studiot

I'm sorry I don't see this. Take an uninflated balloon. The skin is floppy since it is in neither tension nor compression. Now blow it up. The outward radial forces due to the pressure lead to tension in the skin. The balloon takes on a round shape, with radius and tension increasing with pressure. Now let some air out to reduce some pressure. This does not lead to compression, merely a reduction of tension. In fact you can reduce the pressure all the way back to zero without introducing compression. Now inflate the balloon again and then stick some plates to the outside surface of the balloon, so that there are gaps betweeen the plate edges. Again partially deflate the balloon to simulate mantle shrinking. The object will shrink and two plate edges will eventually touch. At this stage this introduces neither longitudinal tension nor compression into the plates. Further shrinking will introduce a reaction force between the two plate edges in contact, but this will only serve to nudge the two plates aside, it will not yet introduce internal longitudinal forces in the plates. Now reduce the pressure still further and eventually one of the plates will encounter a second plate edge. This still will not induce longitudinal forces as the other edge of the third plate is still free to move so can be pushed aside. Further pressure reduction will eventually lead to a complete ring of plates and at this point pressure reduction starts to induce longitudinal compression forces in the plate ring. The plates now have several possible actions or even a combination them. They can hinge, thrusting the junction of two plates outwards. They can squash. Overlap can occur. They they increase their curvature pushing outwards a section of plate between the plate junctions. This is presumably what you mean by arching. This simplistic picture is complicated by any shear forces between the surface of the ballon (mantle surface) and the plates.

Curved, yes. Arched, I would like to explore further. There is a big difference between arched and curved in my book. An arch is a purely compression structure that cannot support tension. Its unique claim to fame is that it transposes transverse loads to circumferential compression, so long as there is a compressive reaction at both ends. That is it rotates the line of action of the load through 90 degrees. If you have tension at one end of a plate due to an opening (a trench?) and compression at the other due to a closing how do you achieve arching action? I'm not saying it doesn't happen I'm saying you need to think this aspect through in more detail. In particular an arch has compression on the underside, whereas a beam has tension on the underside. If you are clever, or conditions are suitable, you can arrange for full or partial cancellation of one by the other.

You didn't understand. What do you measure x in? metres? miles? So what do you measure the change in x in? metres? miles? Why is that not a form of negative length?

HalfWit has given you (post#13) the mathematical definition and reason why a straightforward distance (length) cannot be negative (by definition). What I am asking you to consider is The difference between two distances (lengths) is still technically a distance (length), so can this be negative? That is what happens to (L2- L1) when L2 < L1 ?

Vectors are most definitely not what I am talking about. Expansion and contraction have 1D, 2D and 3D versions. Take a cube, heat it up, cool it down. It expands and contracts Where are the vectors? When it is smaller is the length of side, area or volume that no longer exists negative?

The extension of an unstretched or compressed spring is zero. So if I stretch a spring is the length of the extension positive or negative, given that the spring is now longer? If I compress the spring is the extension now positive or negative, given that the spring is now shorter?

Agreed useful polytropic formulae are [math]\frac{{{V_2}}}{{{V_1}}} = {\left( {\frac{{{P_1}}}{{{P_2}}}} \right)^{\frac{1}{n}}} = {\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^{\frac{1}{{n - 1}}}}[/math] Note that the pressure and temp ratios are the other way up to the volume ratio. There are two versions of the First Law It looks as if you are using the physicists and engineers version [math]\Delta U = Q - W[/math] That is delta U = Heat added to the system minus work done by the system. Note that the first term on the right represents energy in and the second represents energy out. Chemists use the alternative [math]\Delta U = Q + W[/math] In which we consider all forms of energy in as positive in out as negative. For chemists delta U equals heat input to the sytem plus work done on the system.

Are you sure of your sign conventions and arithmetic? Does the negative sign mean heat is also added or evolved? ?

If you have genuinely calculated p2 from the polytropic law then that is the compressed pressure. Pressures are not additive, unless they are partial pressures for different gases. But why not tell us your calculation? That is the normal etiquette for homework help.

Hello, arc, would you like to explain this arch loading a bit further? Arching action in beams, plates and shells is well known and accounts for the increased strength of members in bending as comapred to simple theory. Further the arching action leads to a lower energy state for the loaded member.

But we already have a concept and definition of negative length. Work done = force times distance moved in the direction of that force. So distance in the opposite direction (ie against the force) is negative, as is the work. In mechanics, extension is reckoned positive, contraction negative.

With regard to your model, it is an interesting idea. You can certainly map an octant of 3D space to 3 orthogonal planes, formed as you have shown from folded paper. And as you say all points in each plane can be reached by a radius vector from the origin and 0< an angle <90, which makes 270 in all. This is similar to the process often used called normalisation for a graph or the formation of nomograms. The normalisation process uses the fact that there are as many points between 0 and 1 as there are between 0 and infinity. Note that your map only covers 1/8 of 3D space, although if you introduce signs you can cover 2/8. Since you like models have a look at Mathematical Models by Cundy and Rollet They show how to make some fascinating paper, string, rod, glass and other models in mechanics, geometry, non euclidian geometry (Mobius strips Klein bottles etc), tesselations, knots, fancy curves, fractals, logic and more fields of maths.

I don't think you quite meant that?

Does this include trancendentals ?

Yeah I aways get the short end of the stick.

I can tell you that between 0811 to 0817 GMT (London time) every morning SF is offline in my neck of the woods. If I have made my tea before 0811 then it starts and suddenly freezez at 0811 and comes back on after I've had breakfast at around 0840. On Wednesday this week it was offline for about one and a half hours at that time.

I think you are still pulling technical terms out of a hat, guessing at what you think or would like their accepted definition to be and then building your castle upon your own notions. Unfortunately that impedes communication with others. Why not simply use accepted definition of terms and if you introduce a new notion then use a new term? The most famous system of logic/maths in history is Euclid's 'Elements' It is based on 23 definitions, 5 axioms (he called them propositions) and 5 'common notions', all stated without proof. The very first definition is 1) A point is that which has no part. (This is taken to mean a point is indivisible into parts.) By definition 15 we find out that 15) A circle is a plane figure contained by one line such that all straight lines falling upon it from one point, among those lying within the figure, are equal to one and other. To recap. Numbers and points do not have dimensions. There are multiple definitions of the terms number, point and dimension already in use. If you wish to pursue your 3/4 idea perhaps you should compare with Mobius strips and Peano curves? They have allied interesting properties.

The only statement of yours that I have refuted is the claim you made several times (without proof or justification) that the circle does not exist in either mathematics or reality. I offered real world examples of the existence of a circles, as evidence for my statemnt that they do indeed exist in reality. If it does not exist in mathematics why do you say this In fact we are apparently agreed on a definition. Yes and I have pointed you several times at the fact this this notion of a circle, although different from the locus definition, has implementation in both mathematics and English. In English we talk of a circular walk, a circular argument etc In maths the idea is reflected in the topological notion of a closed loop So you are seeing an adversarial stance where none exists. However I think that talking in circles has taken this thread away from the original point which was about the relastionship between dimension and number. Talking about time (there is no need to shout) would diverge even further, which is why I have avoided it so far. I'm not actually sure whether time is an abstract or concrete noun, or falls somewhere in between in the 'unclassified' basket. In any event, you need to be careful slapping the word time against an axis and calling the result 4D. The forms of physics that create 4D spaces use ct for that axis to preserve compatibility with the other spatial axes.

I think you said that English is not your first language. Well it is certainly mine, so I recommend you take some notice and respond to points made about it. Not all languages have the concept of abstract and concrete nouns, so do you understand this? It is vitally important to an english word like circle which is an abstract noun.

Of course there is, both in maths and reality. Neither you, nor I, nor anyone else can redefine the circle in mathematics, which is what you are trying to do, and imatfaal has already commented on. Mathematically a circle is defined as a particular locus. In the real world we can actually trace out this locus, so the 'real' circle has real existence. It does not matter that there is not perfectly circular real world object. A (circular) cut through an object will do if you want a concrete noun. If you want abstract nouns then consider a range-range navigation system. The position lines of a rover in this system are perfectly circular. And yes the position line exist as much as other abstract nouns such as the colour red or the emotion joy.

Crafting a mundane common or garden example to describe a concept is never as perfect as a carefully worked out formal definition scheme.

duplicate thread http://www.scienceforums.net/topic/80092-properties-of-negative-lengths/

There are two answers to you question on ripples. Mine was posted within 11 minutes of your original post. I do not see a response. I do not see any response to the several members who have taken the trouble to answer your question about mirrors either.

Let us say you are on a circle. By that I mean you are confined to travel a circular path as for instance if you were on the circle line on the London Underground. You only need to know one number to reach any other part of the circle. Now this number may increase steadily and evenly eg 1 km along the line, 2, km, 5 km and so on, or it may change in jumps eg 1 stop, 2 stops, 5 stops along the line. In this second case the distance along the circle represented are uneven. From this point of view the circle is 1 dimensional. But now examine the situation from the point of view of the cleaning contractors for the stations, who, suprisingly, are not allowed to travel on the trains, but must arrive by road. They need two numbers to specify the position of each station, easting and northing coordinates on their map. So they regard the circle as 2 dimensional. Yet again look at it from the point of view of the train authority, wanting to plan an extra line connecting two of the stations across the circle. Yes, they need the easting and northings of both stations, but that is not enough. They need a third number for each station to make sure the new line comes in at the right level. So they think of the situation and their circle as existing in three dimensions. This point of view of the dimension being how many numbers you need to specifiy something works well in ordinary geometry, but recent advances in mathematics has rather upset this. The discovery of fractal geometry to be precise. This is why I urged you to look up Euclidian, Hausdorf and topological dimensions. Mathematically there may be more than one dimension of an object or situation, depending upon the point of view. But a number for instance 1 or pi is the same from whatever point of view you look.

That's a very posh title. I can just about make out some marks on the concrete surface on your photos. What are you proposing that is special (ie more than just random marks) about them? Why do you think that zig zag shapes cannot arise randomly, in a similar fashion to the leylines fallacy? Incidentally a small tip: It is always a good idea (and conventional) to include a scale in technical pictures. I used to use a plastic ruler obtainable from young children's shops when I used to photograph concrete features. This has highly coloured centimetre and decimetre sections, which is adequate for concrete. go well