Math Is Fun Forum

Hannibal lecter

Member

From: Iraq

Registered: 2016-02-11

Posts: 405

The straight lines drawn from the vertex of the conic surface to point

The straight lines drawn from the vertex of the conic surface to points on
surface are on that surface.

my question is there stright line that the book talking about I see it not straight! I see it curved!! what is going here mr bob

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,825

Re: The straight lines drawn from the vertex of the conic surface to point

Without seeing the whole text, it's hard to be certain but I think the logic is this:

A is the vertex of the cone. B is a point on the surface of the cone. As the cone is considered to continue to infinity both above and below A, they have shown three cases for where B might be.

They want to consider a straight line drawn from A to B and prove that C (on AB) lies on the conic as well.

If you draw AB as a straight line then C would certainly be on the conic so they've distorted the line so as to allow for the possibility that C isn't on the conic. So you have to pretend the line is straight so the proof doesn't assume what must be proved.

I'm assuming that what follows is a proof that C is in fact on the conic.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob