# concave up or down? **URL:** \ **Category:** Factual Questions\ **Created:** [March 16, 2000, 9:47am UTC](https://boards.straightdope.com/t/concave-up-or-down/8674 "2000-03-16T09:47:00Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [March 16, 2000, 9:47am UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/1 "2000-03-16T09:47:00Z")
This should be a simple question, but the few dictionaries I have around don’t seem to answer it. Simply, if I have a short curve or arc with the ends pointing up (like a smilie), is that concave up or concave down? Is “(” concave right or left? Is there a less ambiguous way to describe them? ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [March 16, 2000, 10:04am UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/2 "2000-03-16T10:04:00Z")
The curve would be concave up. I don’t know if there’s any standard way of naming “(”. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [March 16, 2000, 10:06am UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/3 "2000-03-16T10:06:00Z")
OK, I’m a little drunk right now; anyway, “(” would be concave right, since that’s the way the concave side is pointing. ---
**Author:** ![Popillia](https://avatars.discourse-cdn.com/v4/letter/p/ee59a6/32.png) [@Popillia](https://boards.straightdope.com/u/Popillia)\ **Post date:** [March 16, 2000, 11:40am UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/4 "2000-03-16T11:40:00Z")
correct me if I’m wrong (and I’m sure someone will) but concave means it curves inward while convex is a surface that is curved or rounded outward. * * * What would they have? Is life so dear, or peace so sweet, as to be purchased at the price of chains and slavery? Forbid it, Almighty God! I know not what course others may take; but as for me, give me liberty or give me death! Patrick Henry ---
**Author:** ![earendel1](https://avatars.discourse-cdn.com/v4/letter/e/c68b51/32.png) [@earendel1](https://boards.straightdope.com/u/earendel1)\ **Post date:** [March 16, 2000, 12:31pm UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/5 "2000-03-16T12:31:00Z")
It depends. In lenses, a “(” shaped lens is “convex-concave” (or “concave-convex”), because the behavior of light (how it is focused) depends upon the direction through which the light goes. If it comes from the left side, then it would be “dispersed” (actually it would have a negative focal point), while if it comes from the right side, it would be concentrated at a single point. In my high school physics class the instructor had lenses that were “double-concave” – )(, “double-covex” – () as well as “concave-convex”. (I apologize for the crudeness of the graphics.) ---
**Author:** ![Crystalguy](https://avatars.discourse-cdn.com/v4/letter/c/dbc845/32.png) [@Crystalguy](https://boards.straightdope.com/u/Crystalguy)\ **Post date:** [March 16, 2000, 12:32pm UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/6 "2000-03-16T12:32:00Z")
> [@](#): > > Originally posted by Popillia: > \*\*correct me if I’m wrong (and I’m sure someone will) but concave means it curves inward while convex is a surface that is curved or rounded outward. > > \*\* Yes, you are right. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [March 16, 2000, 1:15pm UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/7 "2000-03-16T13:15:00Z")
In elementary school they told us that con **cave** goes in… like a cave. ---
**Author:** ![mipsman](https://avatars.discourse-cdn.com/v4/letter/m/e99b99/32.png) [@mipsman](https://boards.straightdope.com/u/mipsman)\ **Post date:** [March 16, 2000, 2:07pm UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/8 "2000-03-16T14:07:00Z")
Concave up holds water, (from my first calculus class). To make matters more confusing, in the fixed income investment business, positive convexity means concave up. ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [March 16, 2000, 2:34pm UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/9 "2000-03-16T14:34:00Z")
> [@](#): > > Polillia wrote: > correct me if I’m wrong (and I’m sure someone will) but concave means it curves inward while convex is a surface that is curved or rounded outward. You’re right in general, but this is a question about how it’s done in mathematics. If you draw a curved line on a piece of paper, you can’t say if it’s convex or concave. So you say it’s concave up if it smiles and concave down if it frowns. Actually, the concavity is specific to each point on the line, because it can be up in one place and down in another. This is basically a visual way to view the second derivative of a function. ---
**Author:** ![Rhythmdvl](https://avatars.discourse-cdn.com/v4/letter/r/85f322/32.png) [@Rhythmdvl](https://boards.straightdope.com/u/Rhythmdvl)\ **Post date:** [March 16, 2000, 4:01pm UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/10 "2000-03-16T16:01:00Z")
If I could be so bold as to flesh out **Curt** ’s answer a bit. (I also hope someone with a better memory than I will come forth and correct the inevitable mistakes that I am about to make). He is right that they are used in the realm of mathematics (and economics, and physics and…) to describe the graphed curves of a derivative. Let’s see if I can remember this right… For a point at a given function f(x) **if** **d’ is positive** - the function is **increasing**. (Typically that means Y increases with X.) **d’ is negative** - the functin is **decreaseing**. (Typically… well, you get the point) Setting d’ = zero gives you relative minima and maxima (i.e. the humps and dips along the length of the curve) **d"** is positive - the function is **concave up** at that point **d"** is negative - the function is **concave** down at that point Setting d" = zero give you the inflection point. (the point where the graph switches from concave up to concave down.) ## Where d’ = first derivative and d" = second derivative. Derivatives are the slope of a line at a given point or instantaneous rates of change. If none of the derivatives are possible, then you know a bit more about the curve at that point. (i.e. if there is no second derivative, you know the curve is a straight line.) I hope that made sense. I also hope I got more than 1/2 of it right. I also hope that I got the UBB codes right. I also hope that I will know when to quit typing. Rhythmdvl Once in a while you can get shown the light in the strangest of places if you look at it right… ---
**Author:** ![InutilisVisEst](https://avatars.discourse-cdn.com/v4/letter/i/d2c977/32.png) [@InutilisVisEst](https://boards.straightdope.com/u/InutilisVisEst)\ **Post date:** [March 16, 2000, 9:19pm UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/11 "2000-03-16T21:19:00Z")
To expound on earendel1’s lenses: |( plano-concave (diverging) |) plano-convex (converging) )( double-concave (diverging) () double convex (converging) C( converging convex-concave (C diverging convex-concave Note: you can start fires with converging lenses only. Nearsighted people lost in woods should take matches. * * * Sure, I’m all for moderation – as long as it’s not excessive. ---
**Author:** ![manhattan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/manhattan/32/7_2.png) [@manhattan](https://boards.straightdope.com/u/manhattan)\ **Post date:** [March 16, 2000, 10:49pm UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/12 "2000-03-16T22:49:00Z")
::test post:: Please ignore this post. If you see multiposts above, please ignore them, too. * * * [Change Your Password, Please](http://204.95.48.199/cgi-bin/ubbcgi/ubbmisc.cgi?action=getannounce&ForumNumber=3&Start=2451545.99&End=2451911&Session=2451598.1854) and don’t use HTML, as it has been disabled, but you can learn about superscripts [here](http://boards.straightdope.com/ubb/Forum2/HTML/000795.html) ---
**Author:** ![MadPoet](https://avatars.discourse-cdn.com/v4/letter/m/8c91f0/32.png) [@MadPoet](https://boards.straightdope.com/u/MadPoet)\ **Post date:** [March 16, 2000, 11:24pm UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/13 "2000-03-16T23:24:00Z")
If you can draw a line from any two points in an object and not cross any points that are outside the object, it is convex. This doesn’t really cover lines though. Concave is cave shaped, convex is vexing to pour water into. * * * [http://www.madpoet.com](http://www.madpoet.com) Please hit Ctrl-A I hit Ctrl. Now what, eh? Damn Canadians. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [March 17, 2000, 12:47am UTC](https://boards.straightdope.com/t/concave-up-or-down/8674/14 "2000-03-17T00:47:00Z")
So a smile is concave up and a frown is concave down. That’s what I needed to make sure, thanks… We were having confusion at work where two people thought it was otherwise. (One was me, another was also a non-native English speaker who lived in the US for close to 10 years) Guess some things you don’t learn unless you grow up speaking the language…