3D graphing of mathematical functions

[Michael GilliganParticipant @michaelgilligan61133]

I am exploring QuickGraph, a wonderful iOS App that plots rotatable 3D graphs of mathematical functions, and I now realise that my schooling barely touched the topic.

I need to find a 'friendly' tutorial on the web, to teach me the basics of 3D functions.

Can anyone advise, please ?

MichaelG.

Edited By Michael Gilligan on 12/12/2016 21:06:32

[Michael GilliganParticipant @michaelgilligan61133]

Introductory text needed please …

[John HaineParticipant @johnhaine32865]

It's a slippery slope Michael… with that app you could probably learn more than you could from most tutorials. What do you particularly want to know? you could get ensnared in stuff like partial differentials quite easily if you wanted to go that far. But I must have a look at that app, it looks cool.

[Ady1Participant @ady1]

I need to find a 'friendly' tutorial on the web

You'll be lucky if you do.

Mathematics is like a gigantic pi**ing competion in complicated explanations gleefully practiced by middle class alien life forms

This one for example is quite literally, and simply, the inverse of a lottery probability (ie 3 balls 56 to 1 etc)

If you tried to edit this very simple explanation into that wiki, it would be deleted

As mentioned, that program could tell you a lot more than any tutorial, and more simply too

Edited By Ady1 on 12/12/2016 21:27:59

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 12/12/2016 21:23:36:

It's a slippery slope Michael… with that app you could probably learn more than you could from most tutorials. What do you particularly want to know? you could get ensnared in stuff like partial differentials quite easily if you wanted to go that far. But I must have a look at that app, it looks cool.

.

Here's a link to the App store, John **LINK**

There's a good library of 2D and 3D functions included, but I don't want to just play about changing numbers.

[infinite number of monkeys writing Shakespeare]

So I started looking at simple stuff like spheres and cones … and realised that I don't really 'have the basics'

Ultimately, I'm interested in the way that natural shapes develop from simple expressions. [particularly, the forms of the Radiolaria] … I have a copy of Turing's thesis on this; which I cannot understand, but I'm hoping that a more interactive graphics environment will help.

I think it's what they call Lesson 1.01 that I need.

MichaelG.

[JimmehParticipant @jimmeh]

Whenever I need something a bit mathsy I refer to MathWorld​ . Its helped me out a lot over the years, particularly with 3D geometry. I know it isn't tutorials per say but its a great resource and may help you to find functions of interest.  Please use recreational maths responsibly.

James

Edited By Jimmeh on 12/12/2016 21:56:22

[Michael GilliganParticipant @michaelgilligan61133]

Thanks for the input, Gentlemen

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

So … Here is the Quartic Surface "Tooth" from James's 'Recreational' link:

… It works fine; but I'm 'Painting by Numbers' without any real understanding.

I guess the next step is just to follow the Wolfram hyperlinks back from there, until I find my level.

MichaelG.

[Enough!Participant @enough]

Posted by Michael Gilligan on 12/12/2016 20:59:58:

I am exploring QuickGraph,

Thanks for that!

If you're into curves and such, you might enjoy the ios app "Harmonograph" for generating – unsurprisingly – harmonograph curves. It really is rather a good, and hypnotic, program.

(Or you could go into the workshop and and build a mechanical version but the app is easier).

[Neil WyattModerator @neilwyatt]

Posted by Ady1 on 12/12/2016 21:26:23:

I need to find a 'friendly' tutorial on the web

You'll be lucky if you do.

Mathematics is like a gigantic pi**ing competion in complicated explanations gleefully practiced by middle class alien life forms

This one for example is quite literally, and simply, the inverse of a lottery probability (ie 3 balls 56 to 1 etc)

If you tried to edit this very simple explanation into that wiki, it would be deleted

As mentioned, that program could tell you a lot more than any tutorial, and more simply too

Edited By Ady1 on 12/12/2016 21:27:59

You are sadly right Ady, two areas of wikipedia are steadfastly defended by experts who rapidly expunge any 'plain English' explanation or interpretation: statistics and linguistics. The only way to try and understand them is to look up lots of arcane terms that are then explained in confusing ways and ultimately you end up going in circles.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Neil Wyatt on 13/12/2016 08:06:32:

… ultimately you end up going in circles.

.

… and in 3D [sphere] there is an inflnity of circles to go round on.

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

Perhaps I could try a specific question:

This page **LINK** by 'benjoffe' has some interesting examples:

https://www.benjoffe.com/code/tools/functions3d/examples

The final item [intersecting fences] appeals to me … but I haven't the foggiest idea how that function works, or even [since it is not shown as an equation] how to enter it into QuickGraph.

So … What do I do next ?

MichaelG.

Please don't answer with "Give-up, you're obviously not worthy"

[John HaineParticipant @johnhaine32865]

Michael, he does give the equation:

(z=) .75/[exp((x*5)^2*(y*5)^2]

He doesn't give the z= bit at the start for any of his examples, and I assume that it is meant to have [brackets] as I have inserted.

?

[Michael GilliganParticipant @michaelgilligan61133]

Thanks, John … I will try that

MichaelG.

.

As you will see … I am struggling; because it is not obvious to me that his expression is 'inevitably' an equation to z

Edited By Michael Gilligan on 13/12/2016 12:49:41

[Michael GilliganParticipant @michaelgilligan61133]

With John's advice, and the liberal application of parentheses … I am nearly there with the 'intersecting fences'

… but mine look pointy, whereas the example by benjoffe has them curvy.

MichaelG.

[MuzzerParticipant @muzzer]

I suspect your axis scaling is simply different. He possibly has X and Y limits of +/- 2 or so. Possibly similar for Z?

[John HaineParticipant @johnhaine32865]

You can see from the plot that the x and y limits are +/-7 in each case. The maximum value of the function is when either of both of x and y are zero, when the denominator is exp(zero) which is unity, so the max value is just the denominator, that is 0.75. I can't see from the picture here Michael. but as x or y get very big do the fences get very thin though their height remains the same?

[Michael GilliganParticipant @michaelgilligan61133]

Thanks Muzzer & John,

This is the same plot, as a mesh, and zoomed-in:

.

It is now evident, I think, that the problem is that the 'digital resolution' of the samples is rather coarse

The App seems to default to +/- 8 on each axis, and re-scale when 'pinch-zoomed' … but the resolution is not really sufficient to do justice to this particular function.

… Does that make sense ?

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

Looking again at Ben Joffe's example [linked earlier], and qooted here:

… I think I am satisfied that my version is effectively the same.

Apologies for the panic

MichaelG.

Still looking for that introductory tutorial.

[John HaineParticipant @johnhaine32865]

I think you can see from this "zoomed in" view that the fences get sharper as x or y increase, which is kind of what you'd expect when you look at the function.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 14/12/2016 15:54:56:

I think you can see from this "zoomed in" view that the fences get sharper as x or y increase, which is kind of what you'd expect when you look at the function.

.

"… which is kind of what you'd expect when you look at the function."

… That ^^^ sums-up nicely why I was asking for help in the first place.

I have very little intuitive undestanding of what that function would look like, and [perhaps more relevant to my interests] I wouldn't have the slightest idea where to start if I wanted to create a formula to produce that shape.

MichaelG.

[Frances IoMParticipant @francesiom58905]

Michael – not knowing your technical background makes it difficult to suggest text books – also not knowing the basis of your interest – most of what you need is covered in the first year or so of an engineering degree (or the first couple of months of a maths degree assuming you have had a deeper grounding in Maths at sixth form level). As no doubt some have pointed out there is no royal road to maths – mathematicians tend to like rigorous development which technique has to be learnt before it becomes habitual (even tho it seems many mathematicians intuit a solution/theory and then prove it). You would I suspect be advised to get an engineering maths book published any time post WW2 which should cover the required calculus, fourier analysis etc – the basic maths will be found in textbooks dating from the late 1800s.

[Michael GilliganParticipant @michaelgilligan61133]

 

Posted by Michael Gilligan on 12/12/2016 21:49:37:

.

… I don't want to just play about changing numbers.

[infinite number of monkeys writing Shakespeare]

So I started looking at simple stuff like spheres and cones … and realised that I don't really 'have the basics'

Ultimately, I'm interested in the way that natural shapes develop from simple expressions. [particularly, the forms of the Radiolaria] … I have a copy of Turing's thesis on this; which I cannot understand, but I'm hoping that a more interactive graphics environment will help.

I think it's what they call Lesson 1.01 that I need.

.

Frances,

Thank for replying; but I think I answered your question in my opening post, and in my response to John ^^^.

• l did not do 'A level' Maths [my Grammar School could not understand that I might want to do Maths if I was in the Biology stream]
• I did not do an 'Engineering' degree … I did Ergonomics with Human Biology; and my only advance on 'O level' Maths was to do some extra Statistics classes

I was hoping that in these enlightened times, there would be an interactive tutorial somewhere on the web, that started at a level which I could grasp without reading all those TextBooks and which would enable me to learn at my own pace; to the level that I need to reach to pursue my interest in the Radiolaria.

Apparently not.

MichaelG.

.

https://en.m.wikipedia.org/wiki/Radiolaria

Edited By Michael Gilligan on 14/12/2016 22:06:29

[John HaineParticipant @johnhaine32865]

Michael, I can't do it now and I'm busy all tomorrow but I'll try and post an explanation of what I meant by "expect by looking at the function". Given you have this tool now, you can probably learn a lot by playing with it for various simple functions and slowly build up your knowledge. I'd guess that Open University maths texts should also be helpful as they can't assume A level as a starting point for example?

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 14/12/2016 23:11:11:

Michael, I can't do it now and I'm busy all tomorrow but I'll try and post an explanation of what I meant by "expect by looking at the function". Given you have this tool now, you can probably learn a lot by playing with it for various simple functions and slowly build up your knowledge. I'd guess that Open University maths texts should also be helpful as they can't assume A level as a starting point for example?

.

That would be great, John … Thank You !

Given a desire to learn; I think maybe I just need to get my toe in the door.

MichaelG.

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