# Talk:Secant line

## Definition

"(Secant) is a line that (locally) intersects two points of a curve". This doesn't make sense to me. If you have two distinct points, then locally near one point, you won't even be able to see the other point. "Locally" as usually meant in mathematics means occurring within arbitrary small neighborhoods around a point. If you choose a small enough neighborhood around one point, your secant line will only intersect the curve in one point in that neighborhood. Furthermore, secant lines can also intersect curves in very many more than 3 points. For instance, the x axis is a secant line through the graph of sin(x) through the origin, and intersects that curve in infinitely many points. Perhaps the definition of secant line should be "a line through a point on a curve that is not a tangent line", and this page should be merged with that of tangent line?B2smith (talk) 05:07, 23 June 2010 (UTC)

## Secants vs. Tangents

Any vertical line intersects the graph of y = cos x exactly once, but is obviously not a tangent line. The line y = 1 intersects the same graph infinitely many times, and obviously is a tangent line. Therefore this childish notion of identifying the concpet of tangent line with a line that intersects a curve only once is nonsense. Michael Hardy 21:38 7 Jun 2003 (UTC)

Yes, childish...very constructive observations...Pizza Puzzle

As I always understood it, secant lines approach tangent lines in the limit. For instance, say you want to know the tangent line of a point x on any graph. Then you can approximate this point by drawing a secant line through x and x1, where you choose x1 to be very close (infinitesimally close) to x. In the limit, where x1 goes to (tends to) x, or the difference x1-x tends to 0, the secant line IS the tangent line. Ifyasaiso (talk) 13:26, 3 December 2009 (UTC)

Seems that the "Secant and tangent formulas for circles" section should be re-written (at least the first sentence) and probably have a picture added, so that the discussion of points A,B,C, etc. makes more sense. 68.81.156.31 (talk) 04:37, 29 January 2009 (UTC)

## Proposed merger

• Oppose. I don't think chord (geometry) should be merged into secant line; this concept of a chord and in particular the word chord are far too prevalent and often used in different contexts. The proposition about "power of a point" does not fit into the secant line article. Michael Hardy 19:44, 7 November 2005 (UTC)
• Oppose - A secant line is not the same as a chord. They are regarded as completly two different things. --Kilo-Lima 16:42, 12 November 2005 (UTC)

I removed the merge proposal from the chord (geometry) page, and I'm doing the same here. This proposal has received no support, and just makes no sense. --Dantheox 06:04, 24 December 2005 (UTC)

## Question

So say the average velocity of a curved line was needed, , if the secant started from (0,0)and ended at (1.2,5), the slope would work as average velocity. If I drawed a tangent at (1.2,5)would the slope of the tangent and secant be the same? —Preceding unsigned comment added by 76.66.43.91 (talkcontribs)

That depends on the shape of the curve, about which you haven't told us anything. In most cases they would not be the same. Michael Hardy (talk) 03:01, 18 September 2009 (UTC)

Well, Slope would not be same is all I needed. Do you know how a graph would look if its acceleration doubled?

Actually, as above, in the limit of the second point tending to the first point (and their difference to 0), the slope of the secant line would be the slope of the tangent line. Ifyasaiso (talk) 13:26, 3 December 2009 (UTC)