Mathematics

An Elementary Proof Of Both The Beal Conjecture And Fermat's Last Theorem. By: Don Blazys The Beal Conjecture can be stated as follows: For positive integers: [math]a, b, c, x, y, [/math] and [math]z[/math], if [math]a^x+b^y=c^z[/math], and [math]a, b[/math] and [math]c[/math] are co-prime, then[math]x, y[/math] and [math]z[/math] are not all greater than [math]2[/math]. Proof: Letting all variables herein represent positive integers, we form the equation: [math]c^z-b^y=a^x[/math].__________________________________________________________(1) Factoring (1) results in: [math]\left(c^\frac{z}{2}+b^\frac{y}{2}\right)\left(c^\frac{z}{2}-b^\frac{y}…

I am trying to prove [math] \vec{a}\cdot \vec{b} = |\vec{a}| |\vec{b}| cos \theta = a_1b_1+a_2b_2 [/math] in two dimensions. I have come to the conclusion that I need to express the area of a parallelogram spanned by the two vectors [math] \vec{a} = [a_2; -a_1] [/math] and [math] \vec{b} = [b_1; b_2] [/math] by their coordinates. So far I have tried to express the height of the parallelogram in terms of these coordinates, but I have not succeeded. Can you help me further?

What exactly IS continuous compoudning? Anyone know?

It seems hard to find algorithms on the web for computing functions like erf() and zeta() etc. Many sites offer algorithmic solutions at a cost, but my project is non profit so I don't want to spend money on it (it will be released free of charge as a web application). So I am wondering if anybody knows a good algorithm for computing these functions for general complex numbers expressed as (a+bi). The ideal algorithm will be one that is iterative or recursive allowing an arbitrary level of accuracy, and solutions that converge quickly. Right now I need 'erf', 'zeta' and 'gamma' (I have one for gamma but it only calculates real arguments). Other popular special…

Given z is a complex number: a+bi, the function real is defined as real(z) = a; For my purpose this is not satisfactory, I cannot break z into its real and imaginary parts. I am wondering if it is possible to express the function in terms of elementary functions: +, -, *, /, ^, cos, sine, log, exp.... Only z or constants must be used as paramaters to these functions, never a or b. Other functions that break z up cannot be used, for example: real(z) = z-imag(z) is not a valid solution. My gut feeling tells me this is impossible, I would greatly appreciate a solution or verification that there is none. Thanks a lot! - Moosie

I was wondering what the theoretical area of contact between two touching spheres would be. After thinking about this for some time I've come to the conclusion that they would basically meet at a single point, much like a tangent to a circle on a cartesian plane, and whatever little information I could find related to this on the internet supports this. Although, apparently, a 'point' has no actual size. I'm finding this hard to come to terms with- if two spehere met at a single point, which technically has no area or magnitude, how are they touching? Wouldn't they have a shared area between them, even if the area was only one atom?

Does such a thing exist? I think the highest perfect number so far was calculated at 10^300 and mathematicians are currently moving towards 10^500.. so far all perfect numbers are even... Do you think odd perfect numbers exist? I did a few calculations of my own... and thought about it quite a bit and I think it could be done.... it would take an infinite amount of time to calculate the exact number but maybe if you could figure out "about" where it is.. the perfect-number pattern which is....(after the main number of course) "6,8,6,8" adds to itself every consecutive, but it also jumps around a bit to. Another question I have is, are numbers themselves capable of pe…

Hi , I am working on some math stuff and I need to check some points , so are theses formulas correct ? ISZ(x) : is it 0 ? isz (x) = cos ( pi * ( (2*ceil( abs(x) ) + 1)) / 2 ) / cos(1) Ins : Real number x Out : 1 if x=0 , 0 if x <> 0 --------------------------------------------------------------- SGN(x) : Sign sgn(x) = abs(x) / ( x + isz(x) ) Ins : Real number x Out : 1 if x>0 , 0 if x = 0 , -1 if x < 0 more here Dirbax thanks

At the present I'm a math student and study one time a week in order to improve my current math studies. I want to be ambitious, but I have had difficulties and I often finds other things more interesting: http://picasaweb.google.com/khelben1979/Matematik# I would like your opinions on these so called math notes, they are not intented for a high quality presentation. They illustrate my current work with my studies and some of my problems. And please, only nice comments.

how do I work out the mean from these figures?

i can't picture it in my head of how it looks like. I see a front view of it in the book "The Road To Reality" by Dr. Roger Penrose. The picture is a woodcut by M.C Escher called circle limit I. http://math.slu.edu/escher/upload/thumb/e/e5/Circle-limit-I.jpg/200px-Circle-limit-I.jpg So i was thinking how the universe of hyperbolic plane is round and nothing outside of the circle is existent. But i wondered how it would look like from the side or will it be the same as the way i am looking at it right now? Or will it look like a curve with an opening with two lines consisting of it that extends infinitely.

Been a long time since the university years, no books on hand, and with terminology in another language, this may be hard to explain/ask... From a fixed point of view, say the tip of your tv antenna at the roof; -The street hydrant is at a fixed direction; elevation and azimuth. Do not care about the distance. -The sun is at another direction; elevation and azimuth. How is the (bisectriz) bisecting vector elevation and azimuth calculated ? Simply sums divided by 2 ?

When does the generic equation of the 2nd degree not represent a conic section or does it always represent a conic section (unless it has no possible solutions in real numbers)? The other topic I would like like to devote this thread to is families (or sometime called pencils) of conics. [math] C_1 + \lambda C_2 = 0 [/math] represents the zero sets of the family of conics passing through the intersection points of conics [math] c_1 and c_2 [/math] please note that [math]\lambda[/math] is a parameter and assumes all possible real values. [math] C_1 + C_2 = 0 [/math] is the same as the logical operation of this must satisfy both [math] C_1 AND C_2 = 0[/math].howe…

It is an old question, it says: In a gambling game, there are three door numbered #1,#2 and #3. There are a car behind one of the doors. If you guess the right door number, you can get the car. Then you made a guess, say door #1, then the host opened the door3, it turned out to be empty. Then he offered you a change to guess again. The question is " should you change your choice to #2?"

Show that: if the sum of the digits of a natural number N is divisible by 3 then 3 | N.

Hey all, I was wondering the other day, if you rotate the plot of [math]y=x^2[/math] 90° CW, you get [math]y^2=x[/math]. What happens when you do the same with [math]sin(x)[/math]? In other words, which function looks like this: Cheers, Gabe

What is the total sum of all numbers? zero?

Hi everyone, I have some homework to do and ive been asked the following question....... a) Construct an internally and externally calibrated calibration graph. This must be done using Excel and also using graph paper and a pencil (i.e. four graphs are required). my question is what is the difference between an internal and external calibration graph? I have the data. Any help will be much appreciated

we teach in türkiye-anatolia ,Natural Numbers to start at 1 and not to include zero.. but, I could never understand how one could not say that 0 were a natural number if zero(0) is a Natural Number,why? someone said:It depends on the frame of reference you use. right?

Hi. What would be the vertical motion amplitude at 5 metres below surface for a seawave of 0,5m amplitude (1 metre peak to trough) at surface? There is some formulas at wiki but unsure how to translate them into what I want to know

x^4 +y^4+z^4 =4xyz-1 denkleminin bütün gerçel çözümlerini bulunuz x^4 +y^4+z^4 =4xyz-1 Find all real solutions of the equation

Hi My teacher asked me to program this thanks to Matlab, but I am not able to understand anything: "Indeed, we first compute the short-time magnitude spectrum and phase spectrum of the segment in a neighborhood (32 ms) of the sample Note that the spectra are obtained through first multiplying the segment by a 256-point Hamming window followed by performing fast Fourier transform (FFT) analysis. Moreover, such operations are carried out for each sample. Second, we compute the short-time magnitude spectra of four neighboring segments which overlap with the original segment by 12 or 24 ms (i.e., two of the neighboring segments are obtained by shifting the analysis…

Hey guys, I talked with a guy who studies mathematics and he told me that his friends from collage found their "limits" (mostly in third grade) and now the don't have a clue what's going on, and just learn mechanically like medival scholars did. He also told me that only some chosen ones still understand it. Does anyone you know of feel a similar effect? And now something completly diffrent, will you press (softly, of course) on your child to do math?

Hey all, I'm curious as to how to calculate the surface/volume of a shape I though of the other day. Since I don't know if what it's called (heck, I don't even know if it exists) and I'm not even close to being good enough with Photoshop to make a picture, I'll have to describe it, which may prove a little tricky. So, here we go. It's three dimensional. Imagine you have a circle with center [math]S_1[/math] of radius [math]r_1[/math] in space. Now imagine on either side of it, an n-sided convex regular polygon with a center [math]S_2[/math] and diameter (that is, the distance between the center and the place where two edges meet) [math]r_2[/math]. The distance bet…

Mathematics is certainly a science in the broad sense of "systematic and formulated knowledge", but most people use "science" to refer only to the natural sciences. Since mathematics provides the language in which the natural sciences aspire to describe and analyse the universe, there is a natural link between mathematics and the natural sciences. Indeed schools, universities, and government agencies usually lump them together. (1) On the other hand, most mathematicians do not consider themselves to be scientists and vice versa. So is mathematics a natural science? (2) The natural sciences investigate the physical universe but mathematics does not, so mathematics is not r…