Mathematics

Hi, Wondering if anyone could tell me how the cosine rule can be the way it is - how it works the way/like it does... Or give me a link to a good explaination for the nature of the rule.. Cheers

Take the binary numbers of a cirtain length, for example. 00 01 10 11 Sort them into how many 1's they have. 00 01, 10 11 Write them in a more familiar form. 0 1, 2 3 And you have a pattern of numbers, which is more interesting with larger examples. 0 1 0 1, 2 3 0 1, 2, 4 3, 5, 6 7 0 1, 2, 4, 8 3, 5, 6, 9, 10, 12 7, 11, 13, 14 15 The first and last rows contain one element. The 2nd row shows powers of 2. More interestingly in all cases all but the last element of the 2nd to last row are prime.

How were numbers like e and pie found? I use them so much in school and have yet to discover how they were discovered.

In the real world a full self-reference is impossible (I can give my name but not my quantum state), if this were somehow incorporated into mathematics, would Godel's Incompleteness proof fail? It's based solely on self-reference, right? Merged post follows: Consecutive posts mergedIf you aren't able to answer, do you know of somewhere or someone else I can ask?

anything by zero is infinity.but is anything by infinity zero?

Hi, if I have a sequence of 1000 random numbers generated by a linear congruential generator of the form: Xn+1=Xn*a+c mod 32 And i know that the 1000 numbers are extracted from the bits 30-16 (15 bits) of the numbers generated with the formula above. (i.e, they range from 0 to 32767). How can i predict the 10 next numbers, i.e, how can i calculate the a, c and seed(Xo) values? I know that it is possible, but i don't have access to the next paper, which i think could be very useful: http://portal.acm.org/citation.cfm?id=66886 Thanks a lot for your help

What is the difference between a statement and a hypothesis?

Hey guys, long time no post! In the past few years I wound up getting a BA in math and then accidently wound up going to grad school. I'm giving an informal presentation in a few days where I will introduce Brownian motion to some colleagues (no laxitive jokes, please!). Anyway, for the presentation I want to pass from discrete Brownian motion to continuous Brownian motion, but I need some help connecting the dots! I'll put what I have so far here and then maybe you can point the way. Thanks! Here we go: Here is a diagram of the simplest Brownian motion: 1 / 0 \ -1 Where each possible outcome (either 1 or -1) has a probability of 1/2. L…

there is correct the expresion [math]\int^{-\pi+\epsilon}_{\pi-\epsilon} d\theta[/math]....where [math]\theta[/math] is a angular coordinate between [math](-\pi,\pi)[/math]....¿what means this?... i believe that this mean that the angular coordinate theta runs from [math]\pi-\epsilon[/math] to [math]-\pi+\epsilon[/math] in the sense anti clock (figure)

The integral is supposed to be the interconnecting thing between the two components. Seeing as how there is a problem, there must be a reltionship, or break down between the two, or three, and so forth, things. The relationship is based on them being related to the problem. The problem is of coure that they need to be 'defined', first as wha they are, and then what they do together. So, if you have two thingies that go together, and they react, te equation will show how they interact. If there was a reaction you will find it by using your 'mytical mathematics' on it. I cannot understand the 'tech', but common sense says that they need to mathematically react, lead…

Here is a strange equation I found: a=b a^2 = ab a^2 - b^2 = ab - b^2 (a + b)(a - b) = b(a - b) a + b = b (a = b) a + a = a 2a = a 2 = 1 This still works, even if you substitute "a" and "b". 2 = 2 2^2 = 2(2) 2^2 - 2^2 = 2(2) - 2^2 (2 + 2)(2 - 2) = 2(2 - 2) 2 + 2 = 2 4 = 2

Can you explain how? how can 0!=1 and 1!=1 Thanx

Many years ago I was shown a simple check for multiplication. The check can indicate a definite mistake; but cannot indicate definite accuracy. The check is performed by adding the individual digits of each part of the calculation. If this results in a number with more than one digit then add the digits of the new number and repeat as necessary until you have a single digit representing each part of the calculation. Example:- 39 leads to 3+9=12, and 1+2=3 58 leads to 5+8=13, and 1+3=4 39 x 58=2262 leads to 2+2+6+2=12, and 1+2=3 If the single digit representing 39 (i.e.3) is multiplied by the single digit representing 58 (i.e.4) we get 12 which leads to 1+…

hi, I was wondering why, in simpsons rule - for calculating the area of irregular shapes, there is a 4 in the formula. like so- A = h/3 (df + 4 * dm + dl)

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"?