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You are not logged in. #1 20060703 08:45:34
mikau's cartioidlast night I googled for an online graphing calculator for polar equations. Quicky found http://gcalc.net/ the calculator's interface is a bit of a nightmare but got the hang of it eventually. Anyways, I was talking to a buddy on AIM and showed him the calculator and how you could draw all kinds of cool shapes with polar equations like flowers, clovers, and cartioids. I told my friend to evaluate r = 1  sin(t), to get the equation of a cartioid, or heart. "Looks more like a buttocks!" my friend said. Last edited by mikau (20060703 09:04:40) A logarithm is just a misspelled algorithm. #2 20060703 08:55:59
Re: mikau's cartioidThis one here may be my favorite so far. a = 3, b = 1.5 Last edited by mikau (20060703 09:03:48) A logarithm is just a misspelled algorithm. #4 20060703 10:04:17
Re: mikau's cartioidSo that would be the mathematical equation for love? "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..." #5 20060703 10:13:13
Re: mikau's cartioidgreat minds think alike. I scrawled the equation down on notepad when I finished it and saved it as "loveequation". Last edited by mikau (20060703 10:13:41) A logarithm is just a misspelled algorithm. #6 20060703 10:14:31
Re: mikau's cartioidLOL! "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #7 20060703 10:23:16
Re: mikau's cartioidpicky picky! Well that little reflex curve seems to appear when b is close to (but less then) a. If I make it taller, the reflex curve tends to dissapear. But I need to make a larger to make it taller so I'd have to find a ballance. Gimme a sec... A logarithm is just a misspelled algorithm. #8 20060703 10:32:54
Re: mikau's cartioidOk heres one a bit taller, but you can see the reflex curve is more mild. A logarithm is just a misspelled algorithm. #9 20060703 11:30:05
Re: mikau's cartioidWell I think the best I got was this. I added a term of 0.25sin(t/2  pi/4)^500 or something like that. I closed the graph already. That doesn't look quite as goo as the other reflex curve. The reason the other looks so nice is because the absolute value term changes direction right there, so thats what produces the sharp point. A logarithm is just a misspelled algorithm. #10 20060703 12:04:26
Re: mikau's cartioidhere's a nice one, a = 3, b = 2, and I added a term of 0.5cos(t) this helps to horizontally compress the graph. Doesn't look half bad. Last edited by mikau (20060703 12:19:40) A logarithm is just a misspelled algorithm. #11 20060703 13:31:13
Re: mikau's cartioidAhhh ... both lovely. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #12 20060703 14:03:17
Re: mikau's cartioidThanks! You may have noticed I suggested it in the suggestions and comments forum. Yeah I mean thats what I figured, you could just plot is as a series of x,y points where x = r cos(t), y = r sin(t). That should work, right? A logarithm is just a misspelled algorithm. #13 20060703 23:03:02
Re: mikau's cartioidIt may be a little "buggy", but this is what I have so far: Plot of 3*(1abs(sin(t/20.75*pi)))+(sin(tpi/2))^2 "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #14 20060704 02:58:58
Re: mikau's cartioidWow! You got right on it! That was fast! Last edited by mikau (20060704 03:37:35) A logarithm is just a misspelled algorithm. #15 20060704 13:43:36
Re: mikau's cartioidThanks, mikau. Slightly updated version: Polar Plot of sqrt(x+5) vs sqrt(x+5) "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #16 20060710 12:59:23
Re: mikau's cartioidMy latest creation Last edited by mikau (20070114 06:31:38) A logarithm is just a misspelled algorithm. #17 20060710 13:50:14
Re: mikau's cartioidIt does! And glad to see the program works, too. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #18 20060710 13:51:36
Re: mikau's cartioidYeah thanks again for setting that up! Last edited by mikau (20060710 13:54:30) A logarithm is just a misspelled algorithm. #19 20060710 18:37:07#20 20060710 19:46:02
Re: mikau's cartioid
Got it from the Grapher  click on "forum" button, then copy text (right click, select all, right click, copy)
When you select a "zoom" rectangle it zooms exactly the rectangle and goes out of square  I am not sure if I am handling that well. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #21 20060711 06:43:33
Re: mikau's cartioidwhy not just make a fixed ratio of 1:1  thereby forcing sqaure 'zooms' #22 20060711 12:04:48
Re: mikau's cartioidBecause nonsquare zooms are also useful, particularly in realworld applications. Population vs time. Temperature versus power. That kind of thing. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #23 20060711 12:09:49
Re: mikau's cartioidI think the zooming should be independant of the aspect ratio. Zooming could just increase size and the aspect ratio could be adjusted in a seperate box. A logarithm is just a misspelled algorithm. #24 20060711 21:16:01
Re: mikau's cartioidThat's a very good suggestion mikau! You(mathsisfun) could put an inputbox where you could change the ratio if you wanted to. 