Talk:Circumcircle
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Perhaps better: circle that passes through all the vertices of a polygon. Patrick 13:48 Dec 24, 2002 (UTC)
That only applies to triangles and cyclic polygons with more than 3 sides. General polygons can have non-touching corners. Think of a square, then pull one of the corners in a bit... the circle is unchanged.
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[edit] circumcircle of a polygon?
I just corrected the introduction of the article, but I don't know the correct definition for polygons other than triangles.
Does anybody know? Thanks --Up in the sky 22:12, 13 November 2005 (UTC)
I think that, according to the Geometry course from EPGY, it's the circle containing all the verticies. Aleph2.0 01:22, 22 May 2006 (UTC)
Long live the countable infinities! Aleph2.0 01:25, 22 May 2006 (UTC)
[edit] cleanup
There are multiple definitions at war on this page, apparently both standard meanings of "circumcircle". One can talk about:
- the circle passing through all vertices (does not exist for all polygons), or
- the smallest circle containing the figure.
In the case of e.g. an obtuse triangle these both exist and are different. Some editors understand the difference but have not stated it sufficiently clearly in the article page. Some have tried to put one definition at circumcircle and one at circumscribed circle (is this a standard distinction?) We need to decide whether they should be in the same article or different articles, and in either case write the page to explain the difference clearly enough that it won't be reverted. —Blotwell 11:06, 17 January 2006 (UTC)
I've tried to modify the introduction to make the difference in definitions more striking, I hope this helps. However, I found this definition within the Wikipedia article itself so I would like a authoritive reference to reinforce the definition put forth in this article. Thus far I haven't found that reference myself. --Smoore 500 03:32, 23 June 2006 (UTC)
[edit] circumcircle/circumscribed circle for triangles
"circumcircle of a triangle is defined to touch the three vertices even though, for "thin circles", the smallest circle that exists only touches two vertices." What the??? This definition is contradictory.
"The circumscribed circle of a triangle is the unique circle passing through the three vertices" At least that is consistent
I came to this page from Delaunay Triangulation. I expected it to refer to circumscribed circles, but it referred to circumcircles. Can someone please clarify this entry to explain the difference?
"The circumcircle of a triangle is the unique triangle that passes through its three vertices." from JR Shewchuk: "Delaunay Refinement Algorithms for Triangular Mesh Generation" (2001) from http://citeseer.ist.psu.edu/shewchuk01delaunay.html I think he meant circle :( --Aarghdvaark 05:10, 1 July 2006 (UTC)Aarghdvaark
Also; "Every circumcircle of a polygon touches at least three vertices.", contridicts "The smallest circle that completely contains the shape within it." doesn't it?
Just working through the logic in my own head, consider a rhombus. This will have two diagonals. The minimum diameter of a circle enscribing the shape will the length of the longer diagonal (won't it?). Taking this diagonal as the diameter of a circle, this circle will therefore not touch the other two corners unless every angle is 90 degrees as the angle constructed from a diameter to the circumference is always 90 degrees (n'est pas?) --Neo 22:14, 20 July 2006 (UTC)
[edit] Agree with merge proposal
I agree to merge this into circumscribed circle. I think it's stupid to have incompatible versions of the definition for triangles and non-triangles, and have only ever seen "circumcircle" used as a synonym for what's described in circumscribed circle (that is, the circle through all vertices). When I want to use the smallest containing circle I'll call it that, not the circumcircle.
I just did the corresponding merge for the sphere stubs Inscribed sphere and Insphere, and Circumscribed sphere and Circumsphere before I saw the debate here. But there it was even more broken because none of the insphere pages talked about having to be tangent to all the facets.
—David Eppstein 16:23, 4 October 2006 (UTC)
- I did the merge. Oleg Alexandrov (talk) 02:49, 15 October 2006 (UTC)
