Mathematics

On my site www.constructorscorner.com I have found a way to break any triangle into 2 right triangles and solve it knowing only 2 sides. I know it sounds unlikely and it could be wrong, but if you go to the homepage you will see 2 trig parabola pdf downloads. The ideas need refined to be simpler, but if you read it all the idea is there. You may also be interested in my math section under the title bar --- ideas and gadgets. Trurl

Just a general question, may be practical or philosophical, what is your motivation for studying mathematics? My motivation is that I believe that a deeper understanding of nature can only be archived by understanding (and generalising) the mathematical structures found in theoretical physics. Much like category theory studies via abstraction the "mathematics of mathematics", mathematical physics deals with the mathematical structures found in theoretical physics without direct reference to the original physical systems. The generic idea is that we learn more about nature by abstraction. This I believe will become more and more true as time goes on and the too…

What does the double asterisk mean here and what does [math]j_p[/math] mean ? [math]j_p : L^p(\mu) \overset{\kappa_q}{\to} L^q(\mu)^* \overset{\,\,(\kappa_p^{-1})^*}{\longrightarrow} L^p(\mu)^{**}[/math] This is taken from here.

I just glanced at the book Representation Theory: A First Course by William Fulton and in the book there is the symbol [math]\mathfrak{S}_{\lambda}[/math]. What does this symbol mean? [math]\mathfrak{S}_{d}[/math] means symmetric group but what does [math]\mathfrak{S}_{\lambda}[/math] mean?

While introducing random walk on given graph, we usually assume that for each vertex, each outgoing edge has equal probability. This random walk usually emphasize some path. If we work on the space of all possible paths, we would like to have uniform distribution among them to maximize entropy. It occurs that we can introduce random walk which fulfills this condition: in which for each two vertexes, each path between them of given length has the same probability. Probability of going from a to b in MERW is S_ab= (1/lambda) (psi_b/psi_a) where lambda is the dominant eigenvalue of adjacency matrix, psi is corresponding eigenvector. Now stationary probability distributio…

I just tried plotting [math]1^{\frac{1}{x-0.5}}[/math] in WolframAlpha, thinking a spike function would result. Instead, I got a straight line which was defined at 0.5. http://www.wolframalpha.com/input/?i=plot+1^1%2F%28x-0.5%29 Is it a plotting error on their side, or is [math]1^{\frac{1}{0}}[/math] defined??

Please post your theories on how this can be solved if you´ve been trying to solve it.. Or not if you consider your work to be private

This is one of the problems in our school math contest; I found it exotic, so I though I would share. Note, I have both the solution and the process by which one arrives to the solution, so this is not homework; I can send it to anyone who requests it. I'm not posting the process here (yet) because it's in Czech and I still have to translate it. I expect to be able to post it by the end of today. Here's the problem: For a given prime number [math]p[/math], calculate the number of (all) ordered trios [math](a, b, c)[/math] from the set [math]\left\{1, 2, ..., 2p^2\right\}[/math] that satisfy the relation [math] \frac{LCM(a, c) + LCM(b, c)}{a+b}=\frac{p^2+1}{p^2+2} …

I need a formula to calculate all three coordinates a third point of a triangle. Here is a sketch of a random triangle just so it makes it easyers for me to explain my problem: TRIANGLE I have x,y and z of points A and B, and lenght all of the sides (a,b and c) The third point, C, must be between A and B in x-z axises (that should reduce the solutions from a circle (actualy the edge of a circle, i dont know the english term) to only 2 points), and I only need the point that is above the line c on y axis. I could calculate that manualy, but i need a formula that works allways becouse i need it for the movement of my robot (it isnt homework, just a project =…

volume x density so I have 5.0x10^-4 km^3 as the volume and 1x10^12 kg km^-3 as density but I'm confused about the measurements for each. Does it become kg km?

Education in America It appears to me that there are two categories of educational techniques. One focuses on creating graduates with large databases and the other focuses on the individual creativity of its graduates. The US system concentrates on large databases and ignores (I think not accidentally) individual creativity. The graduates of US education are great producers and consumers and almost totally without individual creative capability. Our economic system thrives on a policy of habit, pattern and routine. The workplace wants action and not time consuming thought. Thought must be of the kind that can quickly choose between ‘True and False’ or ‘A, B …

What can one dummy tell another about self-learning? I often face the frustration of responders who find them selves confused by my words. This has led me to post my OP “Knowledge is a puzzle” (which I copy and place at the end of this OP) I constantly study books written by authors who hold a critical view of the existing social status quo. The books I study are the books I write about and these essays are the ones I post. Thus my OPs are constantly contrary to the status quo world views. My OPs are essays that do not generally fit the puzzles that readers have been working on all their lives. Thus when I throw a piece on the reader’s table it will almost ne…

I challenge the student of mathematics It appears to me that most people look on math as something with supernatural qualities. I challenge the student of math to develop and post short essays on Internet discussion forums about those fundamental aspects of math that you think people can and should comprehend. What follows is something that I have posted regarding my idea of what ordinary citizens should know abut this very fundamental domain of knowledge. Arithmetic is object collection It is a hypothesis of SGCS (Second Generation Cognitive Science) that the sensorimotor activity of collecting objects by a child constitute a conceptual metaphor at the …

The dot product of two i-sized vectors [math]\vec{A}[/math], [math]\vec{B}[/math] is defined as [math]\sum_i A_iB_i[/math], What if the vectors aren't equal in dimension? What is the scalar product of [math]\vec{A} = (1, 3, 5)[/math] and [math]\vec{B} = (2, 4)[/math]?

Does anyone have any recommendations for book on modern abstract algebra? They should include rings, fields, algebras, groups and their homomorphisms. I am looking for an accessible account of all the basics we should all know. Cheers.

Hello I'm an artist working on an illustrative project which revolves around the theme of a paradox. Using the Mobius Loop as its central iconic symbol, the message I'm trying to convey will be that of "the beginning is also the end " In this illustration I'd like to incorporate symbols/formulas of both religion and science. The snake eating it's own tail is a terrific spiritual symbol. However, is there such a scientific problem / formula in mathematics, physics or biology etc. which deals with this theme of a paradox. ie: that the beginning of the equation is also the same as the end?.. or perhaps a problem which turns back onto itself, creating a…

It has been estimated that 1000 curies of a radioactive substance introduced at a point on the surface of the open sea would spread over an area of 20,000 km2 in 20 days. Assuming that the area covered by the radioactive substance is a linear function of time t and is always circular in shape, express the radius r of the contamination as a function of t. Apparently Area = constant * t. As 20,000 km2 = constant * 20 days, the constant equals 1,000 km2/day Therefore Area = 1,000 km^2/day * t On the other hand Area = pi r^2. So pi r^2 = 1,000 km^2/day * t, meaning that radius r = sqrt (1000/pi km^2/day) * t^(1/2) I got this far but I don't think the answer …

it's not really homework or anything, just something that came into my head. for a regular shape with n sides of length m inscribed in a circle of radius r, write a formula of m in terms of r and n.

Hi all. I cant seem to get my head around this one. I will try and write it as it was explained to me. Is it possible to work out the Probability of e.g Who will win a race based on an individals odds measured against each others, in decimal. i.e 1. 9.9% 2. 32% 3. 19% Their odds are as above. Looking at that, to me the probability of 2 winning is high. But his odds are based on previous form, and the one we expect to win, doesn't always win. Is it possible to work out the probability based on their previous form and that of those on the field around them.

there are two hamburgers. one is poisoned. there are two guards in front of them. they both know which had been poisoned, but one of the guards (you don't know which) is a liar and always lies, the other always tells the truth. you can ask only one of the guards a single question. what question can you ask to know for certain which hamburger is poisoned?

Anyone suggest a book that deals with (the sheaf of) distributions over a smooth manifold? I want to find out how this ties in with the n-point functions in QFT. Cheers in advance

... and explain any implied wisdom (or possibly duhr-duhr-duuhrhrhr) regarding... Pi = n[sin(180/n)], lim n approaches infinity

I've have the following formulae to convert latitude and longitude to UTM: lon_utm = lon * 20037508.34 / 180 lat_utm = Math.log(Math.tan((90 + lat) * Math.PI / 360)) / (Math.PI / 180) * 20037508.34 / 180 I need the equivalent formulae to reverse this. Longitude I can do: lon = lon_utm / 20037508.34 * 180 but I'm completely stuck on latitude (I'm a programmer not a mathematician!) Can anybody give me some help or point me in the right direction please?

Are you smart enough to prove that for every natural number n, (x[math]^{n}[/math] - y[math]^{n}[/math]) is divisible by (x - y), where x and y are two nonidentical real numbers? I already solved its just it took me forever to get lol. If nobody solves it by the next time I visit, I'll post the solution.

matlab? Easy matrix calculator?