Mathematics

is there a way to graph imaginary values on a cartesian coordinate system? for that matter, is there any other way to graph them?

... I dont know where to start. School is too slow for me, and geometry isnt really advanced (im in 9th grade). Its basically all remembering posulates and then applying them to proofs. So I want to get ahead of the game and get into Algrebra 2 (for some reason Florida likes to go from Algebra one to Geometry and then go on to Algebra 2). Does anyone know any good websites or eBooks to help me get started?

Hi there, I've a question here that I'd like yer opinions on: If I have an n*m matrix X made up of n measurements of m variables (assuming all the variables measure temperature and so the units are Kelvin (K)). Does this imply that the covariance of X has units K^2? Also, if S = covariance(X) and S = ULU', what are the units of U, L and U'??

Hi there! I am trying to calculate the complexity of an algorithm and I have concluded that it takes a number of steps given by the following formula (in Mathematica notation): Hypergeometric1F1(-D, 2, -x) This looks like a multinomial of x. The order of this polynomial is D. The last term of this polynomial is x^D/D!, which converges to 0 when D is large enough. On the contrary, the first terms seem to be significant. Do you have any suggestions for the complexity of the algorithm? Is it polynomial or exponential with respect to D? Thanks in advance!

Inspired by Grayfalcon's post. Consider a right triangle ABC, with a = 3, b = 4, and c = 5. Circles centered at A, B, and C of radii 3, 2, and 1, respectively, are pairwise externally tangent. Such circles have, to the best of my knowledge, no name. I shall refer to them as the triangle's G-circles. What are the radii of the G-circles of a right triangle of sides 5, 12, and 13? Of sides 20, 21, and 29?

http://www.planethack.org/public/torrents/ (don't be turned off by the url... its not a spam site or a warez site. its my webspace)

Why do you have to use the mean in a standard deviation formula? Cant you use any other average? Only asking as it is part of my coursework in the advantages and disadvantades of the averages. Any help on this topic too would be most welcome! Thanks, Grant.

I don't think any of the people in here are basic on math but here it goes the basic geometry proving: Prove that if you construct a triangle from connecting the centers of the three congruent circles that are tangent to each other, you form an a equilateral triangle.

I am having trouble with this question even though i have guessed the answer which is correct btw. I want to know how i should solve such a question if it were ever more difficult than just guessing. Here goes:Q The sum of the first 6 terms of a geometrical progression is 9 times the sum of the first 3. Find r. (r being the ratio). If anybody could help i would be grateful, thanks.

Imagine an m x n matrix which has only 0 and 1 as its elements. I couldn't think of a better term for it, so I'm calling it a boolean matrix. 1) suppose m = n. I want to calculate the inverse of a given boolean matrix. Is this faster than computing it for a regular matrix (with elements other than only 0 and 1)? Is there an algorithm (analogous to, say, Gaussian elimination) which always preserves the boolean property at each step? Basically if you can maintain the boolean property, you can do everything using bit operations so it ought to be more efficient (besides there not being any numerical instability problems). 2) suppose m != n. I would like to compu…

can someone solve this system for me...its killing me to do it by hand and i dont have my hands on any software x'' - x' + y' + 2y = t y'' + x' - 2x - y = cos2t where x and y are functions of t i just need the general solutions for x and y.....thanks fellas

This thread should be used to post your favourite theorems, not only their names, but also what they state. Fundamental Theorem of Arithmetic Each integer greater than 1 can be expressed as a product of primes, and, except for the order in which these primes are written, this can be done in only one way. and Central Limit Theorem If [math]X_1,...,X_n[/math] are independent identically distributed, with mean [math]\mu[/math] and finite variance [math]\sigma^{2}[/math], then [math]\bar X[/math] is approximately [math] N(\mu ,{{\sigma ^2 } \mathord{\left/ {\vphantom {{\sigma ^2 } n}} \right. \kern-\nulldelimiterspace} n}) [/math] for large n, no m…

Cantor used the expression 2^aleph0 in order to represent the magnitude of R set. Since base 2 can be represented as a tree diagram, we can use it in order to research a collection of infinitely many elements. For example, let us look at the infinitely long Top_to_Bottom blue tree, which is also represented as {1, 2, 4, 8, 16, ...}. It is obvious that we always find finitely many leafs in any arbitrary level of this tree, so this tree cannot have the magnitude of 2^aleph0. Furthermore, since in any arbitrary level we are still in N set, we can never define aleph0 as a transfinite number. Now let us say that we start by a collection of infinitely man…

I come across this when I was investigating the game Hex, I've heard of it before but can someone with a little bit more knowledge explain this to me. It would be appreciated,

can somebody help? prove or disprove, If G is a group in which every proper subgroup is cyclic, then G is cyclic. in additon, can u explain cyclic

after a little fooling around, here's a something that i found somewhat interesting: let S be the set of all "sqare" numbers {s such that s = n^2, where n in N} let T be the set of all "triangular" numbers {t such that t = (m^2 + m)/2, where m in N} let W be the intersection of S and T, whose elements w satisfy both w = n^2 and w = (m^2 + m)/2 where both n and m are in N. now take the ith element of the set W, wi which satisfies wi = ni^2 and w = (mi^2 + mi)/2 it can be shown that: [math]\lim_{i\to\infty} \frac {m_i}{n_i} = \sqrt{2}[/math] since ni and mi are integers, it is almost imaginable that sqrt(2) can be expressed as a ratio of integers…

There was a time in an alien society where the median age of an alien was thirty(in our solar years). Six years after this point, the median age for this alien society was 36. Is there anyway this information can imply the age or average age that aliens die in this society? How would that be represented mathematically? I think that birth rate for aliens and death rate are the two important things to take into consideration for this problem, but since I am only in basic algebra now, I don't see the way to figure out the answer, although I am curious. Does any one know how to create a mathematical framework taking into account the limited information given?

I downloaded a MS file about maths. I don't know why the symbols and numbers cannot be shown clearly and correctly. Anyone help me>?

r is circle’s radius. s' is a dummy variable (mathworld.wolfram.com/DummyVariable.html) a) If r=0 then s'=|{}|=0 -> (no circle can be found) = A b) If r>0 then s'=|{r}|=1 -> (a circle can be found) = B The connection between A,B states cannot be but A_XOR_B Also s' = 0 in case (a) and s' = 1 in case (b), can be described as s'=0_XOR_s'=1. You can prove that A is the limit of B only if you can show that s'=0_AND_s'=1 -> 1 A collaction of elements, wich can be found on many different scales, really approaching to some given constant, only if it has finitely many elements.

In order to define a framework that is researched and manipulated by a formal language, we first have to define the limitations of the formal language itself. Since any language cannot work without information, we first define what are the minimal and maximal conditions that cannot give us any information, when we try to research them. The minimal concept that cannot be researched is Emptiness, because no information can be found in it. The maximal concept that cannot be researched is Fullness, because it is beyond measurement or manipulation of information. So, formal language can work, if and only if we can measure or manipulate information by our rigoro…

How did mathematican define sin A ( A >90 degree) as [MATH]y/r[/MATH]? Are there any proofs to [MATH]sin 150 = sin 30 [/MATH]>?

this thought came to me while making my previous thread. what was used before the cartesian system?

Since everyone's posting questions here, I thought I'd post a nice question I got on my Analysis III assignment last week. It's a bit involved (and somewhat pointless) but I thought it was pretty nice for some reason: Let [math]f : [a,b] \to \mathbb{R}[/math] be a regulated function, and let [math](x_n)_{n=1}^{\infty}[/math] be a sequence in [math](a,b)[/math] such that [math](x_n) \to a[/math] as [math]n \to \infty[/math]. Show that [math]( f(x_n) )_{n=1}^{\infty}[/math] is a Cauchy sequence.

if anyone is on and able to check my work on these couple diff eqs i would really appreciate it. The prof doesnt assign problems with solutions so i cant ever check my work . That is frustrating....heres a couple x' = 3x - 2y + sin(t) y' = 4x - y - cos(t) i used the differential operator and the method of undetermined coeffcients to get this answer..dont think its right because its so ugly x = [e^(t)] * [Acos(2t) + Bsin(2t)] - (1/10)sin(t) + (7/10)cos(t) y = [Ce^(t)] * [Dcos(2t) + Esin(2t)] + (11/10)sin(t) + (3/10)cos(t) And, if you are up to it, heres another one...D is the differential operator (D-3)[x] + (D-1)[y] = t (D+1)[x] + (D+4)[y] = …