Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20061205 14:56:07
Mystery newfangled trig???I made this diagram in a free CAD program. igloo myrtilles fourmis #2 20061205 22:53:01
Re: Mystery newfangled trig???It looks like the lines have a length of something like 1+cosθ, where θ is the angle between the line and the downward vertical. Something to do with polar coordinates, anyway. Why did the vector cross the road? It wanted to be normal. #3 20061206 11:49:02
Re: Mystery newfangled trig???Your guess is really a nice one!! But it's not how I did it!! igloo myrtilles fourmis #4 20061207 02:36:40
Re: Mystery newfangled trig???Okay, I plotted out the (1 + sin(theta from horizontal)) guess. Last edited by John E. Franklin (20061207 02:41:41) igloo myrtilles fourmis #5 20061207 03:13:14
Re: Mystery newfangled trig???I have no idea what curve it is, but perhaps the filename can give someone a clue? #6 20061207 06:46:04
Re: Mystery newfangled trig???Use a taylor series to see if it converges to any known finite polynomial or natural function. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #7 20061207 07:10:10
Re: Mystery newfangled trig???http://www.mathsisfun.com/forum/postgallery.php?pid=51418&filename=SinPlusOneForRadiusVersusAngleProportionalHeight.png #8 20061207 11:32:37
Re: Mystery newfangled trig???Oh I didn't know you could read the original filename on the forum!! igloo myrtilles fourmis #9 20061213 08:41:37
Re: Mystery newfangled trig???Time's Up!!! igloo myrtilles fourmis #10 20061213 11:00:55
Re: Mystery newfangled trig???But then what happens with the 0 degree angle? By continuing the pattern, that should stop immediately (or if it was made to stop at some point above the horizontal, it would go on for ever), but it clearly has a finite length. What calculation did you use there? Why did the vector cross the road? It wanted to be normal. #11 20061219 14:27:15
Re: Mystery newfangled trig???For zero, I didn't actually do that one, but I did numbers really close like 1 degree and probably onetenth of a degree on my calculator. Can't remember right now. Sorry. I think it is undefined at zero degrees, but the curve might point right at a number. Maybe we can figure it out. Talk to you later. igloo myrtilles fourmis #12 20061220 00:30:13
Re: Mystery newfangled trig???For degrees, it points to 5.729477951 my calculator says from .00001 / sin .00001. igloo myrtilles fourmis #13 20061220 00:50:22
Re: Mystery newfangled trig???For the fun of it, I just did it in radians and you won't believe it!! igloo myrtilles fourmis #14 20061221 04:35:20
Re: Mystery newfangled trig???Well, here's the answer, time's up again!! igloo myrtilles fourmis 