Preserved Topic: Math, and the significance of .741767

OK, I've been playing with this sine/cosine function for my little 5k animations, and I found this number by experimentation, which leaves my sin()/cos() functions standing dead still, or nearly. It happens when I increment by .741767, (approximately), and I wonder if any of you math gurus have an explanation, what's so special about this number? My instinct tells me that if I knew what was happening, I could do ... well, something neat with the knowledge, I don't know exactly what. Mostly curiousity, I found this magic range by building a little tool and finding where the sin/cos functions gave a nice movement, and by trial and error narrowed the 'magic' part of the number down to here.

Your pal, -doc-

Wierd, didn't know that the number was special. The number is in radians, right? Have to look some more on this one. Good practice for tomorrows exam...

To save some space (and maybe speed) you might want to use tan() instead of sin()/cos(), they are the same

_________________________
Anyone who has lost track of time when using a computer knows the propensity to dream, the urge to make dreams come true and the tendency to miss lunch.
- copied from the wall of cell 408 -

If i understood what you were doing with the number, and what results you get, i could probably help

All I have to say is .741767 = .74177 = .7418 = .742, when you round it so thats 740/1000 now to simplify, 371/500 which again, = .742, why is it important? I have no damn clue...

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Aahhh...now I remember...that's just like in 3d, when you try to revolve something more than 90 degrees...the fomula that is responsible for the revolving has problems with that (esp. Truespace...no revolving more than 90 degrees...otherwise it plays somehwat crazy...one must first create a 'stop' between, and then continue on, so that the program 'knew' which way to turn...)

Good one, Ini...

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Hmmm... 3.14159 / .741767 is about 4.235. So it's just a little more than 45 degrees (pi/4 radians).

Well, it'd seem to me that that number would still create a lot of movement. It's small enough that every eight iterations the object should go around in a full circle.

I'm going to make myself a quick thing here to demonstrate it for myself...

yeah, I made it, and it does about what I expected... every eight iterations it completes a cycle. What exactly did you say it's doing?

I knew slime would jump in with his algebraic genius brain

Well, if I increment by just a little more than that (.742647), my object move in a circle clockwise, and a little less (.741047) they go counter-clockwise. I'm not using the sin/cos really, just sin() for the X movement and cos() for the Y. It was just weird, this number right between the two makes for no movement at all, (or nearly so, I didn't bother to pin it down exactly), so it stands for *something*, I just don't know what.

Here' I made a custom version of my 5k page, at http://www.ozones.com/play/doc5k - choose movement "C" to change the increment to the magic number.

Your pal, -doc-



[This message has been edited by DocOzone (edited 05-30-2002).]

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I get a 404 at that page you linked, Doc.

I'm willing to bet that something is happening... maybe something is being multiplied by the .741767, that's making the steps exactly equal to two pi, so each time it goes around in a *full* circle, but if you increase or decrease the number a bit, then it goes in a little more than full circle, or a little less, creating the appearance that it's moving just a little bit.

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No, it's not Ym and Xm, those are multiplied by the *results* of the sine and cosine, they just change the size of the circle that each element sweeps through.

I think I found out what it is! One second...

Yup. I got it.

Take .741767. Multiply it by the number of layers you've got (288). Divide by (2*pi). You get almost *exactly* 32.

See, what you're doing wrong, is you're incrementing cTT=cTT+mV *inside* the for loop that updates each element's position! Now, the fact that you're doing that creates the nice way that all the elements are turned a little more than their neighbor is, creating that nice wave pattern. But that also means that each time interval, cTT is incremented .741767*288, which is evenly divisibly by two pi (the circumference of a full circle). That's what creates the effect InI and I were getting at.

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Hah! I knew pi would have to be in there somewhere, but I wasn't seeing how it related to .741767 at all. The multple increments is not what I'd call "wrong" per sé, and getting just that little bit off gives me a nice flow as you say. So, I should be able to increment by the value I'm already using, divided by 32 also, shouldn't I? (running off to test) Hmm, no, that just does something even weirder, check it out under option "C". I may just make this the toy part, change the colors, and alter the values into things I find accidentally that are neat looking, heh. I love just taking a formula I don't really understand and then animating it, you get such neat effects, a glimpse inside the universe!

Your pal, -doc-

Ah! So cool, now I now what's happening, I can find the "cool spots" nearby where neat looking animations happen. Apparently, setting the increment to ((Math.PI*2)/288)*34 leads to a curve much like I have in the A and B movement, yet stationary. Adding or subtracting .001 from the increment gives me my A and B loops, but using a different multiplier gives some interestng effects too, see the C and D loops (set at 35*... +.001 and 33*...+.001). Cool! Understanding always makes things easier. I discovered the best places to set the increment by tying that value to my mouse positions, and then moving it around and checking the status line, writing down the sweet values. Thanks for your help Slime, you've given me the key to make this thing even cooler!

Your pal, -doc-

Wow. My head is spinning.




Cell 270

???
Cool page tho..

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