Mathematics

Say one has a procedure that describes the placement of objects in some number of dimensions, such as pixels on a grid in a raster image, or nodes in a vector image. Lets say that for example the procedure describes the drawing of a filled in a circle, in the raster example for a larger circle completion takes longer as more pixels need to be set as inside and in the vector version a smoother circle takes longer as more edge nodes are required. In all cases for a generic "any algorithm of this type" the image may need to be rendered entirely before it's possible to know what any one part of the image looks like. This sort of procedure is sometimes refered to as ge…

Are there other triangles like Pascal's triangle? His triangle amazes me, and have inspired me to make my own, and I'm just convinced about that numbers are more than just numbers. But are there other triangles or "models" except those who are listed under "See also" in wikipedia? http://en.wikipedia.org/wiki/Pascal%27s_triangle#See_also I enjoy comparing my own triangles with other triangles and see how it all just fits together. Yeah, I'm a total nerd... But ofcourse, I'm not going to hide that I want to see if my triangles already have been "presented", or whatever the correct wording would be.

An article I read in focus magazine stated that numbers could be represented only using sets as proposed by Von Neumann. The concept as stated by the article is that "The number 1 is defined simply as the set containing just one thing: the Empty set. The next number, 2, is then the set containing 2 things: the Empty set, plus the set representing the number 1 - and so on, each successive number being built out of the previous set, plus the empty set." Therefore 1 = {} 2 = {{}, {}} 3 = {{}, {{}, {}}} and so where [math]s_{n}[/math] is the set that represents the number n and n > 0 [math]s_{n}[/math] = {{}, [math]s_{n-1}[/math]} Is this correct and…

Does anyone have any good tips on how to think about when I want to show that Pn <2 ^ 2 ^ n and Pn denotes the nth prime number and n = 1,2,3, .. ?

How would you define geometry as to encompass all it has become? For me, something like the study of locally ringed spaces would be good. It includes manifolds, supermanifolds, schemes and NCG's. To quote Manin, What are you thoughts?

SO i dont have the radius or the volume but i have an estimate of the density 14.5 10³kg m-3 Im really uncertain of the formula needed to A. get the radius without the volume and vice versa. PLEASE HELP! Thanks in advance! Merged post follows: Consecutive posts mergedsome how must use the values above to get my answer?!

hi, Was wondering how we can be sure when rearranging an equation/formula, that the worked out formula gives us the correct answer, since the formula is the basis for our interpretation...

In algebraic topology there is something called a chain complex. http://en.wikipedia.org/wiki/Chain_complex My question is: Why is the composition of any two consecutive maps [math]d_n \cdot d_{n+1}[/math] equal zero?

Good Time to All, Amici. i got following math problem: to split up number array into two subsets (S1, S2) where X[t] & Y[t] are multiplications of numbers of S1 & S2 respectively, t is index of iteration with condition: |X(0)-Y(0)|==MIN(0), |MIN(0)-(X(1)-Y(1))|==MIN(1), ..., |MIN(n-1)-(X(n)-Y(n))|==MIN(n). for example, let's take an array: 2, 5, 7 then: first pair is {2, 5}, {7} ==> X(0)==2*5==10, Y(0)==7, MIN(0)==3; second is {2, 7}, {5} ==> X(0)==14, Y(0)==5, MIN(1)==6; third is .. ------------------------------------------------ Thanks a lot in Advance.

i need to evaluate [math](A'e^{nA})'[/math],where [math]A=kte |\phi|[/math],with [math]\phi[/math] a angular coordinate between [math](-\pi,\pi)[/math] upon a line integration over a closed path along the coordinate angular [math]\phi[/math].......¿why the result is zero? ....' is the derivate on [math]\phi[/math]

We have a metatheorem (due to Urs Schreiber?) Metatheorem A “red herring” need not, in general, be either red or a herring. So, so simple examples. 1) A manifold with a boundary is not a manifold. 2) A supermanifold is again, not a manifold. 3) Noncommutative geometry considers "spaces" that may or may not be commutative. 4) A Grassmann number is not really a number (as a mathematical object used in counting and measuring). and so on. Anyone suggest some other "nice examples"?

If the integral is [math]\int^{\pi-\epsilon}_{-\pi+\epsilon}d\theta[/math]. where [math]\theta[/math] is a angular coordinate. In the riemman integral , i dont understand if tetha follows the path grenn in figure 1, or [math]\theta[/math] follows the path red in figure 2.

Hello. I understand that [math]\frac{d|x|}{dx}=\theta(x)-\theta(-x)[/math] and then [math]\frac{d^2|x|}{dx^2}=2\delta(x)[/math]. But i DONT UNDERSTAND why when [math]\phi[/math] is a angular coordinate, then [math]\frac{d^2|\phi|}{d\phi^2}=2(\delta(\phi)-\delta(\pi-\phi))[/math]

Variance is a measure of the variation in a data set, defined as Σ(y-mean(y))^2/(n-1). Is there a statistical term for the following calculation: data set time data 1 10 2 11 3 -22 4 34 5 -45 6 56 7 67 8 -78 variation between adjacent data v=(datum(t+1)-datum(t))^2 square root of v to obtain positive values of variation=v^(1/2) Σv^(1/2) median(v^(1/2))

Hi, Recently, I've been looking into the subject of information. After seeing a video on fractals I figured that a fractal is, in some sense, a dimension with missing pieces. The missing pieces can then be interpolated, if one likes, though without adding any new information. The example I've been looking at is the function f:R->R, f(x)=sin(x). It seems obvious that f being a periodic function would contain less information than some other function, say, sinc(x) (defined at zero to be equal to the limit). It also seems logical that the function f(x)=0 would have even less information than both. You could say that whenever there is less information spread …

http://www.youtube.com/watch?v=3eXifzGOfDA Georg Cantor From Wikipedia, the free encyclopedia Jump to: navigation, search Georg Cantor Born Georg Ferdinand Ludwig Phillip Cantor March 3, 1845(1845-03-03) Saint Petersburg, Russia Died January 6, 1918 (aged 72) Halle, Germany Residence Russia (1845–1856), Germany (1856–1918) Fields Mathematics Institutions University of Halle Alma mater ETH Zurich, University of Berlin Doctoral advisor Ernst Kummer Karl Weierstrass Doctoral students Alfred Barneck Known for Set theory Georg Ferdinand Ludwig Phillip Cantor (March 3 [O.S. February 19] 1845[1] – January 6, 1918) was a German mat…

http://www.youtube.com/watch?v=2nAycC7sGVI Educate yourself to a higher learning.... Merged post follows: Consecutive posts mergedand no,i wont baby step it for you.As you see,i done shown you all the greats and how they learned what they learned.... So.... I should be happy to know what i do.maybe if some tried,they can also feel that.Be lucky,i could have charged a trillion dollars because lets be real,the art alone in my image proves im the greatest artist ever.Now add every other knowledge and wisdom. Its weird how one image can show you everything....Hmmm why are we paying for knowledge then?

Never mind, delete this please.

In the commutative diagrams page in wolfram, what does the [math]\phi_{i_{0}}[/math] above the arrows mean?

Given two spheres touching at one point, would that be a surface? I think not, but I don't know how to begin to search for the proof. I thought maybe proving it isn't Hausdorff, but I'm not clear on how to go about it. Anyone can help? Sorry about the bad English, not my mother tongue...

I'm currently taking an online course in mathematics. One of the subjects is about interesting properties that come out of certain number series (or number patterns). Right off the bat, I'll spell out the purpose of this thread so you know where the OP is leading: I'm wondering if we can say that there's something "special" about these number series just because they bear certain interesting properties, or should we say (or prove) that there's always going to be interesting properties of any arbitrary number series no matter what it is? As an example of a number series for which an interesting property emerges, take the following: 1 + 3 = 4 1 + 3 + 5 = 9 1 +…

If [math] f(x) = x^3 + x + 2[/math] and [math]f(a) = 9[/math] then: Calculate [math]f^{-1}(-5)[/math] at "a". This is the question that i'm thinking of it but i can't solve it at all! Does anyone know that how i can get to the answer?

this forum is very good for mathematics.

I'm currently reading this book called Set Theory and the Continuum Hypothesis, written by Paul Cohen, which is a model-theoretic investigation of the topics. I'm trying to rediscover the proof of Gödel's Completeness theorem for myself, but I'm kind of stuck on certain details of the proof provided in the book. In the preface, the author mentioned that he did not "polish up" the final draft of the book, so many important details are left out. Although it is written for people with little to no background in propositional logic, the book assumes that one has a background in abstract mathematics, namely in Model theory. I'm only an undergraduate student not yet knowled…

Let [math]X[/math] consist of four elements: [math]X= \{a, b, c, d\}[/math]. Which of the following collections of its subsets are topological structures in [math]X[/math]? [math]1. \emptyset , X, \{a\} , \{b\} , \{a, c\} , \{a, b, c\} , \{a, b\};[/math] [math]2. \emptyset , X, \{a\} , \{b\} , \{a, b\} , \{b, d\};[/math] [math]3. \emptyset , X, \{a, c, d\} , \{b, c, d\}?[/math] Are they all topological structures in X? If they are not, why are they not?