Mathematics

Forum Rules Okay, so the "old" forum rules was becoming a little old, so I've re-written them. Please, please, please put your mathematics where it should go. For example, anything to do with Calculus or Analysis should go in that forum. Applied Mathematics includes statistics and simple mechanics. Refrain from posting non-mathematical material on these sub-fora; there's loads of other fora on here for various topics in science. Always try to use the correct and proper mathematical notation; we implement a LaTeX system here, and it would be great if people would use it to its full potential. We encourage people to post their problems here; however, if it …

After a recent update to our forum software, typesetting equations on SFN has changed a little bit. Although we are still using LaTeX, for a variety of reasons, we've elected to shift over from our custom-written LaTeX generator to the excellent MathJax library, which will take your equations from post text and render them in your browser. Much as before, the idea is that in your post, you surround equations with special characters, and MathJax will convert the contained text into an equation for you. There's two types of equation that you can typeset: Inline math is displayed in the flow of a sentence, such as \( y= x^2 \). This example was produced by using …

Every other section has one... this one should too (If it has I can't find it sorry). So I'll start off: 1) http://linuxfreak87.googlepages.com/ 1) Covers a lot of stuff, Maths and some physics. 2) http://mathworld.wolfram.com/ 2) Amazing maths resource, lot of advanced stuff. 3) http://www.purplemath.com/ 3) Basic and advanced maths here. Good tutorials. 4) http://www.dansmath.com/ 4) Again more good tutorias and weekly challanges. 5) http://mathforum.org/dr.math/ 5) LOTS of question solutions here, examples too. This one has helped me a lot in the past and still does 6) http://www.ics.uci.edu/~eppstein/junkyard/ 6) Lots of fun geometry…

If asked if -0 =0 one would say yes. But I don't think that is the case. It is quite simple. If you divide a number by 0 your answer would be infinity. So if you divided a number by -0 you must have an answer of -infinity. So somewhere in 0, it must have a value but how can it? There symbol represents that there is no value to it. Could it be that 0 doesn't exist? Well that is impossible for it not to exist because one could say, "What is the answer to 10 - 10"? Is 0 a paradox or is it infinity and an infinitesimal at the same time?

Is it possible for something to have a negative number of dimensions? Or is that just meaningless? How about imaginary dimensions? The reason I ask is that there seems to be something missing in the table of simplex elements to make a complete Pascal's triangle.

Hey all, Where am I making a mistake? [math]-i=(-1)\sqrt{-1}=\sqrt{(-1)(-1)(-1)}=\sqrt{-1}=i[/math] Cheers, Gabe

I just noticed this. Any reason why (x+2)x+2/(x+1)x+1 – (x+1)x+1/xx → e as x → ∞? Does it actually do this? I checked it in Excel but can't get past x = 141.

if y_1 and y_2 are the answers of this equation: (d^4 y/dx^4) + 4 y = f(x) then what's y_2 - y_1? I used laplace Transform! Thanks in advance

Just recently I was messing around with fractals, I came across these by self replicating the shape and then rotating it clockwise (or counter clockwise) 90 degrees each time. It created these beautiful 'frost' alike patterns. I was wondering if anybody has meet these fractals before, and if so the name of them. 1st Fractal, rotated anti clockwise 90 degrees each iteration 2nd Fractal, rotated clockwise 90 degrees each iteration Thanks!

Hi everyone Out of boredom, I asked myself the following question: For which [math]a[/math], [math]b[/math], [math]c[/math], [math]d[/math], [math]e[/math] and [math]f[/math] does the curve, described by the function [math]g(x)=a\cdot\log_b{\left(c\cdot x^d+e\right)}+f[/math] Only have one solution, so touches the curve described by the function [math]h(x)=x[/math] In [math](1,1)[/math]? Found something, and wanted to know if it was right. It's been a while since I 'performed' pure mathematics (over 4 months), so don't be too hard on me The derivative of that function in [math]x=1[/math] should be 1. [math]\frac{d}{dx}a\cdot\log_b{\lef…

Could someone please explain to me why the following is statistically falliciouse: The prosecutor's falicy The DNA profile found at the scene matches the suspects. The probability of a randomly chosen person having the same DNA profile is calculated as 1/100. So... if the suspect left the DNA at the scene of crime, the probability that the DNA from the crime scene matches the suspects DNA is 1. If some random person left the DNA at the scene of crime, the chances of the DNA matching the suspects is 1/100. Therefore, the fact that the DNA from the crime scene matches the suspect's is 100 times more probable if the suspect left the DNA at the crime scene t…

I thought it was nice, even though if he started multiplying figures with numbers like 6 or 8 it would be pretty tedious Math Lesson: A new way to multiply

Stillwell's "Reverse Mathematics" says on p.41, Unfortunately, there is no example of such model. Does anybody know such? For the reference, here are the axioms 1-4:

Say you have three sides of a right triangle that form an arithmetic sequence. The only possible one is 3-4-5. Prove this.

. "button error" hey guys. as we know that [math]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/math] where the discriminant is [math] {b^2 - 4ac} [/math] and I thought discriminant is taken from the quadratic formula, which squaroot the result of discrimination. So, that's mean when discriminant's result is negative, the answer is not available. Yet, I want to explore more about the 'un-available root', I use calculator to calculate the equation that its discriminant is negative. Then, it bugging my mind somehow the x is founded! [math] x^2 - 3x + 4 = 0 [/math] [math] D = -7 < 0 [/math] [math] x = 1.5. [/math] did I miss anything here?

How do you do word problems involving "work" in them. Please, any help is appreciated.

I have no proof for it but just wondering if this equation is new? (-1)^(1/x) = i*sin(pi/x) + cos(pi/x) where x>=4 I've tested this equation and Google calculator gives the correct answer for every example.

ok so if we say that a is a natural number (N) this (a+30)(a+50)(a+70) what can it be divided by? 2, 3, 5, 7? which one(help plz, btw soz maybe its bad math lang)

Hello everyone I have this strange feeling that [math]\frac{(a+b)!}{a!+b!}\in\mathbb{N}[/math]. Can this be proven? If yes, how? Never mind. Counterproof: (15+6)!/(15!+6!) [math]\notin\mathbb{N}[/math]

When it comes to using relational operators on scalar values, there's usually no problem. But what about vectors? Are there any generally accepted rules or consensus when it comes to relational comparisons (ie. =, <>, >, <, >=, <=) of vectors? For instance, consider v1 < v2 for the two vectors v1 = (10, 8) and v2 = (5, 10)... Does one then compare the x and y values pairwise and return a boolean for each value, in this case (false, true)? Or does one check the magnitude of the vectors against each other and simply return (false)? Or something entirely different...? Cheers, Michael

Google docs gives the option to draw an orginisation diagram, it shows hyrachy in an orginisation. me parent son1 me son2 me son3 me Drawing this gives you a box at the top entitled parent with a line going down to me and then branching out to 3 sons. Moving on to another expample. 2n n 0 0 2 1 4 2 6 3 The values in the top row are lables, the second column is increased by 1 each row. The first column is double the second column. If we continue this chart up to n=40 and draw it according to the rules this is the result. http://img253.imageshack.us/img253/7651/image1kq7.png This allows you to see th…

I know nothing about curved geometry but maybe I don't have to, after all. I want to evenly distribute an arbitrary number of points on a hemisphere. I visualized for example 1000 vectors starting from the same origin, on one side of a plane containing the origin. If they are normalized they'll resemble a hemisphere. Being evenly spaced means the 'tips" make for corners of equilateral triangles. I guess there are at least 2 possibilities: on the top of the "dome" there's a point OR the center of a triangle. Basically I want to find the vectors. Can it be explained with matrices at most? Quaternions are a little too hard for me and be it only if there's no other choice.…

So this is an equation I found with interesting properties. Pretty much x+y=z and x-y=z are linear equations of 2 equations 2 unknowns. If you solve for this equation you get x=z and y=0. Now I haven't got a chart for x-y=z, Google shows the x+y=z chart but not the other one, if you have it please show me. Now for z=(x+y)/(x-y) it generates an interesting chart in google, same goes for z=(x-y)/(x+y). I'm not sure if they are off by 180 degrees or simply upside down. Now when you multiple the two together you get z^2=1 which is z=1 not z=0. This seems to be an interesting property and if someone can give me an explanation on this it would be cool. To sum up: 1. Ge…

The surface in above image is a portion of the graph of some mathematical equation. Let's do some brainstorming: Can you guess what's inside the surface? .

Find a 2x2 matrix A and a vector v in R2 such that the transforma- tion x --> Ax + v maps the triangle with vertices (1, 1); (2, -1); (3, 4) into the triangle with vertices (0, 0); (1, 0); (0, 1). How many different pairs (A, v) will do the job?