studiot

One thing to remember is that we do not teach any serious subject all in one go. Mathematics especially requires what I call a 'spiral approach'. Here a very simplified version is first presented, not the whole nine yards (nice expression in English for you). This will tie in with what has gone before and what may be presented in the future as the subject is revisited again and again as we work around the spiral. So in the present context fractions will be naturally introduced after addition, subtraction ,multiplication and division. Note these are treated separately and simply and usually called 'sums' (and in the olden days tables). So a fraction naturally becomes replacing the dots in the division sign with actual numbers. This fits in with your Penrose description and emphasises that it is division being talked about. Which naturally leads to division of pies, apples, sweets whatever. In turn this leads to finding out the difference between dividing a bag of sweets and a single pie. This leads back to proper and improper fractions (and perhaps vulgar fractions). The four arithmetic operations can then be revisited in the light of fractions, leading to the introduction of decimal fractions. Then we have the return to the four operations to work decimal fractions. Looking ahead to secondary school and algebra we are set up to try algebraic fractions and find out why (4-2) / (14-2) is not the same as (2-2) / (7-2. The next bump comes when the teacher needs to keep emphasising that dy/dx is not a fraction, but a complete entity in itself. Having said all this it would be very helpful if you would indicate why you are asking these questions and where you are going with the answers ?

Do you prove Pythagoras every time you use it ? Of course not. The teacher may well explain that if we multiply by 1, which is the same as 1/1 or 2/2 or 3/3 etc we don't change anything. But no suggestion of adding or subtracting would be made . In fact later the same or similar discussion would occur when introducing powers and roots of fractions.

As I recall it was not called cancellation of common factors it was called 'Do the same thing to top and bottom' So either multiply the 2 and 7 by or divide the 4 and 14 by 2, depending upon which way round the question was asked. Often it would be simplify or express in simplest terms 4/14

Google vignette is driving me mad and away. How do fix it so every second attempt to move page, post, change forum section... does not lead to blankout.

Clearly your second childhood has arrived. Only children will say Mom my piece of pie is smaller than his. 😀

I have a Netgear NAS unit with 4 large drives in it as my backup/offline storage. This has performed fine for several years now. However just recently I can't access it. Most of the references have disappeared in Windows File Explorer and I can't access the one that is left. Any idea please ?

We frequently recommend papers. Here is a good book on how to extract useful information from them. I know it was produced for the medical sciences but the lessons are universal. A further tip for students. If you know how the Professors are reading the papers before marking them, it helps in their preparation.

Many elements have been known for a long time and had ancient world names (usuallly Latin or Greek). Iron was Ferrum in Latin symbol Fe Tin was Stannum in Latin symbol Sn Gold was Aurum in Latin symbol Au Silver was Argentum in Latin symbol Ag the French also get Argent (money) from this Copper was Kypros after the Greek name for Cyprus symbol Cu after tha Latinisation Cuprum. Particularly interesting because this was the oldest known mining for copper and why the bronze age started around the eastern Mediterranean. Rome was of course iron age.

And there was I getting ready to solve the rest of the millenium problems before bedtime. 😀 Surely that is self contradictory ? If we can detect effects then isn't that how we detect anything ?

+1 for remembering your (our) childhood.

That's actually my term, inspired by crystallography. Cubic packing of round things like spheres or circles inevitably leads to funny shaped gaps between the round objects. Hexagonal objects, hexagonally packed leave no gaps. @arthur jackson Anyway let's examine one of the dual charged pinheads more closely. I'm sorry I don't have yellow so I have used red (-) and green (+). And I am plotting the force field on a + test charge at various points around the pinhead. On the red side the radial rays point inwards towards the centre. On the green side they point outwards away from the centre The blue rays represent a discontinuity across the diameter where they meet. What is your description of the directions I should assign to these rays ? I haven't tried to also draw the potnetial field, but it must have a corresponding discontinuity.

Thank you for your reply. Why would there be no electric field surrounding an electric charge ? As I understand you proposition you are proposing that at every point in space the exists a split charge all perfectly lined up as in your original diagram. You further propose (diag2) that an EM wave (note the difference between electric and electromagnetic) can be propagated by a medium with these properties. I have a number of serious reservations about this along with clarification questions you have yet to address. This is in effect an aether - the original name for the propagation medium for EM waves when it was though that no wave could propagate in vacuo. You have a rectangular array. Maxwell's model, that I have already referred to, realised that hexagonal packing is more efficient that rectangular. I have now dug out the reference Something to think about. If such an array exists how big are your green and yellow pinheads ? If they have zero extent, what is the meaning of their 'rotation' , given that the zero vector has no direction ? In what way and by what agency are these pinheads moving moving through space ?

@arthur jackson I wonder what the electric field around one of your green and yellow object would look like ?

So we have Maxwell's hexagonal aether agin. Maxwell himself rejected it and commented that it was the only mechanism he could think of or make work for the aether. But we know better today. Please note that all known carriers of charge are material. As swansont has already said there is no magic substance called charge.

I don't see an answer to a single question of mine. So have I wasted my time pulling this material out for you ? Anyone who has ever done any quantum or classical resonance calculations will know that the above quote is a meaningless statement by itself. Energy of what , under what circumstances, over what timescale and within what region of space ? All those pieces of information are needed. the calculations cannot be done without them.

You got it. +1 Haven't you assumed that which was to be proven ?

An electronics engineer ? Well have you seen this article ? What is an Electron ? A new model: the phase locked cavity. R C Jennison PH D Bsc FIEE FRAS FInstP FRSA ~~Electronics Laboratories University of Kent at Canterbury. Wireless World June 1979 pages 42 to 47 There has also been mathematical work( By Drazin) by regarding a photon as a solitary wave or soliton. Here are the first and last pages of Jennison's article.

That I don;t believe for one moment. What was the article and what was it peddling ? Dare I say that you are far more likely to suffer harm from your diesel powered cooker ?

I don't think I got it wrong. T2 (i) = (i) x (i) = -1

The Angstrom is an old unit about the size on a whole atom. Or if you lined up 100,000 atomic nuclei in a row that would be the size of one angstom. That is how much smaller a nucleus is than an atom. And protons and neutrons are smaller still, may be half this size.

I wonder about the bases of your pots and pans. The instructions with my AGA ceramic hob are quite clear. You should only use pots and pans with a (ground) flat base. Pans with ridges or dimpled or other patterned bases are forbidden. I think this is because of what happens in the space between the hob and where the pan base does not touch. A slight overspill or dirt etc can cause superheated gas between the pan and the hob which can have a powerful erroding effect. As regards the hob itself, I was just looking at my grandmother's old welsh bakestone, made of cast iron. This has happily gone through more than a century of gas flame burning directly under it. The temperature of natural gas is about 2700oC and diesel is sbout 2000oC. So perhaps you should consider cast iron? A simple method would be to construct a support grid for an iron or steel plate and leave the plate free to expand and contract ie just resting on the grid.

Until Genady posted this I had never really thought about the issue. I just followed the rules. One very important thing that has come out of my share dealing example is this. It is no use whatsoever finding a single example of a quantity that can be measured/signed as positive or negative. You need two separate quantities. And these quantities must be connected by a multplicative connection.

Here is an example of what I mean Let us consider some deals on the stock exchange. Define Buying 3 shares as -3 shares Selling 3 Shares as +3 shares Selling a share at $5 above par as +$5 or $5 profit Selling a share at $5 below par as -$5 or $5 loss par is the same as face value. Now let us say consider 4 different deals assume that as soon as each deal is done the company redeems the share at face value. Deal 1) Sell 3 shares at $5 above face value That is +3 x +5 = +15 or $15 profit Deal 2) Sell 3 shares at $5 below par That is +3 x -5 = -15 or $15 loss Deal 3) Buy 3 shares at $5 above par That is -3 x +5 = -15 or $15 loss Deal 4) Buy 3 shares at $5 below par That is -3 x -5 = +15 or $15 profit Deal 4 is obviously the case of negative times negative makes positive. So it depends upon how you assign the plus and minus. Which is why mathematically they are called directed or signed numbers.

Look up scotch yoke actuators.

Hello. I am still assembling some of these other approaches, which contain cunning answers for you. Two points. Firstly the correct term is not 'negative numvers, but signed numbers. The signs have different significances in different situations. Secondly the cunning bit comes when you choose suitable combinations of situation so that you multiply two signed numbers.