studiot

I do believe that this relationship was known to the ancientGreeks. Pappus wrote The four books of Euclid's 'Conics' were completed by Appolonius, who added four more and gave us eight books of Conics. However Euclid's books were lost. Aristaeus wrote five further books of the Conics. These books contained all the knowledge to prove geometrically the relationship ie equivalent statements, so perhaps it was never explicity stated, it was used however.

Hello gwyiomi, since this is homework, I was looking for your start on the problem, or at least your thoughts on how to start, but couldn't find them. Hint: Can you rewrite the equation of the line in a more useful manner?

I think we are loosing the point that nobody's theory is perfect (even Einstein's). Every theory is only a model and the wise man knows when to use it and when to look for something better. He does not automatically say "The theory did not work out 'here' so should be discarded for all other purposes, as so many posters do."

Amaton have you seen this thread and my post #7 in particular. http://www.scienceforums.net/topic/78136-what-is-mathematics/ Mathematics was officially plural in the days before America was discovered, and was taught in Latin as a group of disciplines at European universities. In modern times it is now officially singular, but the s is retained.

This would appear to be a homework question. You need to tell us what start you have made with the problem.

Not really. It is impossible to set up a truly 2D coordinate system on the surface of a 3D object. Take for instance a sphere. You can specify where on the surface a point lies, but you cannot tell the distance between two points without at least one measurement in the third dimension. The same is true of any 3d object.

Please explain.

Thank you for the correction on timing, imatfaal. But we do have geometry and we do have dimensions, though some argue about how many; and others worry about the (apparent) granularity of reality. Granularity is a real issue and addresses the difference between a quantised or discrete view of reality and the mathematics of continuity and continuous functions. Professor Shan Majid has written a book about this.

But in general they don't contradict, one or the other ( or even both) is just misapplied. Science is a developing subject. Developing in the light of new facts, observations, information. Here is a short story from the past. In the 1880s and 1890s scientists used the best physics available to calculate the age of the earth. They were able to estimate the temperature of the sun reasonably accurately and also the size of the earth. Using thermodynamic laws of cooling which were well established by then they worked out how long it would take for an earth sized chunk of stellar material to cool to the temperature of the earth. They came up with 4000 years. This caused great controversy at the time. They had no knowledge of any other source of heat for the earth so they applied perfectly good theory inappropriately and came up with a wildly inaccurate answer. We know today that radioactivity has kept the earth's temperature as it is for around a million times as long. As regards classical v quantum mechanics. Do not make the same mistake trying to consider applying classical mechanics to 'particles' that obey the same laws as billiard balls. Quantum mechanics is our best model to date of how they actually operate, but it is incomplete and will one day be replaced by better in areas where it has difficulty.

We see thread after thread complaining that; Relativity is wrong QM is wrong Newton is (was) wrong Aunt Sally's cake recipe is wrong. etc There is no perfect theory. Usually because they are incomplete. But that does not mean they are not useful, so long as we understand the limitations and stay within them. As a for instance Take a theodolite and measure the vertical angle to a remote point up is positive, down is negative) and you can calculate the vertical height of one above the other by trigonometry. right? Sometimes, but I have seen situations where a positive vertical angle has been recorded in both directions. This effect can never be resolved by trigonometry, it needs new theory.

You do not need to apologise for your English. It is plenty good enough. It is your thinking I am having trouble following. What do you mean by "information" and "interaction". If you are going to complain base your argument on exactitude you need to offer exactly precise definitions

Consider what is meant by your statement "Know the path" That implies either an absolute coordinate system that we know does not exist or that you can breach the uncertainty principle to specify any path that accurately.

Perpendicular, yes but it is also horizontal. Attached is a sketch of apparatus that you could use to investigate the resistance.

Looks more like metaphysical preaching to me. I still haven't understood what you are trying to tell or ask me. Please just state your question or issue in not more than 15 words.

So what about it? You still have to provide a point for discussion.

I shall have to defer further discussion till next week since I shall not be about during the Bank Holiday weekend. However in order to replicate the conditions you are asking about, think of a bar magnet being pulled along across polished iron table, at tight angles to the NS axis. In what direction is the relative motion? In what direction is the flux or field? So in what direction is the induced EMF? The part of the table where there is no flux because it is not under the bar magnet provides a retun path for circulatory eddy currents.

Duh?????????????? The video is 25 minutes long. so what is your point?

1) It is impossible to avoid muplicity of notation. Take your example of vectors. Vectors are members of some set which we call a vector space V. Since there are lots of different types of vector there are lots of different vectors spaces V. V', V'''...... However there are plenty of other objects, that are not vectors, but are members of sets. So we could use general set notation for our vectors, at the cost of having other, non vecotr, objects with the same notation. Or we could introduce a second notation, specific to vectors, to maintain the distinction. But general set notation would still be correct. 2) Much notation has been determined by what can be easily presented. Presentation includes, hand written, printed, display screen. Each medium offers its own advantages and difficulties. I note in another thread here at SF there is discussion about a presentation that is not available through this forum's implementation of LaTex.

Well it would appear to be the aqueous calcium carbonate system with some potassium perchlorate thrown in to spice things up. You are on the right track with the charge balance. The first thing you need to do is to assign a coefficient to each species eg a(H+); b(OH-); c(Ca2+)....e(CO32-).... and so on. They represent the relative numbers of each ion present in the solution. These coefficients are pure numbers and will normally be the smallest set of numbers that satisfy both the charge and mass balance requirements. At the outset they are unknown and your task is to determine them from the question data. What you then need to do is write down a numeric equation ie containing numbers only connecting the coefficients and the charges on the ions - this is the charge balance equation and yes you collect positive on one side and negative on the other. eg from my list above (ax1) + (cx2) = (bx1) + (ex2) As to the mass balance, which you have included in the question title, this is where you introduce context data such as 150g of calcium bicarbonate were dissolved in 1.5 litres of water.........again connecting the coefficients to each other but this time via the mass quantities and molecular weights of the species involved and the chemical reaction equation or (in this case equations) involved. You should remember that the solvent may also play a part with some of the species. We can also discuss this further if you wish.

No You should look up wave packets. There are some cool animations here. http://en.wikipedia.org/wiki/Wave_packet http://www.physics.nyu.edu/~ts2/Animation/quantum.html http://www.optics.rochester.edu/~stroud/animations/ http://www.youtube.com/watch?v=hqwa1nktc_E

The short answer is yes, but you may have to modify your experimental ideas a bit. Ask a diver about sound in helium atmospheres. eg http://scubageek.com/articles/wwwheliu.html

Glad the penny has dropped. Hopefully you can see what the original question meant when it said you can extend this as many times as you like to higher powers.

Yes, at last somehting correct. I already have twice. and others have also stated that the losses are the normal I2R losses. Is there? Have you heard of 1)Lenz law 2) Flemings left hand and right hand rules

Looks to me like some instruction in some programming language for generating a recursive loop. If this is true then the equals sign is not meant to be read as equality but x(p) is replaced by x(p+k) where k is already defined previously in the program and the loop runs through for stated values of p,

Despite me saying that eddy currents do not oppose things you keep returning to it. Why is this? The effect is nothing like Lenz law where the generated EMF indeed opposes the change to the existing. Rather you should think of it as going into a MacDonalds and ordering a burger. You obtain a burger but there is a cost involved that you have to pay. So it is with any dissipative loss to any system, mechanical, electrical or thermodynamic. The process, like the taxman, exacts a charge for doing it. To oppose, the system would have to provide or generate some force or emf that indeed tends to drive the process in the opposite direction. Dissipative agents can never do this. A simple mechanical example is a spring. The harder you pull it out the harder it pulls back. Once you have caught this idea I will explain why eddy currents are circulatory in nature.