PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (200)
Orphanage
Unclass'd
Unproven (510)
Corrections (11)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: High Entry average rating: High
Apollonius' circle (Definition)

Apollonius' circle. The locus of a point moving so that the ratio of its distances from two fixed points is fixed, is a circle.


If two circles $ C_1$ and $ C_2$ are fixed with radii $ r_1$ and $ r_2$, then the circle of Apollonius of the two centers with ratio $ r_1/r_2$ is the circle whose diameter is the segment that joins the two homothety centers of the circles.



"Apollonius' circle" is owned by drini. [ full author list (2) | owner history (1) ]
(view preamble)

View style:

See Also: harmonic division

Keywords:  locus, homothety
Log in to rate this entry.
(view current ratings)

Cross-references: homothety centers, segment, diameter, centers, radii, circle, fixed, fixed points, distances, ratio, point, locus
There is 1 reference to this entry.

This is version 3 of Apollonius' circle, born on 2001-10-06, modified 2007-10-09.
Object id is 154, canonical name is ApolloniusCircle.
Accessed 5059 times total.

Classification:
AMS MSC: 51-00 (Geometry :: General reference works )
Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)