Hatrack River Forum: Mathematical vocabulary question

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Posted by dkw (Member # 3264) on :

What is the name (there is a name, isn't there?) for the point in a curve when the slope, which is gradually increasing, is equal to 1?

It has been too long since my last math class. [Embarrassed]

Posted by rivka (Member # 4859) on :

Are you talking about a saddle point? Or a maximum?

. . . no, wait, the slope is zero for both of those . . .

Posted by BannaOj (Member # 3206) on :

The inflection point, I think, is what you may be thinking of. Where the 2nd derivative equals zero turning from positive to negative (the function switches concave to convex or vice versa). I don't think the slope actually has to equal one at that point, just a constant though. For example:
f(x)=x^3 f'(x)= 3x^2 f''(x)= 6x

In this case when the second deriviative equals zero, the first derivative (the slope) also equals zero.

AJ

[ November 18, 2004, 10:26 AM: Message edited by: BannaOj ]

Posted by Bokonon (Member # 480) on :

dkw, I don't think you have given enough context. If the slope wasn't increasing, it would be linear. If you mean the point in a curve where the values of f(x) increase drastically for small changes x, that would be an assymptote.

I don't think that there is any particular name for those types of points.

-Bok

Posted by Bokonon (Member # 480) on :

Banna, I thought that too, but it appears that the strict defn of inflection point is where the slope changes signs.

-Bok

Posted by dkw (Member # 3264) on :

Not inflection point. I mean a curve where the slope keeps increasing (the curve stays concave). The point before which the rise is less than the run and after which the rise is greater than the run.

Posted by BannaOj (Member # 3206) on :

I can't think of a name for it. That's not to say there isn't one. I can ask one of my math friends tonight though. However on any function, it would be easy to find the point, named or not. All you do is set the first derivative to one.

AJ

Posted by dkw (Member # 3264) on :

Yeah, I know how to find it. But I really think there should be a name for it. It's a very important point in this particular graph. [Big Grin]

Posted by rivka (Member # 4859) on :

quote:
I can't think of a name for it. That's not to say there isn't one.

*laugh* That's almost precisely what my mom just said when I asked her.

Posted by BannaOj (Member # 3206) on :

You know I bet there's a name for it in economics terms. In fact I'm sure there's a name for it in economics, but I can't remember it.

Posted by rivka (Member # 4859) on :

*thinks she just figured out what dkw is graphing*

[ROFL]

Posted by Morbo (Member # 5309) on :

If there is one, it's very obscure. I don't think there is, though.

What's the term for change in acceleration, 4 letters, synonomous with rude idiot?

Posted by dkw (Member # 3264) on :

Jerk.

But that's not the point. I need this word.

[ November 18, 2004, 10:54 AM: Message edited by: dkw ]

Posted by BannaOj (Member # 3206) on :

Jerk doesn't do anything here, because you can have a point like dkw is describing on an equation as simple as x^2 where the 4th derivative is clearly zero.

AJ

Posted by Morbo (Member # 5309) on :

I know, Aj, I was just being cute.

Posted by ElJay (Member # 6358) on :

dkw is being cute, too. [Wave]

Posted by BannaOj (Member # 3206) on :

could it have something to do with logarithms? what is the log of a function where the slope equals one?

AJ

Posted by dkw (Member # 3264) on :

It is apparently called "precipitation transition" if you're graphing rainfall - aquifer recharging. I got all excited and then I realized that that was a content-specific term.

Posted by BannaOj (Member # 3206) on :

dkw, I suspect you will only find particular names given to that point in applied mathematics. I don't know that it is as meaningful a point in "pure" mathematics.

AJ

Posted by kaioshin00 (Member # 3740) on :

d loga(x) = 1/(x lna) so when the slope equals 1 is where x times ln of the base = 1.

Posted by BannaOj (Member # 3206) on :

Here's a discussion of it with reference to a specific equation:
http://www-personal.umich.edu/~sarhaus/image/FONSECA/CHAPTER5/fonseca5.html

Posted by dkw (Member # 3264) on :

*sigh*

How am I supposed to write mushy love letters when mathematicians won't make up the words I need?

I don’t suppose anyone knows what the discipline-specific term would be in traffic safety research?

Posted by BannaOj (Member # 3206) on :

Here they set the slope to 1 in genetics
http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=mga.section.2668

Posted by BannaOj (Member # 3206) on :

and here I innocently figured it was for a Sermon Illustration...

Posted by dkw (Member # 3264) on :

[Big Grin]

If I found it, it would probably be used that way eventually. But the immediate use was personal.

Posted by BannaOj (Member # 3206) on :

http://www.drivers.com/article/303/ (search for "slope")

Posted by Morbo (Member # 5309) on :

quote:
How am I supposed to write mushy love letters when mathematicians won't make up the words I need?

Just make up your own jargon, (preferably in this case with a sexy acronym.) That's what mathematicians do. Sometimes it catches on.

Posted by Morbo (Member # 5309) on :

Equilibrium Risk Ogive Stochastic--Eros

Posted by blacwolve (Member # 2972) on :

*peaks in thread and backs away slowly*

Posted by BannaOj (Member # 3206) on :

Would it sound sexier if you said the point at which the slope equals "unity" instead of "one"?

AJ

Posted by ElJay (Member # 6358) on :

I'm just waiting for Bob to chime in with an answer. Or is he afk today?

Posted by dkw (Member # 3264) on :

He doesn't Hatrack from work. So this is secure space until at least 5pm.

Posted by Farmgirl (Member # 5567) on :

quote:
It is apparently called "precipitation transition" if you're graphing rainfall - aquifer recharging. I got all excited and then I realized that that was a content-specific term.

Hey! A term I actually know!

Posted by kaioshin00 (Member # 3740) on :

quote:
How am I supposed to write mushy love letters when mathematicians won't make up the words I need?

There's no real solution.

Posted by dkw (Member # 3264) on :

[ROFL]

Letter written. Thanks AJ. And thanks kaioshin. Turning this into a pun thread makes it somehow complete.

Posted by Mike (Member # 55) on :

Bok:

quote:
Banna, I thought that too, but it appears that the strict defn of inflection point is where the slope changes signs.

This is not true (in other words, you were right [Smile]

). See, for example, http://mathworld.wolfram.com/InflectionPoint.html for the correct definition. The wikipedia page is incorrect, or at least misleading; the confusion, it seems, is that some stationary points are inflection points, but there exist stationary points that are not inflection points and inflection points that are not stationary points.

Posted by Bob_Scopatz (Member # 1227) on :

The point of no return?

The vanishing point?

You miss my point entirely?

What's the point?

A pointed comment?

The pointe of developing housing with cutesy names?

Oh, heard a good joke:
What do you get if you cross a pointer and a setter?
A: A pointsetter -- a popular dog around the holidays.

Posted by ElJay (Member # 6358) on :

Is it bad that when I read your joke I thought a "pointsetter" would be a tool, like a nail set, and wondered why it would be more popular around the holidays than other times of year? Was actively trying to figure it out what it would be used for before it clicked.

[ November 18, 2004, 07:32 PM: Message edited by: ElJay ]

Posted by Kwea (Member # 2199) on :

It is a dog that points out where all the presents are hidden, silly!

And it is red....

[Taunt]