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Related: Culture Forums, Support ForumsQuestion for math geeks
Given a particular angle, how do you determine the equation of the curve that best "fits" into that angle?
I'm sorry that I don't know the proper terminology, but you can see therefore why I'm having trouble researching the solution for myself. For all I know, it might be terrifically simple but I'm over-thinking it.
For example, if you have a 45° angle, what's the formula for the angle that snuggles into it most comfortably? What's this process called, if indeed it has a name?
A request for anyone who's passionate about the subject: be merciful and not too complainy about my awkward terminology; if I knew a better way to ask the question I would do so, so don't jump on me for a lack of precision, please!
Thanks!
HopeHoops
(47,675 posts)Orrex
(63,225 posts)I appreciate your inpu!
HopeHoops
(47,675 posts)Orrex
(63,225 posts)I didn't specify numbers, because I don't yet have them, but I think that I gave a better description of what I'm seeking.
Thanks!
pokerfan
(27,677 posts)Smaller circles will fit 'deeper' into the angle.
HopeHoops
(47,675 posts)Well, a portion of it at least. The choice is mostly a matter of how precise your representation needs to be. A parabola is easier to adjust for three dimensions than a circle - just by where you cut off the sides.
Response to HopeHoops (Reply #1)
Tesha This message was self-deleted by its author.
Dr. Strange
(25,925 posts)But yeah, I think a hyperbola would be the best. The sides of the angle could be the asymptotes, and you can jiggle the eccentricity to have the curve snuggle up as close as you want.
Response to Dr. Strange (Reply #25)
Tesha This message was self-deleted by its author.
Lionel Mandrake
(4,076 posts)where a is the angle in radians. This is one half of a hyperbola.
Orrex
(63,225 posts)Thanks!
Lionel Mandrake
(4,076 posts)I hope this is what you were looking for.
madinmaryland
(64,933 posts)should not be attempting to understand it. eom
Orrex
(63,225 posts)madinmaryland
(64,933 posts)pokerfan
(27,677 posts)Lionel Mandrake
(4,076 posts)then the relationship is tangential.
Snuggling and kissing - who knows what that might lead to?
Even a hyperbola which approaches the angle asymptotically can be said to osculate with the angle at infinity. But that's kind of standoffish and not very sexy.
madinmaryland
(64,933 posts)Lionel Mandrake
(4,076 posts)A curve C containing a point P where the radius of curvature equals r, together with the tangent line and the osculating circle touching C at P
The term derives from the Latinate root "osculate", to kiss, because the two curves contact one another in a more intimate way than simple tangency.
To read more, search for "Osculating curve" on Wikipedia
madinmaryland
(64,933 posts)Lionel Mandrake
(4,076 posts)pokerfan
(27,677 posts)Lionel Mandrake
(4,076 posts)swimboy
(7,285 posts)SwissTony
(2,560 posts)We have a pretty good idea on intersecting straight lines and angles. What needs to be "fitted"?
Dr. Strange
(25,925 posts)Orrex
(63,225 posts)backscatter712
(26,355 posts)This takes me back to my days of learning computer graphics as a computer science major.
Beziers can be used for taking a group of control points, say the points used to describe a pair of lines forming a 45 degree angle, to create a curve that tracks the angle somewhat.
http://en.wikipedia.org/wiki/B%C3%A9zier_curve
Another related mathematical construct is a NURBS curve. NURBS curves have the virtue of being more controllable than Bezier splines.
http://en.wikipedia.org/wiki/Non-uniform_rational_B-spline