Mathematics

Any thoughts would be appreciated.

Take a 2D enviroment that contains a straight line where the x and y coordanates of the two ends of the line are known and also the position of a car and the angle it is facing (7 values). The car moves forward in a straight line. Is there a simple, reasonably computationally fast way to work out if the car ever intersects (crashes into) the line? Would it become much more complicated if one of thease additional pieces of information was needed? either where did the intersection occur or given multiple lines which one was intersected first.

number system goes from 0 to ∞ (and 0 to -∞ for negatives) as far as i know nothing in our physical world holds no mass and all matter is energy (correct me if i am wrong) now, my question is: can nothing be calculated?

I am getting on in years and since retirement I have been giving Fermat's Last Theorem some thought. I believe most people are attempting to solve this puzzle in the wrong way. There may be NO good reason why (say) A^3 + B^3 = c^3 should not have a whole number solution. However there is a very simple reason why the relevant "wrong sum" A+B=C cannot logically be deduced. Please note, I am not saying it cannot exist - only that there is a simple reason that it cannot be deduced. The reason applies to all powers>2. Perhaps this was Fermat's starting point!? I should be interested if this thought gets any response. More later - perhaps a conjecture if not quite a…

hellooo all . I just wanna hear from you all people , suggesting me some standard books with author to understand all mathematical concepts with physical realisations and practical Examples....for ALL MATHEmatical topics in PURE and APPLIED mathematics ... must feel happy to start with nice books suggested by friends over here.... Thanks in Advance by non LINEAR +-*/

If 45lbs of 45F water plus 7lbs of 85F equals 52lbs and 51F water. How much lbs of 45F and 85F do you need to get 52lbs of 65F water and what is the formula for achieving it?

Hi, Can anyone help me with this: Let Bqnr be an arbitrary tensor. [Here q n are contravariant indices and r is covariant index.] Suppose we have a quantity X(p, q, r) such that X(p, q, r) Bqnr = 0. Is X(p, q, r) identically zero? Thanks a lot in advance. john_mawlai.

0 / 2 = Half of 0 Half of 0 / 2 = Quarter of 0 .5----------5----------5 ...4--------4--------4. .....3------3------3.... .......2----2----2....... ...........1-1-1........... 5-4-3-2-1-0-1-2-3-4-5 ...........1-1-1........... .......2----2----2........ .....3------3------3..... ...4--------4--------4.. .5----------5----------5 I don't understand why '0' is the end. 0 is open to each way, it shouldn't only move forwards "0 1 2 3 4" in this fashion. We created that system, it's not the natural system.

Hello. Well known, x2= 4py : http://dy185677.en.ec21.com/C_180_Cm_Satellite_Dish--2988376_3112840.html has the focus at its axis, and the axis aims direct to the radio sorce, as learned decades ago. But this one has the focus offset from the axis : http://www.bikudo.com/product_search/details/13760/satellite_dish_antenna.html Is the radio source not collinear with its axis ? How does the latter aiming works? Is there any ray-tracing graph on the web for an offset focus parabola you can link please ? Never came across that second version in my years of analytical geometry For both antennas, the focal point is, that, a point. If the radio source d…

Hi all, (I wasn’t sure should I post this to Physic or Math forum. I decided to go for math.) Can anyone help me understand ‘connection’ between value and a physical unit. Somehow I always assumed that there is ‘invisible times’ operator between them (anticipated multiplication). For example when I write ’20 kg’, a always assumed it actually means ‘twenty times a kilogram’. But now I am not so sure anymore – for example, you cannot write ‘kg 20’. It doesn’t mean the same (or does it?). In some cases, it is beneficial to think about units as factors. For example one can write the following expression: ‘20 W * 3 s’ (twenty watts times three se…

I'm not very familiar with checkers, and even less so with chess. But after I heard of polar coordinates (has to have been more than half a year ago now) and its nature of being analogous to rectangular ones... I imagined, would you be able to play a game that uses a rectangular-coordinate grid... whether chess, or checkers, or something else... on a polar-coordinate grid?

In this link. What do the #'s in the solution mean? Also there could be 0 to 4 solutions for given values of x, q, w, r, t and u. How do the equations provided return those up to 4 values?

What is the correct thing to say when speaking of a curved Reimannian geometry: 1. The base manifold is curved, not the tangent bundle over it. 2. The tangent bundle is what's curved, not the base manifold. 3. The curvature of the base manifold is "induced" onto the tangent bundle over it. As a result, both are curved in the same way. Huh?

Based on the paper Recursive Binary Sequences of Differences by R. M. Richman, an article on the Guardian website tells us how to pour the perfect [two] cup of coffee. I think it was Alfréd Rényi who said "A mathematician is a device for turning coffee into theorems." The result is fairly intuitive: if there is a flavour gradient in the coffee pot then the average of the top and bottom should match the strength of the middle, when you're dividing the pot into two cups - assuming a well behaved distribution of flavour (I don't think you could apply the same principle to fairly sharing a bottle of beer, since there are no virtually dregs in the top or middle). T…

Suppose I have f(x)=e^x, how can it be proven that it is smooth?

when we want to tell the computer "for example" to do calculation like calculating the circle's area, we may give the following instruction in different versions, A: Result = [math]r^2{}[/math] * 3.14 B: Result = [math]r^2{}[/math] * 3.1416 C: Result = [math]r^2{}[/math] * 3.14159265 example, input: r = 100000 A: Result = 31400000000 B: Result = 31416000000 C: Result = 31415926500 but yet when we go with real numbers, it start to be worse ... so the best solution would to be, let the machine shows you the best it can do ! this means, let the computer do the division ... and this would be my version of Circle Area Calc .. in C, long d…

So awhile back I found some interesting problems from older versions of the Michigan Autumn Take Home Challenge, but sadly they do not post answers to the past exams. While going through a few of them I ran into some that stumped me: 1. Which is greater [math]10!!!!!! [/math] or [math] 10^{10^{10^{10^{10^{10^{10}}}}}}[/math] (Note: In evaluating towers of exponents, precedence rules state that evaluation should be from the top down rather than from the bottom up. For example [math]2^{3^{2}}[/math] should be interpreted as [math]2^{9}[/math] ) I know that factorial growth generally outstrips exponential growth, so I would guess 10!!!!!! is greater, but I really a…

Can anybody help , with a basic tutorial for the introduction to tensors - with a workable example , perhaps. My algebra and calculus , is ok but slightly rusty.

This is for a coding project I'm working on. It's not to do with men walking on spheres but it's a good way of describing the problem. Can anyone produce equations, code or similar to calculate outputs for given inputs. Inputs are: x, y & z coordinates of the spheres center radius of the sphere start latitude coordinate of the man start longitude coordinate of the man start angle of the man distance for the man to travel For the following scenario: Imagine the sphere centered at given coordinates where the north pole is at the topmost point. A man stands on the sphere at the latitude and longitude specified where 0 latitude is the north pole, …

To my knowledge: [math] 3 \cdot 5 = 5 + 5 + 5 [/math] However [math] 3 \, \mathrm{m} \cdot 5 \,\mathrm{m} = 15 \, \mathrm{m}^2 \neq 5 \,\mathrm{m} + 5 \,\mathrm{m} + 5 \,\mathrm{m} [/math] What is wrong?

Hi! I'm looking for Runge–Kutta's 11th order method. Maybe somebody knows where I can find it? I’m tired to search Google for hours... %)

The book I'm reading (Probability and the Logic of Science by Jaynes) has an example in it that I'm just not following. [math] If [/math] [math] \bar{A}=AD[/math] [math] then[/math] [math] A\bar{B}=\bar{B}[/math] Which I get, but then continues to: [math] and[/math] [math] B\bar{A} = \bar{A}[/math] which I don't get, considering the boolean identities he provides. Anyone know how to do this?

Let h be a hyperbole given by the equation: [math]h : \frac{(x-m)^2}{a^2} - \frac{(y-n)^2}{b^2} = 1[/math] Its asymptotes are then: [math] a_{1, 2}: y-n= \pm \frac{b}{a} (x-m)[/math] We were told in our math class that every line parallel to the asymptotes of a hyperbola intersects the hyperbola in only one point. So let us define a line l which is parallel to one of the asymptotes: [math]l: y=\frac{b}{a}x + c[/math] From what I've been told, this line should intersect the hyperbola only once for every real value of c excluding the ones for which [math] l = a_{1, 2}[/math]. Let's pretend we don't know that, and try to calculate c so that the result…

What do the underbraces in the following equations mean?

This is a good collection of links to audio/video courses and lectures on mathematics from colleges/universities. http://www.infocobuild.com/education/audio-video-courses/mathematics/mathematics.html This contains many courses and lectures on math: linear algebra, calculus, differential equations, statistics, probability, and more.