The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » geometry.puzzles

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Re: Locus for ratio of cosine of angles to be constant
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List   Topics: [ Previous | Next ]

Posts: 359
Registered: 9/16/06
Re: Locus for ratio of cosine of angles to be constant
Posted: Nov 18, 2013 7:18 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> cos(s) = cos(p) ecc where ecc is a constant.
> Use differential relations between r,th (polar) and
> d x,y (cartesian) coordinates with respect to arc
> length s.
> dr/ds - dx/ds ecc = 0 which integrates to
> r - x ecc = r - r cos(th) ecc = p, an arbitrary
> y constant.
> 1 - ecc cos(th) = p/r the polar equation of all
> l conics.
> Given constant is eccentricity and arbitray constant
> t is semi-latus rectum.
> This rotational definition imho is much better than
> n the standard distance definition of conics with
> respect to the meaning and significance of
> eccentricity.

Graphic showing equivalence of these two definitions is given:

It considers the right angle subtended by tangent point to directrix line segment at focus.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.