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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.

circumcircle of a polygon?[edit]

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)


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)

circumcircle/circumscribed circle for triangles[edit]

"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 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)

Agree with merge proposal[edit]

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)

Baker's formula[edit]

I'm trying to make a modest change to this article by adding a link to my article about computing the circumcenter of a triangle using complex arithmetic, but someone keeps removing this change.

My article is at

If you disagree with my math, then please contact me at [redacted].

Otherwise, stop removing my changes.

Thanks very much.

Henry Baker, PhD Santa Barbara, CA — Preceding unsigned comment added by (talk) 21:27, 2 June 2012 (UTC)

Don't publish your contact info here; if you make a user account, we can talk to you on your User Talk page, or indirectly by email if you activate that feature.
The problem is not that your formula is false (I haven't tried it) but that it is original with you. —Tamfang (talk) 21:39, 2 June 2012 (UTC)
Dr. Baker, you have two choices here. You can either learn how Wikipedia works and why your edit was rejected and them work with other editors in an attempt to come to a conclusion that the majority supports, or you can ignore the rules, have your edits deleted again and again, and either go away in frustration badmouthing Wikipedia or stay and get into a rip-roaring fight that you cannot win. Your choice.
Assuming that you want to take a course that has the greatest probability of you getting what you want, here are a few clues to get you started.
Get a username and communicate through your Wikipedia talk page. We don't use email except in emergency situations because we want everything to be completely open to everybody.
When you wish to talk about Circumscribed circle, talk about it at Talk:Circumscribed circle You posted here instead. Circumscribed circle and Circumcircle are different Wikipedia pages. EDIT: the pages got merged and the talk pages did not. Not Dr. Baker's fault. Nonetheless, Talk:Circumscribed circle is the place to discuss this.
Read WP:ELNO and WP:CONSENSUS. Those are the policies you need to learn.
We get a lot of academics here. Alas, some of them are completely ineducable. If you take the time to learn how Wikipedia works, it will be a big help to you. --Guy Macon (talk) 22:02, 2 June 2012 (UTC)
You people are insane. It would appear that Wikipedia is the one place in the world where not only is plagiarism ok, it is required!
BTW, if the standard you use (published in a paper journal, where libraries have to pay thousands of dollars for a subscription) were rigidly enforced, Wikipedia would be perhaps 1/10,000th of its present size.
Let's focus on mathematical correctness on these Wikipedia math pages. I'm honored that you've done the historical research to prove the novelty of my work; perhaps I should suggest that Euler already developed this formula (he's the constant counter-example for priority in mathematics).
Your founder, Mr. Wales, is currently consulting for the British govt to see how to get British research out from under these "pay walls". Let's see what he has to say about this particular discussion.
Henry Baker, Ph.D. — Preceding unsigned comment added by (talk) 23:27, 2 June 2012 (UTC)
Hmmm. Posted here again after being told Talk:Circumscribed circle is the proper place? Check. Calling us names? Check. Bloviating about how stupid Wikipedia's policies are without bothering to read them first? Check. Argumentum ad Jimbonem? Check. Pontification and sarcasm? Check. Tentitive conclusion: high probability of being ineducable.
Here is some good advice from Jimmy Wales himself. Follow it and I am sure that you will get the response you deserve.--Guy Macon (talk) 23:55, 2 June 2012 (UTC)

Gee, I guess the British govt isn't going to get what they hoped for out of Jimmy. Pity.

It's clear that any further math discussions with you folks would be casting mathematical pearls before swine.

I have a nice life; you petty tyrants apparently don't. Pity.

Bye! — Preceding unsigned comment added by (talk) 00:10, 3 June 2012 (UTC)

Ah. I see that you have chosen the "ignore the rules, have your edits deleted again and again, and go away in frustration badmouthing Wikipedia" option. --Guy Macon (talk) 00:35, 3 June 2012 (UTC)