studiot

I don't see that the centroid (or centre of gravity) is purely mathematical, simple versions were included in my O level Physics, not in my O level Mathematics. It was in both A level (applied) Maths and Physics. It did not appear in maths degree, I do not have a physics one to compare, but it was heavily used in my engineering degree, where it was assumed to be known about. [math]\bar x = \frac{{\smallint \smallint \smallint \rho xdxdydz}}{{\smallint \smallint \smallint \rho dxdydz}}[/math] But yes the centroid is a property of an object, but not a material property. And it is time independent. Density is a material property.And it is time independent. [math]\rho = \frac{m}{V}[/math] Another object property is the metaheight used in floating bodies such as ships and icebergs. [math]h = \frac{m}{M}d\cot (\theta )[/math] I know I said the focal length of a lens but I was really referring to the lens equation, which is time independent. This is more than just a property, is is a relationship between three physical quantites. [math]\frac{1}{u} + \frac{1}{v} = \frac{1}{f}[/math] Charle's law is time independent, and enjoys the status of a Law of Thermodynamics in Physics. [math]\frac{{{V_1}}}{{{V_2}}} = \frac{{{T_1}}}{{{T_2}}}[/math] I don't know if you would include balanced (stoichiometric) chemical reaction equations but they are time independent but refer to change. [math]C + {O_2} \to C{O_2}[/math] So I think the examples are there if you care to look.

What is this in relation to? Are you asking about conservative and non conservative fields or forces? Gravity is conservative, friction is non conservative. Or are you asking about zero v nonzero curl?

Steel dust? Are you trying to clean up the result of grinding? The resulting powder will be mostly carborundum or similar. More information please.

I suppose with all your restrictions it boils down to What can I do if I drop T from MLT dimensions. So, how about the formula for the focal length of a lens. (There are plenty of other optical formulae in that stable) Or the formulae for the coordinates of a centroid. The ration of two triple integrals should be mathematical enough for you.

Go to more reply options (underneath right of the quick reply box) More R O underneath left under Attach Files click on choose files. Upload your jpeg from the box which opens. You will see a new line appear under the text input box listing your jpeg When it has uploaded click in the text posting box where you want to put the file and then click on add to post in the line under the text input box. I look forward to your picture.

A pleasure, done.

Here is the first page of Mathematical Foundations of the Quantum Theory. Is this the sort of thing you want?

Well pitched answer keen +1

I believe I introduced counting to this thread in post38 and enquired if it was considered mathematics. If you wish to use a different definition please, at least, make it clear that your definition is/maybe different. With regard to the cuckoo, I'm suprised you didn't look it up, it's quite a story. The target bird is usually a blackbird or a thrush, but may be a smaller bird such as a sparrow or robin. The blackbird builds a nest and lays on average 2 to 4 eggs. Whilst the blackbird is out feeding etc the cuckoo comes along and lays 1 or two eggs in the blackbird's nest. The blackbird knows (can count) how many eggs it laid and will reject the foreign egg(s) so the cuckoo throws out 1 or 2 blackbird eggs from the nest before it leaves. When the blackbird returns it counts the same number of eggs (birds fuss around if the number is different) and eventually hatches and raises the cuckoo(s) as well as its own remaining chicks. Quite a sophisticated setup n'est pas?

Whatever you do, don't smooth it. By schemes I was referring to how you divide up the x axis into segments. This is related to the number of terms in the series you want to take, given that you are truncating a series. Computer programs have all that built in and provide instructions as to how to enter the data. My comment about the prop was similar to your question. The prop noise sounded like white noise to the ear and I was looking for patterns or periodicities in the noise. Are you attempting this by hand or by computer? Hand methods have largely been superceeded, but were called harmonic analysis.

Isn't that a definition of counting? Anyway, do you know what the responses are that I am referring to and why I chose the cuckoo and mentioned a 'target bird'?

Is that so? I wonder how you deduce this ? Or is it one of the many claims you are going to make without evidence. Have you ever heard of the cuckoo? Both the cuckoo and the target bird can count to at least 5. It is really quite sophisticated, but not as sophisticated as the fractions you seem to claim animals can cope with.

But that's what proof testing is. Suppose you have loading sling. You will want to know that it will perform up to and beyond its rated lifting capacity. You obviously can't test it to destruction to find out what its ultimate capacity is so you test it to a 'proof' level, which is greater than it will be called upon to lift in normal working (its rated capacity), but not great enough to break it or even damage it. In the UK lifting devices have to be proof tested every year like this. You pictured a bridge. I have proof tested hundreds of bridge deck beams in this way before installation. That is measured the performance at a load less than breakpoint, but higher than working. There is reams of theory about this.

We have proof testing because tests to destruction can never be repeated, but when made ultimate results are never rejected. But you did make some other good points.

In the absence of further comments from ydoaPs I can only go by what he said. Please quote where he said precisely the above. This quote has an entirely different meaning from your version.

From your response I assume that you regard counting as mathematics, although you didn't specifically answer that part of my question. In respect of your comment, as far as I can tell, it is only humans who compare counting methods. Animals are not that advanced. But were the earliest human counters that advanced either?

It is well known in biological science that some animals can count, I'm sure one of the life sciences members could tell us which birds can count eggs and chicks. So is counting mathematics and does it have to be a human invention?

I believe it has been tried, though I don't know the result as I don't know much about the maths of economics. The applications of the FFT are much wider than just electrical engineering, I last used it to analyse the vibration frequencies of a spinning aircraft propellor, from the wind noise generated. The FFT requires the data to be present in a specific format for analysis. There are several schemes.

What do you mean a timeseries and what is it for? Well you need to organise your question in the light of the information below. Fourier series and transforms are a way of representing the original function of time as the sum of a series of functions of frequency because they may be easier to work on than the original function. In the case of the FT you also need the inverse transform when you have done calculating. Fourier series only apply to periodic functions Fourier transforms can also apply to non periodic functions There is also the fast fourier transform (or finite fourier transform) , FFT, which is different again and is used to work with XY data as opposed to analytical formulae. Over to you

Quickly a multiply connected curve crooses or intersects itself, a simply connected curve does not. Figure of eight. - Multiply connected Circle - simply connected. Parabola simply connected.

I think you have it bass ackward sir! Measurement is in the title, the introduction and specification of this thread. Distance is not. It only appears amongst a collection of examples presented by ydoaPs. I can;t see how anyone reading post1 can take anything other than measurement as the focus. This said, the rest of your reasoning falls.

Do you not differentiate between the measurement situation for a continuous variable where values arbitrarily close to zero are permissible and variables where only certain values are permissible?

Hello pavel, If you genuinely feel that zero resultant is the same as no force, try this experiment. Go and stand in the middle of an empty horse park, where there are no forces acting on you (except gravity and the ground reaction). Now obtain two equal on opposite horses, stretch out your arms and hitch a horse to each one and shout giddyup. Do you still feel that they are the same?

Well I think there is a difference and zero is not always arbitrary. Pavel asked a wider question than his charge example so I will addres that. Sometimes zero or not present make no (practical) difference. But would you describe absolute zero of temperature as an arbitrary reference or zero being the same as the absence of temperature? Some physical qwuantiies have continuous values that reduce to zero in certain circumstances, which may be very important. For instance the resultant of a system of forces is always present and zero is neither arbitrary or equivalent to no forces being present at all. I am rushing this because I see swansont hovering, maybe more later.

All too many books for science follow the stuffy 'lecture at the audience' approach. Even those with the most amazing graphics that are really showy. This makes the reader passive, except perhaps for forced 'exercises'. This sort of thing is fine for those who are already interested but will not stimulate those who are not. Science is about doing. 8-10 year olds are about doing. So I suggest you use this fact to create a book that they can do with, and learn some scinece along the way. Perhaps a bit like the National Treasure films (But with real science). Perhaps a crime mystery withs lots of CSI But present them with problems and take then through solutions, and choice of solutions. Old fashioned science teaching often promoted the idea that there is only one solution. So I am suggesting you create a theme or challenge to work through. This could be the basis for a series of books if the idea turns out successful.