Mathematics

how can i calculate the surface aria of a parabolic mirror

104 x 104 +4 = 108 4x4 = 16 104 x 104 = 10816 109 x 109 +9 = 118 9x9 = 81 109 x 109 = 11881 A little trick I use.

Is this really possible? I doubt I can explain much about what I am interested in to the first man whom I see on the street. Maybe that is a reflection on me rather than the subject matter. Any thoughts on this?

Here is a question I have always wondered how the answer is correct, because I can't manage to make it seem right. A chap at the fair is tring to find a prize that is hidden in one of three caskets. He chooses a casket, whereupon the man running the stall opens one of the other cases, which is empty. He then asks the chap if he wants to stick with the casket he chose originally, or switch to the remaining one. which casket will give the chap the greatest odds of winning? The answer in the back of the books states that if he switches, his chances of winning are doubled. so the chap should take the remaining casket. This always seems quite odd to me. It s…

I've seen it played numerous times in the Clock Game. The goal is when you are faced with a ton of possibilities, and you try to eliminate as many possibilities as you can, so that you are left with only one possible answer. This can make the Clock Game easy to win, even if you have no earthly idea what the price of the item is. "five hundred" "Higher." "seven fifty" "Higher" "Nine hundred" "Lower" "Eight hundred" "Higher" "Eight fifty" "Higher" "Eight eighty" "Higher" "Eight ninety" "Higher" "91, 92, 93, 94, 95, 96, 97, 98, 99-" "THAT'S IT!" The fridge is worth $899. The Clock Game is the most common example, but not the only one, where this …

While using several operators(e.g.grad,div,curl) we often separate them and treat them as vectors in their own right,performing most algebraic and vector operation on them.How is this possible? are not operators and their operands inexorably linked together.In order to separate them we would need to define a whole set of specialized rules just to use them. This is not an isolated example several times while solving differential equations we replace the differential operator with a variable ,say 's'(and hence this technique in some areas gets its name as the s-operator method) (ref:http://en.wikibooks.org/wiki/Circuit_Theory/Second-Order_Solution)and proceed to manipulat…

The title speaks for itself. I guess the question should be narrowed down to irrational numbers, since the rest are all rationals. I'm leaning towards no, although that's just intuition speaking. Note that I'm not asking if we can find a closed form expression for a given number; just if it always exists.

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.