3D graphing of mathematical functions

You might get a good idea of one of the points John made by looking around for maths ignoring constants. Silly idea on the face of it but can be useful. For example

say something ----> 5x^2 all the 5 does is scale the basic function. The X^2 might be said to set the shape. The important aspect.

I used that sort of notation, -----> as the open university was mentioned. I did M100 that was later changed a lot because of a very high drop out rate. The -----> may be read as maps too. It an approach that allows more maths to be done on functions rather than numbers. So thw something above might be f and f is a function. not a=b etc. Things like integration look entirely different. That for instance is a big I. So you might come across something like I o f. Which would be read as I circle f. There is also a square. Never had much use for it so memory fades. Other things are also chucked in, morphisms and etc. I ^-1 is what you would expect it to be. It's inverse as would f^-1.

Just mentioned as I think this form of notation is more widely used now - by mathematicians. The OU course books cover this well. They also do a load of primers to get people to the same level. Good job too on M100 the scope covered was ridiculous. That may have changed.

I suspect your best bet really would be a book aimed at software people. Can't help there but I did work with some one who was into this as a hobby so do know that books are available. He was probably a higher level graduate inn electronics. That does in some cases cover some unusual maths but using old style notation. Maybe that's changed now but I haven't seen any signs of it.

Mathematicians aren't strange people really. Like most fields they have their own jargon and it's what they do - most if not all of the time. I have known a few graduates that wanted to do maths initially but didn't 'cause they thought it was probably too hard. What I found very difficult was that ok it may be wonderful that things are like that but what on earth do you use the maths for.

Oh forgot if this function f was used it might be shown as something like f(x)  read f of x.

John

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Edited By Ajohnw on 23/12/2016 13:01:07

I had a nose around on the web but it's pretty hopeless unless it's to buy something. Searching curve sketching might help but you'll see use of derivatives and probably few basics.

One other thing that I should have mentioned is something like f(x)=5x^2. That defines the function. There are probably variations on the same theme. What doesn't seem to be around is a good explanation of modern notation. I'd assume while it may be difficult to follow many people would have a grasp of the older styles. If not some cheap books going by the name of Schaum's Outline Series may help. They cover all sorts of things and probably go down to basics. They probably all aim at applied maths. The OU thingy was and may still be pure maths.

John

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Without it you couldn't do any real engineering. Over 40-odd years in the profession I've found more and more that maths is absolutely essential and getting more so. You can't design things in the real world by just experiment and experience, most of the time that's just too expensive and sometimes fatal. Only using mathematical methods can you model and analyse how designs will work without making them first. Even if you are trying out how bits fit together using a 3D CAD package you're using complex maths within the package

Therefore z=0

Russell

Pure maths doesn't really worry about the actual application John. A brief cut and paste from a google for it

Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts. This was a recognizable category of mathematical activity from the 19th century onwards, at variance with the trend towards meeting the needs of navigation, astronomy, physics, economics, engineering, and so

Applied which would have been far more appropriate for me wasn't taught by the OU. Instead it gave a very broad basis in a pure mathematical sense over a number of fields that some tend to specialise in. These days a course that would probably be more ideal for what I was after would be called applied maths possibly plus computation.

If some one does a degree is say engineering of some sort they will be taught applied maths related to the field the degree covers.

I'm not disagreeing with you. I agree entirely when it's needed. Taking the course wasn't a waste of my time at all really. It would have been nice to see some practical applications at times though. It pretty obvious in some areas but not so much in others. Sometimes that becomes clearer when I do see a practical use.

As to the quote I posted take a look at this link. It's still about.

**LINK**

A teacher at my son's school managed to persuade him to take a pure maths A level. I tried to dissuade him but failed. He did too, besides the point - it wouldn't really relate to the field he wanted to go into and a degree in that would cover any additional maths he needed adequately. He also dropped a course that he was sure to pass. I think the teacher was just drumming up numbers so that he could teach it - rather late in terms of exam time too. This for a kid that had won a maths challenge too.

John

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Trouble is, like physics, what seems pure with no practical application turns out to be vital in the future. Like group theory turns out to be important for designing error correcting codes used in mobile communications. Riemann studies non-Euclidean geometries that turn out be useful for thinking about gravity and results in corrections that have to be made to GPS to correct for clocks slowing down at different altitudes. Number theory turns out to be important in encryption. Who'da thunk it.

.

Absolutely !!

This page is heading nicely towards 'applied' study of Radiolarian morphogenesis : **LINK**

http://www.morphogenesism.com/project/P8/p8.html

Surely, in this time of 3D printing, such studies have very practical potential.

MichaelG.

Edited By Michael Gilligan on 23/12/2016 21:12:41

Here is the link to the referenced tutorial **LINK**

http://www.grasshopper3d.com/page/tutorials-1

[towards the bottom of the page]

MichaelG.

Radiolaria look just like Diatoms to me. Wrong again!

Trivia corner: Microscopy was a popular hobby in Victorian times, much more genteel than turning metal in a grubby workshop. Much time was spent arranging diatoms into intricate patterns that couldn't be seen with the naked eye. I like the idea of a hobby that's so exclusive it's invisible.

Dave

Dave,

Klaus Kemp still arranges diatoms, to Victorian standards.

**LINK**

http://www.diatoms.co.uk/

MichaelG.

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Also see Stephano Barone : http://www.diatomlab.com/diatom-shop.html

... and if you are hooked, have a look at these [clickable images]

http://www.mikrohamburg.de/HomeStereo_E.html

Edited By Michael Gilligan on 23/12/2016 22:11:14

Amazing work being done by Klaus Kemp, and Diatoms as art must be popular - it's a business!

His website led me to a coincidence. Are you the same Michael responsible for this letter in "The Amateur Diatomist"? Having strange interests I tried to read the paper but the link is broken.

Cheers,

Dave

13th October 2014

Re: Diatom Cleaning by Incineration

Following the very interesting and successful demonstration, at Pool-in-Wharfedale on Saturday; I thought this paper might be of interest.
Experimental studies on diagnosis of death from drowning by means of detection of vegetative planktons (diatoms) II. Detection of diatoms from putrefied and cremated bones of drowned bodies.

Best Wishes

Michael Gilligan

13th October 2014

Dave,

Indeed, I am that man

Sorry about the link ... I may have downloaded the paper at the time.

If I can find it, I will send you a P.M.

MichaelG.

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Better than that ... Try Here: http://ousar.lib.okayama-u.ac.jp/en/search?all=diatom+cremated

Edited By Michael Gilligan on 23/12/2016 22:41:23

Many thanks for providing a working link Michael. It made unusual reading over breakfast this morning!

I've been interested in microscopy in a small way for many years and am semi-prepared to do more now I'm retired. In practice, I've not had the time.

Before retiring, I looked at pollen and pond water in a haphazard way. I have a set of Pathology slides (as used to train pre-digital doctors), that could be studied for years. The only thing I've done with any semblance of method was a classic 'Hay Infusion' study. Notes and drawings every day for a month, took the Notebook to work to show a friend, and lost it!

Off to the Christmas whirl now. Roll on normality.

Cheers,

Dave

Interesting I came across the use of diatoms to determine drowning some time ago in a book on pathology.

For cleaning I use what is the fairly safe oxidiser approach. Sulphuric acid, potassium permanganate and a fully saturate solution of oxalic acid. It's an interesting example of what I call the web effect. Some people still use a whole series of boiling acids. That is needed when the source is diatom deposits. I didn't fancy it despite advice from some rather well known people. I came across the method in a book that is intended for late teenagers attending study centres such as Dale Fort. Wanting more info just in case I spent a lot of time searching for it. Nothing at all. Mentioned it on a forum and a few months later it was all over the place. Later still some one found a paper. A rather misleading one from what I can gather.

Some people use bleach. Ok but it can dissolve the lot.

Klaus did sell prepared slides on ebay and probably still does. Bidding is often fierce for them. There is also a person in France that did crop up on there as well who does excellent slides. Each diatom has to be placed individually in order to get a decent slide. The usual strews can be very disappointing. In the right mountant lots of them are things of beauty. Others are a resolution challenge - best not get too far into that area. It can lead to a vast increase in gear.

John

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Edited By Ajohnw on 24/12/2016 10:35:41

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Just to confirm ... Yes, this ^^^ is a very informative site

I first had to install Java on the Mac.

[Apple's paranoia on my behalf allows me to authorise its use for specific sites only; which is some comfort in these evil times.]

MichaelG.

Have regularly felt a bit like 'all take, no give' on this forum, always having my beginner-y questions helpfully answered, I'm pleased that I can offer input for once:

I'm currently studying a theoretical physics degree. If you have a reasonable grasp of elementary (secondary school level) maths then working your way through say an A Level maths revsion guide would give a budding home engineer extra insigbt for plotting, trigonometry etc.

Ignore those wallies who dismiss it as pretenious bulls*it (have not syndrome...) any advanced maths you can get to grips with is immensley satisfying. Enjoy it!

Thanks for the encouragement

I am finding that 'having a desire to understand, for a specific reason' is helping a lot.

MichaelG.