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Bisection of a line segment using a compass and rulerA shape and its skeleton, computed with a topology-preserving thinning algorithm.Circumscribed circle, C, and circumcenter, O, of a cyclic polygon, P
A point is said to be equidistant to a set of objects if the distances between that point and each object are equal.[1]
In two dimensions the locus of points equidistant between two given (different) points is their perpendicular bisector. This result can be generalised to three dimension where to locus of equidistant points form a plane.
For a triangle the circumcentre is a point equidistant from each of the three end points. Every non degenerate triangle has such a point. This result can be generalised to cyclic polygons. The center of a circle is equidistant to every point on the circle. Likewise the center of a sphere is equidistant to every point on the sphere.
Latest comment: 14 years ago7 comments6 people in discussion
The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.
Support. Fascinating that an article that has had such a traumatic history could become such a good stub. Well done to the rescuers, and it must prove something, dunno exactly what. Andrewa (talk) 19:51, 17 August 2011 (UTC)Reply
Oppose I thought about trying to rewrite the first sentence to use Equidistance and basically failed. In mathematics it is a property of sets of points rather than an object in its own right. If someone with better grammatical dexterity would care to have a go I could be convinced otherwise.--Salix (talk): 21:12, 17 August 2011 (UTC)Reply
Oppose. WP:NOUN says Nouns and noun phrases are normally preferred over titles. It does not say that nouns must always be used. I think this page merits an exception to the general rule: the use of "equidistance" as a noun is extremely rare. Jowa fan (talk) 01:19, 18 August 2011 (UTC)Reply
Comment I added a note at WT:WikiProject Mathematics#deletion_of_equidistant referring to here, so that I hope I do not seem to be subverting others' views. It seems that others already spotted it anyway! I can see both sideds of both sides so have no strong view of this, hence listed genuinely for discussion. I think, on the whole, the mathematicians should have the final say (with a slight caveat, is it a mathematical term or is it in general English usage, that is where I waver.) Si Trew (talk) 06:57, 18 August 2011 (UTC)Reply
To clarify, when I said the mathematicians should have the final say, that was not meant patronising though I see it could seem so, but rather, if it is a technical mathematical term, those at WikProject Mathematics are best to discuss (and perhaps User:Thryduulf's support at the latest RfD should be taken into account too, which would make it two supports and two opposes). Not that we are sitting here counting votes of course, and I have myself kinda "abstained" so could fall either side of the fence; but just saying that my opinion as "not a mathematician" is to say, what would people be more likely to search for? But it is perhaps a sledgehammer to kill a gnat anyway, since we are just reversing a redirect, and I am rather persuaded by Salix' statement that he tried to write it as equidistance and failed. So I will put a definition below, but I am coming around to the point that as it is, it is far more concise and says what it means wheras with equidistance one has to jump through syntactical hoops and put it in the passive:
Equidistance is the property of a point that is has the same distance from all other objects in the universe of discourse.
The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.
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