Mathematics

When I read " We work out this example as if it were 3(x - y) - 5(2y - x). We begin by multiplying out using the distributive property" Does "multiplying out using the distributive property" just mean multiplying everything inside the bracket by what's outside it, in this case 3 & 5?

What is the fastest proof of the Pythagorean theorem in the world? Thank you J5

Is the equation: (T/T)a^x=T(a/T)^((xln(a)/(ln(T))-1)/(ln(a)/(ln(T))-1)) true or false? If true, then can we "cross out" the T's and make them "disappear" the way we were taught in school? Don.

I hope this question isn't to general but i feel like learning something new, so... I'm wondering what anyone can tell me about matrices/Matrixs? My teacher only spent one lesson on them and didn't really elaborate on anything... first i'm wondering if matrices and matrixs are the same thing?? Basicly i know what they look like, i can add two together and i've learned how to times them together also. So what else is there? What can we use them for? Remembering that i'm 15, i'm in the highest classes but if if it is something that shouldn't really be attempted for a while i'll understand, but any information would be greatly appreciated... Thanks!!

Hi I was just wondering if you can help me out on this. Note: this isn't a homework question ok! How you convert the wavenumber in cm^-1 into nm. I know if it said that you had to convert that wavenumber into nm^-1 it would be X 10^10. You people think that I might have to multiply it by 10^-10? Any help appreciated.

this maybe a little silly...but i have here a debate... Is algebra and calculus necessary for a comman man to live in the society??? That is, are they used in the pratical life?? I vote that they are not necessary for a common man.. What about you...

this is quite simple, if you divide 10 by 3 on any calculator or ask any professior, it/they will say that it is 3.3 to the inf yet this is fundimentaly wrong you do not get an infitite number when dividing 2 finite numbers so there fore 10 /3 = a number yet the reason we define it as inf is due to our lack of a word to describe said event the same applies to dividing by square roots, there is no need to multiply by resipricals as there is to reformulate the equation all that needs to be done is invent a new numeric language that accounts for all of the fallacies of the current one

In my presentation of my progress in my project on Topology, I mentioned something about how Non-Euclidean surfaces have curvatures [math]\neq 0[/math]. My math teacher pulled me aside afterward and proposed to me the following: Around a point on a Euclidean surface is 360º. You said that in order for this value to change, the surface must have some curvature. However, [at this point he took a piece of paper and pointed to a point lying directly on on edge] about this point there is 180º. I interjected at this point, claiming that I was talking about an edgeless plane, and he continued: [Making a crease at the point and then joining the two halves of the edge on w…

Or the they can be called "order of precedence"? I'd like to know why this is necessary -- how was it established. I'm making it a point to understand the necessity behind these things so I'm not just blindly following rules. You know...so my math skills are more intuitive. I'm asking for a relative, so Please Excuse My Dear Aunt Sally. ...I couldn't resist throwing a corny joke in there.

Is it?

Hey all, I just wanted to ask, I was thinking the other day and a though struck me. Given a number [math]x \in N[/math], then [math]x[/math] will be prime if [math]GCD(x\#,[/math] [math]x) = 1[/math], where [math] GCD(a,b)[/math] is the greatest common divisor of [math]a,[/math] [math]b[/math], and [math]x\#[/math] is the Primorial. In other words, [math]x[/math] is prime if [math]x[/math] and the product of all primes smaller than x are coprime, or relatively prime. While this could be used to prove a numbers primality, I think it'd be inefficient, if only because one would have to know all the primes smaller than x. It is possible to use a normal…

I am doing this 3D app that has some annoying trig in it, that is kind of messing with my head, as I am not the best trig guy on the planet...so please help! I start with 4 equilateral triangles, to make a tetrahedron, and all I want is to really have each point in the triangle touch a radius of a sphere. I map everything in horiz/vert degrees, to get the base down... I start with the "top down" and draw out on graph paper, an equilateral triangle and put a dot in the center, and draw a circle around it. I make isosceles triangles by drawing lines from the dots to the points, so you have three of those inside it, and it looks like the center point out of each…

Framework of the idea (1 phrase) In the equality A^n – (C^n – B^n) = AA^(n – 1) – (C – B)R = 0 the number u = A + B – C has k zeros at the end, but the last k + 1 digits in the numbers A^(n – 1) and R one can transform into 00…001, but then the number u = A + B – C has k + 1 zeros at the end. In any case the proof merits of careful analysis. ============ Short PROOF of FLT: If a + b – c = 0 mod(n^k) and a=/ 0 mod(n), then (c – b)^(n – 1) = [(c – b)^n]/(c – b) = a^(n – 1) mod(n^(k+1)) and therefore a + b – c = 0 mod(n^(k+1)) – cf. my Forum: http://www.ivlim.ru/fox/forum/FORUM.asp?FORUM_ID=20&CAT_ID=1&Forum_Title=%C2%E5%EB%E8%EA%E0%FF+%D2%…

So for a Senior project, my partner and I were assigned the topic "Mathematical Curiosities", which is quite a broad scope. We have, however, since narrowed it down (with some work on the properties of Möbius Strips) to the field of Topology, specifically manifolds and their properties. We can't, however, think of any good actual project ideas. I want to actually do something as opposed to simply exploring. I was wondering if you guys might have any suggestions? For instance, the string theories are starting to tie topology into physics and we were curious as to whether or not we could work that angle (since I'm going to major in physics in college). Anything would be wel…

Hi everybody, I am trying to solve a mathematical problem that came out of a TV programme I was watching; I will explain how this happened, and I hope someone can help (I believe the problem has long been solved). I think the programme was called 'psychic challenge', a sort of game where they wanted to check whether some people were 'real' mediums or not by putting them through some tests. One of the games consisted in showing the 'medium' 5 men and 5 women, and knowing that they were 5 couples, match each wife to her husband. One of the mediums guessed just one out of five, and everybody was happy with that, but then it occurred to me that if you matched these…

CAN ANY ONE PROVE THIS? ( n! ) /( r! (n-r)! ) = ( n(n-1) )/ 2!

Fractals One Two Three Four I like fractals. But what are they? Yeah, but no. Doesn't cover strange attractors very well. Doesn't even cover all the stuff you can make using procedures similar to the one that produces the Mandelbrot set. Only covers some fractals. I got one which covers all fractals. Lets take a look One Chaotic Two Nested & Chaotic Three Nested Four Chaotic Nested in fairly straightforward, it means self recurring. like a tree. Chaotic means like a cloud. Not random, but not entirely ordered ether. Mathematical Chaos allows apparently random numbers to come apparently from nowhere, from …

1. For [ ( p → q ) ʌ q ] → p make up the statement for p and one for q, then write a statement of this form in words to illustrate that this statement form is sometimes false. 2. The negation of statement form like pʌq can be written "not(pʌq)" or " it is false that pʌq" but these are considered trivial negations. A non trivial negation will change the form of the statement. For example using DeMorgans Law the negation of (pʌq) can be written (not p ᴠ not q). Using some of the logical equivalences on the tautology sheet write a non trivial negation of each of the following statements: a) If roses are red then violets are purple. b) Triangle ABC is isosceles or…

http://www.authspot.com/Thoughts/Is-Luck-Real.255107 This is something i found and i was wondering if someone could explain the math in the third paragraph.

basic question: 1/ on day one, 45% of people are in favour of x 2/ on day two, 50% of people are in favour of x assume a margin of error of [math]{\pm}[/math]0% and a certainty of 95% (i.e., 5% chance of each statement being false). so, what's the certainty of the conclusion 'therefore, support for x has grown between days 1 and 2'? I suppose that if there's a 5% chance of each precept being wrong, and two precepts (i.e., 2 chances for a precept to be wrong), then there'd be a 10% chance of... what? the conclusion being not neccesarily true? The certainty of the conclusion seems as if it'd be 10%, but that feels a tad wrong. e.g., precept 2 could b…

This may seem completely random, but my roommate and I were having an argument about whether or not there is a set of parabolas that, when paired together, a circle tangent to both of them could be a unit circle. He's positive that it's possible, but I'm not convinced, knowing that parabolas increase at different rates at different times, and a unit circle, being a constant shape and having a constant diameter, could not effectively be placed in between them for infinity. Any ideas? (And if you need clarifications, just ask. It seems a bit confusing, and I'm not in the state of mind right now to fix it.. Sorry! )

Not sure if this belongs in the maths forum, so one of the mods will have to clean up after me if it doesn't. On another forum I'm involved with a discussion of random functions. One poster is arguing that if you take any random process or function and add it to a non-random process or function, that your end result is still random. Is this true? If not, can it be shown in some sort of proof that this is not the case?

Im pretty certin its was a japanese mathmetician, formed an equation that works, knowone knows why it works so well, its a bit of an unsolved problem.. The back story: Reading on wikipedia a few years ago, I think I was reading on unsolved problems, ive been back there since and cant seem to find it... As many will find out, im into the big picture, not so great at specifics.

Just a very wild idea. It starts by defining a "point" as being a Plank length (there is some logic behind this idea) and then using this measur the circumference and to calculate pi by dividing the circle into triangles with the plank length on the circumference. A circle with a radius of one plank length has a pi = 3.0. Pi increases as the radius grows –but will it end with a rational number?

Can somebody please explain to me why zero violates common sense? Every other number including infinity, divided by itself equals one, so why doesn't the same apply to zero as well? After all, since there are numbers which are less than zero, zero itself is logically a number too, and zero does go into itself once. It just seems totally counter-intuitive that 0/0 doesn't equal one. And while we're talking about counter-intuitive math, can someone also explain why a negative times a negative equals a positive, even though a positive times a positive doesn't equal a negative. Please don't use fancy terms that none but a math major could understand.