Let P be a point, not the center, in the interior of a (round) disk D⊂ℝ² and let A and B be points on ∂D such that the line segments AP and BP have equal length. Choose an arc AB. What's the shape bounded by the arc and the two segments called?

  • 2
    $\begingroup$ For $P$ at the center, that's a "sector". ( en.wikipedia.org/wiki/Circular_sector ) I don't know of a name for $P$ elsewhere. How about "pseudo-sector" or "generalized sector"? (BTW, this might be a cleaner description: Given P on the diameter bisecting arc AB, the figure bounded by AP, BP, and arc AB.) $\endgroup$ – Blue Jan 10 '11 at 0:02
  • $\begingroup$ What leads you to believe that this object should have a name? $\endgroup$ – Tpofofn Jan 10 '11 at 1:07
  • $\begingroup$ I call this a "slice" ;) $\endgroup$ – Matt Calhoun Jan 10 '11 at 1:25
  • $\begingroup$ @Jasper Loy "By '(round) disk' do you simply mean circle", well, a circle is one-dimensional; I meant the thing it bounds. $\endgroup$ – msh210 Jan 10 '11 at 16:39
  • $\begingroup$ @Day Late Don "a cleaner description": Yes, thanks! $\endgroup$ – msh210 Jan 10 '11 at 16:42

I suppose you could call it an isosceles curvilinear triangle, although that doesn't capture the curvy part being an arc of a circle.


It's called a circular segment.

Edited to add: As Jasper has pointed out in the comments, this is not what the question asked. So I don't know the answer.

  • 2
    $\begingroup$ I'm pretty sure that a circular segment is only the region between a chord AB and minor arc AB. $\endgroup$ – Isaac Jan 9 '11 at 21:42
  • $\begingroup$ @Isaac: Yes, my Wikipedia link agrees with you. It looks as if the region between a chord AB and major arc AB doesn't have a name. How about 'circular cosegment'? $\endgroup$ – TonyK Jan 9 '11 at 22:17
  • 1
    $\begingroup$ If you "don't know the answer", please delete your answer. $\endgroup$ – Lord_Farin Nov 26 '13 at 9:17
  • $\begingroup$ @Lord_Farin: I don't know what inspired you to check back through almost three years of my answers, but I'm sure it's not healthy... $\endgroup$ – TonyK Nov 26 '13 at 9:38
  • $\begingroup$ @TonyK Someone else did. It showed up in the 10k Tools. Rest assured, it's nothing personal. $\endgroup$ – Lord_Farin Nov 26 '13 at 9:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.