# Math and Grammar - apparent disconnect ? **URL:** \ **Category:** Factual Questions\ **Created:** [April 12, 2003, 1:31am UTC](https://boards.straightdope.com/t/math-and-grammar-apparent-disconnect/168162 "2003-04-12T01:31:03Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![andy\_fl](https://avatars.discourse-cdn.com/v4/letter/a/49beb7/32.png) [@andy\_fl](https://boards.straightdope.com/u/andy_fl)\ **Post date:** [April 12, 2003, 1:31am UTC](https://boards.straightdope.com/t/math-and-grammar-apparent-disconnect/168162/1 "2003-04-12T01:31:03Z")
A Circle is defined as - The locus of a point which moves such that its distance from a fixed point is constant. In cartesian coordinates : x^2 + y^2 = r^2. Now obviously, a circle is a curve or a line. What baffles me is that how can we say “area **of** a circle = pi()r^2”. Should’nt it be “area **in** a circle = pi()r^2” ? because the circle is a curve and curves have no area only length. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [April 12, 2003, 1:36am UTC](https://boards.straightdope.com/t/math-and-grammar-apparent-disconnect/168162/2 "2003-04-12T01:36:44Z")
A circle (or any other two-dimensional shape) is also defined as the area encompassed by its periphery. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [April 12, 2003, 1:43am UTC](https://boards.straightdope.com/t/math-and-grammar-apparent-disconnect/168162/3 "2003-04-12T01:43:05Z")
No, I don’t think the circle includes what’s inside it. However, the area **of** a 2-D shape is taken to mean the area that it encloses. The reason is that you never need to talk about the area of a 1-D figure, so it’s not ambiguous. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [April 12, 2003, 2:06am UTC](https://boards.straightdope.com/t/math-and-grammar-apparent-disconnect/168162/4 "2003-04-12T02:06:39Z")
From [Dictionary.com](http://dictionary.reference.com/search?q=circle): > [@](#): > > Circle > > 1. A plane figure, bounded by a single curve line called its circumference, every part of which is equally distant from a point within it, called the center. There are a number of ways to define a circle, and this is one of them. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [April 12, 2003, 2:36am UTC](https://boards.straightdope.com/t/math-and-grammar-apparent-disconnect/168162/5 "2003-04-12T02:36:45Z")
Okay, fair enough. I think that’s not the most often used definition in geometry, though. If someone refers to a point on a circle, you can bet they’re talking about a point on the outside rim. ---
**Author:** ![g8rguy](https://avatars.discourse-cdn.com/v4/letter/g/7cd45c/32.png) [@g8rguy](https://boards.straightdope.com/u/g8rguy)\ **Post date:** [April 12, 2003, 3:06am UTC](https://boards.straightdope.com/t/math-and-grammar-apparent-disconnect/168162/6 "2003-04-12T03:06:55Z")
My WAG: I’ve never seen anyone in math define a circle as anything other than the points defined by the usual x[sup]2[/sup]+y[sup]2[/sup]=r[sup]2[/sup] type definition. But of course, when Joe Average speaks of a circle, he probably means the definition that **Q.E.D.** gave, and circles being one of those things we’ve known about for ever and a day, the phrase “the area of a circle is [symbol]p[/symbol]r[sup]2[/sup]” has entered the language and gets used even though from a strict perspective, you’re right in saying that a circle has no area itself but only encloses an area. It makes sense to me, anyway… ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [April 12, 2003, 3:50am UTC](https://boards.straightdope.com/t/math-and-grammar-apparent-disconnect/168162/7 "2003-04-12T03:50:08Z")
I think it’s a case of apostrophe. The full phrase to be substituted for “of” is "bounded by " . As long as there is no ambiguity I don’t think it matters much in Math. ---
**Author:** ![j.c](https://avatars.discourse-cdn.com/v4/letter/j/73ab20/32.png) [@j.c](https://boards.straightdope.com/u/j.c)\ **Post date:** [April 12, 2003, 6:22pm UTC](https://boards.straightdope.com/t/math-and-grammar-apparent-disconnect/168162/8 "2003-04-12T18:22:35Z")
In my own personal life experience, I find that math and engineer types speak well, because they care about precision. ---
**Author:** ![Omphaloskeptic](https://avatars.discourse-cdn.com/v4/letter/o/bcef8e/32.png) [@Omphaloskeptic](https://boards.straightdope.com/u/Omphaloskeptic)\ **Post date:** [April 12, 2003, 8:40pm UTC](https://boards.straightdope.com/t/math-and-grammar-apparent-disconnect/168162/9 "2003-04-12T20:40:24Z")
When speaking precisely, mathematicians usually use **disk** to refer to the interior of a circle. (A **ball** is the interior of a sphere. You can also refer to n-balls and n-disks to to talk about the interiors of higher-dimensional hyperspheres.)