:00

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