studiot

You can find one of those any week The House is in session, particularly on the day of PMQT.

We have only just reached the eighth page so we have a long way yet to go here. There are twelve pages on the last website ( a mathematics one) and there could well be others on other sites I haven't seen.

The OP originally pedelled this stuff as "A new function in Spherical Trigonometry", coupled with the claim that spherical trigonometry only deals with great circles, not small circles. I don't think it bears any relation to that either

But what does this have to do with direction?

I note that Oban has suffered two earthquakes in the last week so I wonder what riots you will tie into these?

Only a little confused? +1 I don't see the point of the planes at all. They only serve to confuse things. You have a pole which wanders halfway round a small loop (ie 180) on a sphere as the slider is moved from 0 to 90. This is like a demonstration of half a Chandler wobble. So?

Look here for a discussion about What are trigonometric functions and their inverses. http://wmueller.com/precalculus/newfunc/invtrig.html It provides graphs for the main functions. Once you have a handle on this we can proceed to examples of use.

Oh dear! Trapped by terminology again. But at least it shows where your misunderstandings lie. You have mixed up the concepts of scalar, vector and multiplication. So the above does not make sense. The word scalar comes from scale and actually provides a clue as to the meaning, unlike many 'false friends' in the technical world. The essential property of a scalar is that you can use it to scale a vector. That is you multiply the vector by a scalar to get a bigger or smaller vector. But you must end up with another vector of the same type as you started with. Direction and angles are not scalars since you cannot do this with either of them. In fact you can only 'multiply by an angle' in limited circumstances and you do not get a vector as the result. For our purposes of geometric vectors scalars are numbers, but not all numbers are scalars. We can assign a number to direction but it is not a 'magnitude'. This number represensts a deviation from a reference direction. In 2D it is unique, in 3D a second number is required for uniqueness. This may underlie what you are thinking of, but I'm not sure. I'm sorry I thought turning your cards over meant showing your cards and explaining what was on them. There is nothing in this file that can't be posted in the thread. This is preferred at ScienceForums. I have no idea what most of this means as it carries on the misconception about vectors, scalars and multiplication, but the last sentence echoes what I said about vectors not existing in the same space and offered to expand on.

Well perhaps progress is being made, sounds good. I never have considered direction to be synonymous with unit vector. They may not even exist in the same space. (I will expand on that in a moment). But two things from the above quote. 1) I think a good part of everyone's difficulty is that you are continually suddenly pulling apparantly unconnected mathematical ideas out of a hat or somewhere without any explanation of why you are now incorporating them. It is very confusing. This time I am referring to 'symmetry' 2) Please explain why you are now enclosing the direction in modulus lines Now for the bit about vectors they don't tell you in school when you are studying vector triangles or parallelograms. Vectors often do not exist in the same space we are working in, they exist in their own space. The part of the vector common to both spaces is their direction. This was one of the things about direction I was going onto after the infamous post 64 from the other site and that I have reproduced here (in post 108). It is a very important property of tangent vectors for instance. Finally Yes indeed it is an important standard application of something very similar to what many suspect you are talking about. Since I realise that you are not talking about simple standard applications, but something more advanced, I have been trying to offer standard applications you may not have heard of, in case one resonates with you. So we all await seeing the cards turned face up. And if you wish to discuss the comment about direction and spaces then I can explain further with a diagram.

Since you like Wolfram alpha, perhaps you might like to look through this about principle axes and see if it lights up any lightbulbs. http://reference.wolfram.com/applications/structural/AnalysisofStress.html

Yes I misspelled people. My apologies. Actually my post said nothing about your spelling. This is to do with the fact that you don't break up your text into manageable chunks. Doing that makes it easier for everyone.

Waves are repetitive physical phenomena that have a definite time interval between the repetition. The time interval is called the period of the wave. Trigonometric functions are also repetitive mathematical functions with a definite period between repetitions. So it is not suprising that we often use combinations of trigonometric functions to represent waves mathematically. We do not generate physical waves by running something through a trigonometric sausage maker. So are you looking for actual examples of the use of the more complicated trigonometric formulae or are you looking to understand the generation of EM waves by electron acceleration?

Change the extension to .txt or something that will lodge here or put it into a zip file. Provide instructions to others to change it back before use.

Steve, I think this call is time to refer to previous discussions on direction. You will also note that this starts off by suggesting what many have already said, notably you need two points to establish (a reference) direction. Please note also that you originally presented the following as your proposed 'function' but could not tell me if the angle units were radians or degrees, although you only talk of degrees. Are you now ready to answer that question?

The microphone in the studio converts the sound wave to an electrical wave. This electrical wave copy of the sound wave is superimposed on a radio carrier wave and received at the radio receiver. The loudspeaker in the receiver is a form of electric motor that moves backwards and forwards (rather than going round and round) when driven by an electric current. The backwards and forwards motion pushes the air to create a sound. So if the speaker is driven by an electrical copy of the original sound wave it pushes the air in the receiving room to create an audible copy in the air. Like any motor the greater the drive current the stronger the motion and in this case the louder the sound. So the reciever contains electrical amplification circuitry to make the driving electrical signal larger or smaller. That is make the whole of the electrical copy large (or smaller) in the same proportion. This is controlled by the volume control.

These are called skew lines. I won't offer you any more textbooks, these days on the internet there are many offerings on the subject. Take your pick. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=angle+between+skew+lines&gbv=2&oq=angle+between+skew+lines&gs_l=heirloom-hp.1.0.0j0i22i30l3.922.6734.0.11750.24.19.0.5.5.0.203.2235.2j12j2.16.0....0...1ac.1.34.heirloom-hp..3.21.2420.bsVJXvT_MRc I'm glad to see you are now trying to use the same terminology as every one else. That will help your case no end. As regards the circulation of a vector field, the maths is hard, but the explanation is easier. If you consider any vector field and draw a closed loop in its space and take a unit (or other) vector for a walk around the loop then you can calculate an important property of that field called the circulation. By take a vector for a walk I mean start somewhere on the loop (say point A) and align your moving (walking) vector with the vector field at each point of the loop until you come back to A (complete the loop). As you move around the loop the walking vector will turn to point this way and that. When you return to A it will be pointing in the same direction as when you started. Now at each point of the loop there is another vector, the tangent vector of the loop. Now form the dot product of these two vectors. Now integrate (add up) all these dot products around the loop. The thing is that for some vector fields, like gravity, this will be zero. But for other vectors fields, like the velocity field of moving air, it may result in a calculable non zero number. In Physics it is this circulation which is responsible for generating the lift force to allow aircraft to fly. In symbols we have [math]C = \oint {V \bullet dl} [/math] Where C is the scalar circulation V is the field vector and dl is the differential length vector along the curve.

It should be noted that it is perfectly possible to separate the direction and magnitude attributes of vectors. The zero vector has no direction (or indeterminate if you prefer) Any vector in a direction field has no magnitude (or indeterminate magnitude if you prefer)

I have seen your name on the forums, but rarely in the threads that I participate in so I have little or no experience of your questions. I sympathise with your desire to learn and to receive answers appropriate to your level of understanding. But please understand that it can be quite dispiriting to see someone asking what are basically the wrong questions, because they don't know enough to ask the right ones. If they then listen to a development of the subject, sufficient to show them the way and even provide some sort of answer to their original question then it is great. Note also that such a development may need to be spread over several posts and can involve substantial effort on the explainer's part. But some (and I'm not saying you do this) refuse to work through to get to their goal, usually unpsetting all parties in the process. As regards to your English language style. Imagine your lecturer at college (including art college) putting up a powerpoint phrased as your post#41. Yes it is readable Yes I understood it But a lot of stuff presented like that, peple turn off because they think "If the questioner can't be bothered to present their case smartly, then they are showing they don't care. So why should I?" This is very much like the standard advice in going for a job interview. If the applicant shows they don't care, how will they act in work?

The notion of direction has many interesting properties of its own. Walk steadily away from the North Pole (ie place your back to it) and keep going. Where will you end up?

So are you suggesting that a well qualified scientist with 25 or 30 years experience under his/her belt should not consider the tenderness of a fifteen year old?

Regardless of how complex you make your answer, there is another consideration IMHO. There are a wide range of posters of incorrect material starting threads. By this I mean that some are obsessive about particular incorrect view or proposition they hold too, regardless of atempts to point them in the right direction. Little can be done for these. But there are those who have an incorrect idea, but are prepared to be shown why they do not have enough knowledge to see that their proposition is inappropriate, although on the face of it their idea seems good. We should nurture this latter group, not jump hard on them, particularly if they are still school pupils. I remember when I was in secondary school I had this idea, after studying very elementary architectural and builders' structural mechanics, that I would like to apply 'structural mechanics' to molecular architecture, using the same principles, as nobody seemed to be doing this. In those days we did not have the internet and I was left to work out for myself why my idea was inappropriate at a much later date, when I had aquired the necessary wider knowledge. But how many here have had apparantly viable ideas like this in their younger days, only to have it brutally squashed by someone further along the path?

Like the linked diagram, thanks. +1 This is a good reason to visit SF, to be told about good work that others have done and we did not know about before.

Not at all I was quite serious.

Since you know it all, but are unwilling to enlighten us, I can only say that I am sorry you cannot make it 'work', whatever you mean by that. I can only repeat my first response. The mesh method is a very general method that always allows analysis. So you must have applied it incorrectly. But since you won't tell us what you have done, I can't comment.

Hello Steve, I think we have been through 50 shades of the true meaning of the words direction, function and property on a dedicated maths site and established you do not refer to the conventional definition of either. I have had a new thought that there is a property that might interest you. Unfortunately it requires vector calculus to perform any calculations with it, but it is understandable in plain English without that. It is called the circulation of a vector field and has the attractive property, from your point of view, of being a scalar that has some relation to the notion of direction. Perhaps Mordred will explain it?