studiot

A weir controls the flow and flow regimes of the water particularly when the flow is low. As water and flow levels rise, it has a decreasing effect on the water. The hydraulic characteristics of the weir in relation to the flow, depend, amongst other things, upon its length (e width across the river). The 'fingering' pattern of the layout increases this length considerably. Your pictured weir is the subject of current improvement and naturalisation plans. and http://thamesriverstrust.org.uk/projects/river-brent-eel-pass-projects/river-brent-eel-pass-inception-report/ http://www.thames21.org.uk/wp-content/uploads/2014/05/brent_river_corridor_improvement_plan_final_2014.pdf

Perhaps I should have given the full reference G H Hardy A Course in Pure Mathematics (10 Ed 1952) Cambridge. I do not have his series book. However the following extract from Fort 1930 Infinite Series Oxford proves [math]\sum\limits_0^\infty {{a_a}} [/math] the infinite sum tends to infinite (Theorem 32) and the finite sum converges (Theorem 33) Ferrar A textbook of Convergence Oxford 1959 Has a similar discussion to my Hardy above.

Yikes

Unfortunately p333 of my 10th edition Hardy contains miscellaneous examples on chapter VII (additional theorems in the calculus), not your referenced comment. Secondly I can't trace your other references of the form 13.17 and 13.10.11. However in Chapter 1V (Limits of functions of a positive integer variable) where he proves the theorems I referred to he discusses the use of sums and products of infinite series and shows that the conditions of allowability of manipulation by mathematic is that the series is convergent. But (my comments now) the theorems above show that the series is not convergent so those manipulations are disallowed.

So there is considerable overlap.

+1 I like it. and you can spend the saved money on good single malt.

I hope that was a joke, but I will explain if you require.

Hardy p342 Theorems on series. 1) A series of all positive terms must be convergent or diverge to infinity 2) A necessary and sufficient condition that Sn is convergent is that there exists a number K such that u0+u1+u2+u3+.............un < K for all values of n For any K, Let un = K Then Sn > K Hence by 2 the original series is not convergent Hence by 1 it is divergent to infinity.

This question lends itself to a Venn diagram for discussion. But only so long as we can agree boundaries and there is only one ring for each of the three words.

I though I gave the reference clue to look up. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=quadrivium&gbv=2&oq=quadrivium&gs_l=heirloom-hp.3..0l10.1906.4813.0.5156.10.9.0.1.1.0.187.1219.0j9.9.0....0...1ac.1.34.heirloom-hp..0.10.1250.gTxBIo5Xegg The four disciplines of the quadrivium is the origin of the plural in the word 'mathematics', although today we use it as if it were a singular noun.

I don't know if this is the correct place to put this but there is a new art exhibition (by a scottish lady sculptor) opened in London. This is called anthropocene, after the latest geological age to be identified and provides a 'spine' of linked scultpures linking the geology of the British Isles over geological timescales. http://www.angelaspalmer.com/ I apologise if this is considered advertising, but is it also of scientifc merit.

You all seem to be missing the point. The boundaries of all three words, maths (with whatever spelling), logic and philosophy are not clear or rigid, neither is what is included or excluded. It is not even clear if for each one there is one system more than one system. So the original question, as posed, is too vague to be meaningful or properly answerable.

With the greatest respect, have you read the OED lately? To quote the philosopher R G Collingwood

You have mathematics (maths) in the plural so the first need to to clarify Which Mathematics? (I refer to the quadrivium) The second clarification needed is to ask do you regard philosophy as singular and in that case what is included?

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'?