Talk:Circular segment

message: Write-up on Circular Segment well done. There is a simpler Trig approach
Removed the hand drawn diagram as it is not relevant to the derivation of the formula and it does not add anything to the article. 165.222.186.195 11:52, 13 September 2006 (UTC)
thread_title: No title

message: Isn't the area 1/2 r^2 theta, where theta is in radians. Don't think you need trig, unless i have misinterpreted this article  —Preceding unsigned comment added by Addy-g-indahouse (talk • contribs) 11:00, 24 October 2007 (UTC)
replies: text: That's the area of the circular sector. This is a circular segment. Look at the picture. --76.173.203.58 (talk) 06:53, 14 June 2009 (UTC)

text: Go ahead; nobody is stopping you. --76.173.203.58 (talk) 06:53, 14 June 2009 (UTC)
thread_title:  One sec^2...... pun intended 

message: The final formula for the area of a circular segment has a little problem: In the first case (where theta in radians) the sinus actually takes degrees as an argument! It should be changed to accept radians as an argument, why convert radians to degrees for the sinus?  —Preceding unsigned comment added by Hiddensob (talk • contribs) 09:44, 7 May 2011 (UTC)
thread_title:  The area formula should be changed 

message: ^ The comment that Theta is in radians is absolutely not superfluous!  Not everyone needing to use this equation did Mathematics even beyond age 16 (which for some of us is a bloody long time ago)!!  — Preceding unsigned comment added by 202.96.219.34 (talk) 07:15, 25 May 2011 (UTC)
thread_title:  Theta is in Radians everyone! 

message: This is all just made up. Do any of you know what you are doing? For example, there should not be any 180 degrees in the formulas and at the same time pi.  You are mixing degrees and radians. Jfgrcar (talk) 16:37, 4 August 2013 (UTC)
replies: text: Of course there should. I suppose you mean the arc length formula, s = \frac{\alpha}{180}\pi R? Formulae that relate radius and arc length need the angle to be in radians. The article provides formulae with the angle \alpha degrees as well as \theta radians, presumably for the reader's convenience—and you find both 180 and π in the formula to convert degrees to radians. -- Perey (talk) 04:54, 13 September 2013 (UTC)
thread_title:  Messed up 

message: What is the formula to get the angle if the area and the radius is known?  — Preceding unsigned comment added by 115.70.29.185 (talk) 08:43, 21 December 2020 (UTC)
replies: text: It's highly unusual that one knows or measured the area directly, and also got the radius.  Those two quantities are transcendentally related to the central angle, which is why I suspect this is a trick question. Here is the transcendental relationship: a=\tfrac{1}{2}r^2(\theta-\sin\theta) so, using a substitution from the Taylor series, \sin\theta=\theta-\tfrac{\theta^3}{6}, \theta\approx\sqrt[3]\tfrac{12a}{r^2}.  Sbalfour (talk) 17:41, 2 March 2021 (UTC)
thread_title:  Angle from area and radius 

message: There's only a few parameters of a circular segment: the chord length, segment height, arc length, and area.  Then there's two incidental quantities, properties of the circle: radius and central angle. And that's it.  Some are usually given or can be easily measured: chord length and height.  The arc length may or may not be given, and can't easily be directly measured.  The radius, central angle, and area are usually the unknowns, and must be computed.  That gives us the structure of the presentation.  First, givens; second, incidental quantities; third derived quantities (arc length and area).
I also think the presentation should be limited to one realization of each relationship; anyone with a modicum of algebra and trig can substitute arctan for arcsin, (r-h) for h, and etc.  The article isn't a math textbook with every flavor an exam could ask about.
So I'm going to do a bit of reorg.
Sbalfour (talk) 17:02, 2 March 2021 (UTC)
replies: text: I've substantially redrafted and simplified the presentation; just the basic formulae.  There's a zillion perturbations of these, like you find in a Schaums mathematical reference - that's not the purpose of the encyclopedia.  The article is about circular segments, not a mathematics cheat sheet. Sbalfour (talk) 17:01, 3 March 2021 (UTC)
thread_title:  General order of presentation 

message: Another editor queried, "what if I have the radius and area and want the angle?" and I answered him above. There are only six quantities associated with a circular segment: height, length, angle, radius, arclength, and area. Given any two, the others can/must be computed. That would be done by substituting and solving the requisite equations stated in the text for one of the other variables, in turn.  As a proposition in linear algebra, there are only two independent variables, four dependent ones, and 6 equations relating them, some of which are redundant depending on what quantities are given (independent). In set theory, we have a set of 6 choose 2, which yields a set of (6*5)/(2*1) = 15 unique pairs.  It is plausible for one to ask, given some pair, how to solve directly for the other four quantities.  That's the kind of question that could occur on a geometry examination, but as an enlightening encyclopedia exposition, exhaustive and exhausting.  At some level, it is more informative to assume some understanding of the relationships, than inundate the reader with information (so the article does not have 15 sets of four equations to solve for every possible pair of givens). Sbalfour (talk) 23:00, 5 March 2021 (UTC)
thread_title:  A comment on completeness 

message: Defining a circular segment as a region of two-dimensional space makes the "more formal" definition less specific than the informal one, by introducing the possibility that the space isn't flat. For example, the segment might be the shape of a soap bubble that's being blown through a D-shaped loop of wire.  Wouldn't plane area be both more accurate, and more intuitive to readers?
If the term is also used in a non-euclidean context, we can simply change In geometry in the opening sentence to In plane geometry, after which there's no further need for phrases like two-dimensional space unless we want to explain what a plane is. Musiconeologist (talk) 17:29, 31 March 2024 (UTC)
replies: text: I've now changed it to refer to a plane region, but kept In geometry for now. Musiconeologist (talk) 18:53, 31 March 2024 (UTC)
thread_title:  A region of two-dimensional space