studiot

Since there is continued interest in this subject, the proof of the proposition is remarkably simple. The Greeks knew the parabola as a curve such that any point on the curve is equidistant from a given point (S in my sketch) and a given straight line (MN in my sketch). The distance to the line being the distance along a perpendicular to the line. LR is the latus rectum. The proof follows immediately from the definition.

But you had steel bar in your recipe. However we seem to be digressing. You are right that pozzolanic materials are significantly less energy intensive than OPC cements. Another plus point is that they are generated on a large scale from former waste products. In this guise they are known as PFA or fly ash.

Quite energy intensive then?

Thank you for your references, Ed Earl. However the thread you originally replied to was this one, not here. http://www.scienceforums.net/topic/36783-conics-general-question/

Not all steel reinforcement is textured. And I did say carbon fibre is slippery compared to steel. Just as a matter of interest how would you make textured carbon fibre reinforcement? Steel is cold worked to produce the texture. You can't do this with CF.

Here is an extract from my copy of Neville, but first I posted a reply to your question in the parabola thread. Did you look at it, you never came back. Note1) The Romans did not use steel reinforcement. Note2) Carbon fibre reinforcement brings its own issues with it, not least that of bond strength within the matrix. That is the transfer of the loads from the matrix to the fibres. Carbon fibres are very slippery compared to steel.

Have I got this right? I have transposed you formula using A,B,C,D for the parameters 326.705 < ABC3(1-D)(1+D)2 < 378.29 You can use the superscript icon for the powers Since you have a (1-D) can the parameters take on negative values (do you understand why I am asking this)?

A quadrant is a quarter circle. So there are four quadrants in one circle, 8 quadrants in two circles and so on. Now imagine a rotating arm, whirling round and round in circles. After one circle it has been round four quadrants.... So it travels round a fifth sixth, seventh and eighth quadrants in traversing a second circle. It's just that these last quadrants are overlaid on the original four. So your is fifth dimension overlaid on one of the original three?

The first recorded use of Pozzolanic materials was by the Romans, although the Etruscans may have used them before. So they have been known for a long time. The added durability of properly designed mass concrete containing pozzolans is worth having. However there are one or two caveats in the structural use of the material. 1) The rate of strength gain by the curing concrete is lower with pozzolanic cement replacement than with straight OPC. The eventual strength is the same but you have to be careful with formwork striking times. 2) The resultant concrete has a lower pH than with OPC, resulting in decreased protection against carbonation. Whether this will affect the longevity of structures containing reinforcement has yet to be seen.

Well what does the equation of motion (flow equation) say about the variation of velocity with distance along the x axis?

Friction always obeys N3. What is often overlooked is that the action and reaction always act on different bodies, whether due to friction or otherwise.

Then you will appreciate the sheer elegance of what Newton said and the way he phrased his three laws. None are redundant or wasteful, all three are necessary and together they can be used to build up the laws of classical mechanics. Many have offered modernisations of the wording over the years, pretty well every such attempt has actually missed something in the 'upgrade'.

The conclusion that the earth is much older than simple cooling theory would predict originally came from observing the geological record ie the thickness of various strata using knowledge of accretion and sedimentation rates. Radioactivity was not known at that time. Thus it was known at that time (mid to late 19th century) that there was a contradiction between cooling physics and geology. When radioactivity was discovered it was also observed that the process of radioactivity generated a great deal of heat. It was realised, over the subsequent half century that this heat could account for the discrepency. Radioactive dating as such was not actually used. However it was observed that the chemical make up of radioactive rocks conformed to what would have happened over the longer timescale, ie the ratio of uranium to radium, to lead and other decay elements. This only happened after the half lives were measured accurately and added confirmation to the heat theory.

What is an energy/momentum/force please? Which one do you mean, Energy, Momentum, Force? Any what do collisions have to do with it, I don't recall Newton requiring any collisions, which is the point of this question in my first post In other words do you consider a block sat motionless on a table to be subject to Newton's Third Law or not?

OK I will ask the question again. studiot, on 06 Sept 2013 - 08:50 AM, said: I asked what you understand is states. Or if you will, "state Newton's third Law". Then we can examine your proposition that it involves energy, which I don't agree with. I don't think the man ever mentioned energy in any of his three laws.

All technical courses/education involve what I call the spiral approach. That is because in order to study one areas you need results from another. So any course will run through all areas picking out a (hopefully) coherent set of results, so that you encounter what you need around the time you need it. The the spiral ramps up a notch as the course revisits each area in the light of the newly gained knowledge form other areas and so the process continues. In the sixties, I did a heck of a lot of analytical chemistry in my first year of 'industrial chemistry'.

I do believe I asked you a civil question in a non derogatory way, unlike some in this thread. Please have the courtesy to answer.

What do you understand Newton's third Law to state? Is it a law of motion or statics or both? How does this lead on to a discussion of energy?

I am arguing for a balanced view. I am also arguing for not mixing up separate issues and using one to bolster the argument for or against another. I see three spearate issues here. And you have only scratched the surface of the any of these. 1) Firstly, Pi is a particular number on the number line. Should we replace it with another number in formulae, equal to double its value, thus removing the need for a 2 in certain formulae. 2) Alternatively should we incorporate that 2 in another part of the formula? For instance [math]circumference = 2(\pi R)[/math] The 2 could be applied to the pi or the R [math] = (2\pi )®[/math] or [math] = (\pi )(2R) = \pi D[/math] I see the diameter v radius issue as separate from the pi v 2pi issue. Why should we specify a circle by its radius, not its diameter? We do not do this , sorry we cannot do this fro any other conic curve eg an ellipse so why is the circle special? In fact it has been found convenient to have both diameter and radius available and to choose the most appropriate for the job in hand. 3) Thirdly, if we did introduce a new constant why choose tau? This symbol is already heavily overworked in many different disciplines, unlike pi which has only a few alternative uses (continuous product and Buckingham's theorem.)

Other than cutting the paper into strips, what has the OP offered for us to solve his problem for him? What are you thoughts raiool? The exercise is not about beating the 'record', it is about gaining a feel for engineering. How will us telling you the solution help your engineering education? +1 john cuthber for a perceptive comment.

Except for the greater part of humanity that uses the diameter because they actually have to measure this quantity. This challenge still stands, unanswered. Yes, indeed equation 1 is spherical excess, but again the point I am making is that it contains an odd multiple of pi. The last equation is the Fourier series for the initial displacement of a stretched string of length, l. As such it applies to guitars, pianos, harpsichords etc.

Was that your answer then?

md65536 So why did you take my comment out of context? I made no other claim that each formula contained a noneven multiple of pi. In response to your question about 'natural' I challenge you to offer me a method of directly measuring the radius of a ball. Directly measuring the diameter of a rod is easy, directly measuring the radius of a rod is much more difficult and error prone, but can be done. When I pointed out earlier that for many objects in the real world the diameter is more natural than the radius, in that it is more accessible considerable contempt was offered in return. Any formula involving an extra calculation such as 2piR v piD is both more costly in effort and more contains an extra step and possible source of error. Of course piRsquared is easier than piDsquareduponfour. So please do not misrepresent my words.

This is utter nonsense. You highlighted my entire post where I offered you a selection of snap formulae containing non even multiples of pi in response to a claim that the are all even multiples and wrote something unintelligible to it. When asked for amplification you wrote the above. Did you not recognise the formulae, they are all in common use. 1) is of great interest to navigators, surveyors and astronomers 2) is of interest to in many disciplines and sports as is is the volume of a ball 3) is similarly of multifold interest as the area of a circle 4) should be known to school pupils studying trigonometry 5) is of interest to those string musicians who also have an interest in the science of their art

You did ask question 1 specifically and received a specific answer, to which you did not respond. Why should you now expect responses to the others? Edit: In response to sayonara cheerful optimism here is my answer again.