studiot

Some interesting historical values for pi The Rhind Papyrus (1650BC) [math]{\left( {\frac{{16}}{9}} \right)^2} = 3.1604[/math] The Bible 3 Archimedes (250BC) [math]3\frac{{10}}{{71}} < \pi < 3\frac{{10}}{{70}}[/math] Tsu Chung Chich (AD 450) [math]\frac{{355}}{{113}} = 3.1415929[/math]

Discussion is only useless with those who won't listen. You made an all embracing sweeping statement "Electrons are particles" Now, I have a different understanding of the word 'particle' from yourself. Furthermore I claim grandfather rights on my definition of the subject since my definition goes back at least as far as Newton's corpuscles. However I have been prepared to listen and I now thank you for helping me update my view of the current state of particle physics. Having followed the discussion I do not see that you have proved your point. In fact you have failed to respond when I observed that your hero is lax with mathematical terminology. Your thesis is that we should take on trust the above statement apparantly because someone says so rather than on account of proof. Like all physics 'an electron' is a model. Models are useful when their response to a property of interest is the same or indistinguishable from the actuality. A particle is a model. In my view a particle is an entity where the entire property or properties of interest can be considered to act or be concentrated at one point. A particle need not be small that depends upon the nature of the system under consideration.

Surely the only definition of importance is the one employed by a poster making a point, rather than some hearsay definition from another source outside SF and this thread. I am particularly chary of a source which makes this sort of statement. A functional is a particular term for a mapping from a vector space of functions to the space of real numbers. How does any definition of a wave fit this?

Thank you for your answer however I am unable to spot a clear and unambigouus current definition of a particle, elementary or otherwise in post#131. I have quoted the part I think you are referring to but coloured the words which worry me. As I read this text it clearly states a historic definition and a refutation of this definition, but does not provide a current definiton.

What makes you think that the K-T extinction event (dinosaurs) destroyed all life? There have been five (known) major extinction events showing in the fossil record and the K-T was nowhere near the most extensive. That was the P-T event. You should look up both.

Hello VEI, Actually infinities and their applications are already pretty well defined in mathematics. Note I use the plural since there are many infinities. You should look up 'cardinality'. The fact that there are many infinities, some bigger than others is why we can often evalute expressions such as [math]\frac{\infty }{\infty }or\frac{0}{0}[/math] to yield a finite result

Man hat im 1987 diese buch verlangt. Is this modern?

Yes the vertical fin of the tail plane is more akin to a keel than a wing. Fish, of course have such devices - they are called fins. However the keel has an additional function. Its large area provides large resistance to the sideways component of force generated by an angled wind, as compared to low resistance offered by the streamlined shape in the forward direction. This is the significance of item 2 on my list. Incidentally in water the criteria are not supersonic/subsonic but super critical/subcritical flow. go well

There is also the issue of 'elementary'. I had always understood the word to mean indivisible (in this application into smaller/more fundamental particles) Does an electron meet this requirement?

Two big differences between a keel and a wing. 1) The asymmetry of the wing is designed to produce a force at right angles to the flow. If you did this with a keel the vessel would be permanentlt pushed sideways. 2) The driving force of an airplane has no intended component at right angles to the direction of thrust and motion.

Alluded, yes but stated, never. In particular I don't think you used the word 'elementary' to qualify the word particle before.

So what do you (both) mean by a particle? In other words by what characteristics might an imaprtial observer determine if an exhibit conformed to the definition? And a wave too?

Actually you need to be pretty careful what you mean by a particle or a wave. I would be interested in protagonists' definitions.

There is a big difference between the hydrodynamics of a sailboat and a swordfish (and an aircraft for that matter). The disposition and balance of forces are all different. The saiboat is actually the most complicated since the driving force is rarely directly along the main axis. JC Mcswell has already hinted at this in post#4.

The reason that 'streamlining' an object produces a relatively blunt nose but a long thin tail is that the nose and tail perform different functions in the fluid. The purpose of the nose is to part the fluid to the max width of the object. The rounding helps do this smoothly a needle shape does not improve this. The tail however is to reduce or avoid creating turbulence in the 'wake' which goes to remove energy from the object and is felt as 'drag'. So no, a sharper nose will not reduce drag. A further practical consideration is that since the nose is moving forwards it encounters (bumps into) objects and a razor adge would not last very long compared to a more robust one. go well

Good morning, ajb. When I found the comments box on the blog I didn't comment because you have raised a serious subject and the only comment there was non-serious and I think your subject deserves better, even if people not from the UK are (likely) disinterested. I don't think you can view either Mathematics or A-Levels in isolation. Both have changed greatly since there was a coherent structure of education syllabuses forty, fifty or sixty years ago. This structure worked both vertically and horizontally between different types of exam and also linked the requirements of companion subjects to the mutual benefit of all. The late 1970s and 1980s saw an explosion of 'out with the old and in with the new' so that by 1987 I was in the position where I was helping a graduate Civil Engineer with the three dimensional curvature of a large viaduct and I was shocked to learn that under the new deal he had been all the way through school and university without being taught the basic properties of a circle. Last Christmas I was given an interesting present. A book called The O Level Book - Genuine exam questions from yesteryear. It was certainly questions pupils in the 1950s and 1960 were expected to answer.

Thanks but I am still puzzled. I followed the link and came to a paper entitled "Mathematics in A-Level Science 2010." This is a different subject from ajb's headline since A-Level Mathematics is a different subject group from science. There is Mathematics in many A-Level subjects, besides Science some of which may well not appear in the Science syllabus.

Flipping through this thread I couldn't make out your prime interest so here are some (probably irrelevent) comments. I found Aris a good book, but rather dated. Tensors are almost useless in real world fluid mechanics, but you can certainly spin a lot of theory with them. I would recommend the companion Dover book by Harley Flanders - Differential Forms with Applications to the Physical Sciences DFs are the modern 'alternative' to tensors in many applications and the gaining ground rapidly. HF contrasts both approaches. Another good book is Tensor Geometry by Dodson and Poston If you want to study mathematical fluids, but with a practical bent, you would have to go a long way to get a better book than Elementary Fluid Dynamics by Acheson. go well

I saw this blog by ajb and wondered why it is locked. http://www.scienceforums.net/topic/66103-blog-post-ajb-a-level-mathematics-is-not-equipping-students-with-the-right-skills/page__pid__674786#entry674786 Does the site owner not wish the subject to be discussed?

Compare this from post 1 Each of the i, j, k components are treated separately, as Klimatos said. So the acceleration in the i direction is [math]\frac{6}{4}{t^2}[/math] etc I assume that t is time so if you integrate this once with respect to time you will get a velocity along the i axis. [math]{v_i} = \int_0^1 {\frac{6}{4}} {t^2}dt[/math] Since we want to run for 1 second I have shown the integral limits 0 and 1 You must add the initial velocity in the i direction to this which according to your original post is +1 To get the distance moved along the integrate this velocity with respect to time. This is the distance along the i axis and therefore the i coordinate. You are asked to find the position after 1 second, not the distance travelled. The position is given by the i, j and k coordinates in the same manner, although the integrations are much easier for j and k. The distance travelled would be the length of the curve. I have to go now, but others here seem keen to help.

My questions are designed to highlight some point or other. Acceleration is a vector in the same direction as the force. Because it is in the same direction we can use the i, j k components of the force as the components of the acceleration vector if we divide each by the mass. Using your original data I make the acceleration components as [math]a = \frac{F}{m} = \frac{1}{4}\left( {6{t^2}i - tj - 4k} \right) = \frac{{6{t^2}}}{4}i - \frac{t}{4}j - k[/math] You are introducing formulae for motion under constant acceleration. I ask again is the acceleration constant?

OK so you seem to have realised that you can calculate the acceleration. Is the acceleration constant? Is acceleration a scalar or a vector? What about Klaynos' suggestion?

F=ma yes that's good. So what can you calculate given mass and force? Come on, you are nearly there.

So for part (1) You have two vectors, the initial velocity and the force acting. Since you also have the mass, what can you calculate from the mass and the force? What can you apply this result to to get a final distance travelled?

So how do you think a perceived energy difference would show up? What would be different measured in each frame? Frames extend throught the universe so what do you mean about measuring the same photon in different frames? You still haven't provided sufficient information to describe/define the situation. When you do you might see what others are trying to point out.