Talk:Circumscribed circle
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[edit] Discussion: Merge with circumcircle
I assert that circumscribed circle and circumcircle not be merged. They are fundamentally different concepts with different definitions, and to merge them would show a profound lack of geometric sophistication. For example, if you draw a five-point star, this star has no circumscribed circle (since the star has 10 vertices), but it does indeed have a circumcircle. The circumcircle does not have to touch every vertex; instead, it merely has to be the unique circle with the smallest radius such that the entirety of the star's interior is bounded within it. User:KyleGoetz
[edit] Triangles: Circumscribed circle is a circumcircle
A circumscribed circle for any triangle is the same circle as the circumcenter. Whoever wrote otherwise is absolutely wrong: http://mathworld.wolfram.com/Circumcircle.html User:KyleGoetz Just to clarify this with my comment above concerning the differences between a circumcircle and a circumscribed circle: for a triangle, they are the same; however, for other polygons this may not be true. User:KyleGoetz
I think it is very wrong to have a definition for triangles that is incompatible with the definition for polygons in general, but I also don't think the circumscribed circle and circumcircle are ever different. At best note the "smallest enclosing circle" version in passing as a variant usage rather than making it the main definition of the word. As source I cite this paper — it's my own work, so I'm not going to edit into the actual article, but it's a well respected survey from a number of years ago and clearly states (top of page 9, and theorem 1 page 13) that circumcircle = circumscribing circle for triangles, and that the smallest enclosing circle is something different. The only single word synonym I've seen in professional usage for smallest enclosing circle is minidisk or minidisc (or miniball in higher dimensions). —David Eppstein 04:49, 15 October 2006 (UTC)
- Yeah, there is no difference between circumscribed circle and a circumcircle. Any polygon has a circumcircle, and when polygon's vertices happen to be all on that circumcircle, it is called a circumscribed circle. Oleg Alexandrov (talk) 05:05, 15 October 2006 (UTC)
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- Er. There are polygons which have all vertices on a circle, but for which that circle is not the smallest enclosing circle. Polygons other than triangles, even. So I'm not sure which circle your comment is referring to. To me, "circumscribed circle" and "circumcircle" can only mean a circle passing through all vertices, even if that circle is not the smallest one enclosing the polygon. Anything else needs a different name. —David Eppstein 05:17, 15 October 2006 (UTC)
- OK, then my changes to the article were wrong. I still think that my merger of circumcircle into circumscribed circle was a good thing. I will try to fix my errors tomorrow. Oleg Alexandrov (talk) 05:34, 15 October 2006 (UTC)
- Thanks for fixing my mistake! Oleg Alexandrov (talk) 16:03, 15 October 2006 (UTC)
- OK, then my changes to the article were wrong. I still think that my merger of circumcircle into circumscribed circle was a good thing. I will try to fix my errors tomorrow. Oleg Alexandrov (talk) 05:34, 15 October 2006 (UTC)
- Er. There are polygons which have all vertices on a circle, but for which that circle is not the smallest enclosing circle. Polygons other than triangles, even. So I'm not sure which circle your comment is referring to. To me, "circumscribed circle" and "circumcircle" can only mean a circle passing through all vertices, even if that circle is not the smallest one enclosing the polygon. Anything else needs a different name. —David Eppstein 05:17, 15 October 2006 (UTC)
