Mathematics

TheString-Mathematics The ancient Greekslaid some mathematical foundations of theory, but their ideologicaldefects embedded therein. The ancient Greeks assumed that: the worldare composed of atoms, the atoms are taken for granted is a dot-like,the dot is, of course can not be divided. But now, This definitiondoes not meet the objective facts. the frontier theory of physics,string theory and superstring theory showed elementary particles arenot point-like but infinitely thin one-dimensional entity, that is,strings. Then, using strings to define the Measure is in line withthe natural way. I call it as the string-mathematics. For example, astraight line shoul…

What they have in common the maths models of Euclides, Newmann & Riemann? It would be possible to establish a model that would bring together the three?

I am die-hard fan of maths and like to solve problems in most easiest way possible,because i'm just damn lazy to solve by bigger methods. It seems (overheard) that vedic maths is one such tool which takes us through easiest ways to solve. can i know how? the links related to it? the complete information about it? A complete thread on vedic maths.

Hi guys, I'm a newbie here and Maths isn't my forte, so please be gentle with me I have been thinking that if we took a string and marked points along its length, we would describe the position of each dot according to its position with respect to the length of the string. Yet, if we coil this up, it becomes a 2D shape, so that each point now has 2 coordinates, and similarly winding it up into a ball would give it 3 dimensions. What I am getting at is that if we knew function to describe 'winding' of a line into a sphere, could we use it to condense 3 (or more)- dimensional data into a single value for the unwound string? I'd really like to know whether I'm…

Imagine there is a population/database/dictionary and we would like to distinguish its elements. So for each element, let us somehow encode its individual features (e.g. using a hash function) as a bit sequence - the most dense way is to use sequence of uncorrelated P(0)=P(1)=1/2 bits. We can now create minimal prefix tree required to distinguish these sequences, like in the figure below. For such ensemble of random trees of given number of leaves ([math]n[/math]), we can calculate Shannon entropy ([math]H_n[/math]) - the amount of information it contains. It turns out that it asymptotically grows with at average 2.77544 bits per element [math](\frac{1}{2}+(1+\gamma)\…

Consider generating a 4-length code using only 3 digits. The possible number of permutations is 34=81. However what if all 3 digits had to be used. How many permutations exist? In other words only one duplication of a digit is allowed, but it could be any of the digits. Drawing a tree I can see some sort of pattern for n=3 r=4 and n=4 r=5 but I can't get it to gel and extrapolate to n=3 r=5 where two duplications or a triple is allowed and so on. Is there a generalised formula that allows this to be calculated? TIA Update - to put it another way if n is the number of elements and r is the number to be selected then if I write the permutation as P(n r) then…

Perfect squares end in 1,4,5,6,9 and zero. Nice symmetry. Especially with the squares of 1 & 9 (5 +/- 4) ending in 1 2 & 8 (5 +/- 3) ending in 4 5 (5 +/- 0) ending in 5 4 & 6 (5 +/- 1) ending in 6 3 & 7 (5 +/- 2) ending in 9 WHAT ABOUT SQUARE ENDINGS? 100, 400, 900, 1600; of course, if a number ends with a zero, its square ends in 00 Is the only other repeated end for a square 44? 144 1444 3844 7744 12544 19044 26244 35344 44944 56644 68644 are all perfect squares their square roots are (50n +/-12)2 and n = 0,1,2 . . . For further amusement, 213,444 = 4622, and is the second member …

Im having a little trouble grasping a little maths that Cantor came up with. Its the one where you write every single decimal real number in a list, then you take the first decimal digit of the first number, the second digit of the second number in the list, the third digit of the third number etc. to get a 'new' number. you then change that number in a set way, and you have a completely new decimal. my problem is that although you have a number that has a different first digit to the first number, so its not the first one, and its not the second one, and so on, you will still have written every possible decimal real number, so how is it not in the list?

I've wondered this for a long time: Why the heck is the famous Monty Hall Problem even to this day so controversial? I mean, I'll admit that when I first heard the problem I was like "Give me a break; two doors left means there's a 50/50 chance, so switching your choice is pointless," but once I grasped it fully I was quite frankly embarrassed that I didn't get it right away, because it's pure common sense. For those of you that don't know the Monty Hall Problem, this is it. A game show host presents a game show contestant with three closed doors and tells her that behind one of the doors is a new car (i.e. one out of three doors is a winner), and behind the othe…

Here is an argument I want to get checked. I first posted it in Philosophy since its immediate concequences are probably most of philosophical interest. But now ,on second thought, I decided that Philosophers lacks the necessary qualifications: They dont usually show any logic ability. Their forte is NOT checking proofs The question of Paradoxes is of some Mathematical interest: It is known how to remove them (preventing self reference) , but then they can no longer be derived,analysed and solved. So Dear Mathematician: Is there an error somewhere in the argument below? (Ahem...I did not intend underlining everything above, and neither this line...sigh) Defin…

This is a question that has been perplexing me for a number of years. Unfortunately, I don't have the experience with geometry to answer it myself, so I am hoping someone here can help. Note: No this is not homework help - It's the basis for another idea that's been percolating around in my brain, which I may add to the end of the thread, assuming this turns out the way I expect. Let us suppose we have a right triangle, ABC, with sides AB and BC, and hypotenuse AC. If we draw one line that bisects and is perpendicular to AB and another that bisects and is perpendicular to BC, will the intersection of those lines fall exactly on AC?

Hi guys First up I'm useless at "complex" mathematical formulae and so would greatly appreciate some help Secondly this is a totally low brow request for help based upon goofing around so apologies if this is a bit informal. Right-Me and my housemates have FIFA soccer on Xbox...recently we began debating who is the best player and so I decided to start an excel spread sheet to take down some stats and hopefully work it out, working out win percentages and basic stuff like that is no problem, however let me describe the 2 aspects that are problematic 1) We all play regularly but some people more, some people less so we can't just do a basic league where …

Many years ago, in college, a textbook ordered me to prove that from any point on the directrix, the two tangents that can be drawn to the parabola intersect at a right angle. (Maybe I've got that wrong, but that's how I remember the problem.) I worked on that for months and was never able to solve it, even after the professor told me how to do it. Drove me nuts. So I've never forgotten it. But I've also never found a proof of it. I'd appreciate seeing it proven if anyone cares. But of course I have no right to take anyone's time, so... no obligation or anything. Just something I've been curious about for a long time.

Which type of Integral is this?? I want to solve this integral in MATLAB.

explain the difference between area, surface area and volume

Dear friends, I kindly ask you to help me show that if X is a normally distributed random variable with parameters mu and sigma squared, then its distribution Phi_x is related to the standard distribution via: Phi_X(x)=Phi((x-mu)/sigma) Many thanks!

Hi there, I've been doing some questions out of a book, and came across this question which I found interesting. I was wondering if there are other mathematical techiques that can be used to solve a problem like this? Question: The rotational period of Earth is 23.933 hours. A space shuttle revolves around Earth's equator every 2.231 hours. Both are rotating in the same direction. At the present time, the space shuttle is directly above the Galapagos Islands. How long will it take for the space shuttle to circle Earth and return to a position directly above the Galapagos Islands? Solution: The time taken to travel is [math]\frac{\theta}{\omega}[/math].…

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?

Hi guys, first real post. I'm not very knowledgeable in science, so I'd like some help with this. I know that Time Travel (to past, not future) is theoretically possible, but doesn't the Chaos Theory say otherwise? If I were to travel into the past, just by me being there would change the present, which probably would in turn keep from, or delaying me, traveling in the past in the first place. Wouldn't there be billions of variables that would occur if say, you travelled back 200 years. I would also like to know if traveling to the future is even theoretically possible, because I don't really see how it is.

Hello, everyone! Can you explain me what can we measure in 4 dimensional space? If, in 2d - Area, 3d - volume.... Thank you!

What is a tensor and why is it useful? I have grabbed "Vectors, Tensors and the Basic Equations of Fluid Mechanics" by Rutherford Aris, but it is not a gentle introduction (some of the notation used is not explained at all!).

All right, here I have a concept. It can be proven right or wrong within 3 minutes. If you liked my SSA triangle then you will love this. http://www.constructorscorner.net/ideas_and_gadgets/math/math_hunch/hunch_00001/hunches_section0007/RSA2Lane.html Remember I am a student, not a scientist. It is a concept not a theorem. The point is not to call me stupid. It is to give guidance. I posted here for instruction. I will not claim it works. Remember student not scientist.

I think the problem below is an nCr problem [n!/(r!*(n-r)!)], but I'm not quite sure how to approach it. Any help would be appreciated. There are 20 numbers, 1-20. Someone would randomly pick 5 numbers. I need to create sets of 10 numbers so that at least one set contains the 5 numbers that the other person pick. What's the minimum number of sets I'd need to create?

two rich men who have no idea how much money they currently have in their wallets meet. rich man A says to rich man B: "i'll bet you that i have more money in my wallet than you have in yours. In fact, let's switch wallets." should rich man B accept the wager?

If you know some interesting or fun facts about square roots, I would love to know them. I have few so far: - square root of 2 is the diagonal of a square who's side length = 1; square root of 3 is the diagonal of a cube who's side length =1 - a list of the most popular square roots and their answers any information that will inspire others to learn more about square roots is appreciated!