Re: For the Mathematicians.

Thanks again for all the information. You've had a very impressive as well as a varied career! I shall be poking around your dissertation as it sounds quite interesting. Roger > On Jan 23, 2022, at 7:25 PM, doc hawk via use-livecode > wrote: > > > Roger rumbled, > >> Thank you very much

Re: For the Mathematicians.

Roger rumbled, > Thank you very much for your reply. You’re quite welcome. Accumulated knowledge is wasted if not shared! I used to find it online quite easily. But not any more. >Again I thank you for taking the time to respond. Is your dissertation >readable to a LiveCoder that has no

Re: For the Mathematicians.

Thank you very much for your reply. It looks like I did indeed bite off more than I can chew. But I really appreciate that you’ve given me some avenues to explore. I’m a retired Physicist that loves math, and particularly how to use computers to model the real world. Again I thank you for

Re: For the Mathematicians.

roger reasoned, > Yet, as I mentioned in the beginning, Graphing tools like Good Grapher on the > Mac can do it. And, I wonder how? My guess would be using either differentials or differences, and drawing from the current point for a small distance, with some watching for branch points.

Re: For the Mathematicians.

Yet, as I mentioned in the beginning, Graphing tools like Good Grapher on the Mac can do it. And, I wonder how? Thanks, Roger > On Jan 23, 2022, at 4:51 PM, doc hawk via use-livecode > wrote: > > Implicit functions are not, in general, directly plowable, as there is no > general y(x)

Re: For the Mathematicians.

Implicit functions are not, in general, directly plowable, as there is no general y(x) explicit function available. You *could*use differentials and derivates to take small steps, if you’re careful and watch for points with multiple solutions (in the example function, when it crosses either

Re: For the Mathematicians.

Hi François, My aim is to find a way to plot any and all implicit functions, not to plot only the lemniscate. But, that is a very interesting Wikipedia entry. Sorry I wasn’t clear! Thanks, Roger > On Jan 22, 2022, at 4:37 PM, francois.chaplais via use-livecode > wrote: > > In >

Re: For the Mathematicians.

In https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli use the formulation in polar coordinates. You sample theta, compute the corresponding radius r, convert the polar coordinates to usual cartesian coordinates, and draw a line between

Re: For the Mathematicians.

Thanks, Thomas. I’ve done some of that but you suggest some better keywords to search with. I will give it another go. Roger > On Jan 22, 2022, at 12:34 PM, Thomas von Fintel via use-livecode > wrote: > > I am not a mathematician, but this kind of equation is called implicit > function,

Re: For the Mathematicians.

I am not a mathematician, but this kind of equation is called implicit function, implicit equation or implicit curve. If you search for that combined with draw or plot, you might find explanations. But it seems to be complicated. Hope this helps. Thomas > Am 22.01.2022 um 17:56 schrieb Roger

For the Mathematicians.

This equation for the lemniscate, (x^2+y^2)^2 = 100*(x^2-y^2) is an example of a 2 variable function f(x,y). I am trying to figure how to plot such functions in LC. I can do simple functions like y = f(x) and x = f(t), y = f(t). Calculators such Good Grapher on the Mac do these f(x,y) functions