Mathematics

Now and then I play around with Maths and Scientific thinking. Only later on I check on the available knowledge store. Two days back I thought of testing out the following equation : x y = y x where both x and y are Positive Integers and x is not equal to y. I guessed that there won't be a solution to this equation then I realized that 2 4 = 4 2 and perhaps this is the only solution possible. Are there any other solutions ?

Just what the title says. Say for instance I have [math]ln(x^2/3)[/math]. I want to be able to turn that into [math]2ln(x...[/math]But, I'm not sure exactly what's happening to a number or what the exact operation is when you take an exponent out of the argument of [math]log(x)[/math]. So, I'm not sure exactly what the result is if I assume [math]ln(x^2/3)=2ln(x/sqrt(3))[/math] because every time I try to do something like that, I get some complex constant left over. It "seems" like when you move exponents out of the argument of a logarithm, you're exponentiation everything in the argument by 1/exponent-you-want-to-get-rid-of and for some random reason that exponent then …

I'm not solving a differential equation with an unknown function but it seems it should be similar. What I mean is I want to solve for an unknown operator that has some arbitrary transformation of terms and variables. If for instance I had x^5 and I wanted to find some operator that made x^5 turn into x^4, I should get ^4/5. But let's say I didn't know that property of exponents as a given, how would I mathematically investigate the apparent transformation of variables to find that operation that has the properties of turning x^5 into x^4?

That is is this function oscillatory?

Just what the title says. Say I have some random equation like 2^x, then I have some random equation that I tested and it gives me the points (1,2), (2,4), (3,8), (4,16), (5,32), (6,64), (7,128) but there's no proof it works for (8, 256) other than by testing it to see it works for x=8, if I assume the curve is continuous, is there any sort of weak proof that says it's the equation 2^x? Every taylor series should be unique, yet for any given equation that was derived purely from integers, I could use some kind of a*cos(bx)+c that generates a coefficient of "1" for any given integer. For instance, the equation y=2^x generates (1,2), (2,4), (3,8), (4,16), (5,32), (6,64), (7…

I have been doing research on entropy encoding for some time.. I found some interesting relationships between Arithmetic coding and other methods such as Huffman Coding. I made an article to explain them and am presenting here for review: http://siara.cc/arithmetic_coding_new_approach/ I have also attached a PDF version for convenience Arithmetic_Coding_Formula_based_approach.pdf. Please let me know your ideas.

Having a hard time quantifying certain equations because most the values are below 1. One issue is standard deviation, simple enough but when squaring these numbers they get smaller etc...Also working with angles below 1 degree. For some reason doing opp/sin(x) gives a hypotenuse barely 4^-10 over the adjacent. I've tried a few basic things..multiply by say 100000 then divide by a multiplier that counts the resulting exponent (with standard deviation). Is there a particular trick to working with values below 1? As a side note 3162 is my new favourite number. Regards.

I am looking for reason why anything raised to the power of zero is 1. On a side note any reason why log's of zero are undefined.

Suppose I have a number, any random number like .3252389472395872394729..., is there software that will test possible exact formulas containing certain parameters, like if I want it to test if that number could be some coefficient of pi or e or e*pi or sin(tan(cos(sin(tan(cos(42424244424)?

What exactly is mathematical physics in contrast to non-mathematical physics? I would imagine it is physics done in the way of pure maths, as in designating axioms, definitions, some inference rules implied by the context, and then deriving theorems about the subject matter, or similarly constructing structures that correspond to physical phenomena. But then what is the difference between that and, say, solving some equation and deriving the result using the informal tools of calculus/algebra. Each step in the derivation might not be given a justification like a proof step, and there may be differences in formatting and fullness, but wouldn't it be the same applicatio…

Hi, Math is far from being one of my best subjects, so im looking for some help in this area. How can I measure the bulk density of a dry powder into cubic feet using a 1 cup measurement? Thanks for any help!

I want the geometrical interpretation of the following: > If fxx * fyy} < fxy^2 and fxx has the same sign as fyy at a point, then why is that point a saddle point? Because,in the case that they have the same sign,one would expect that point to be a minimum or maximum point,not a saddle point. Bear in mind,that i have checked the intuitive explanation that is available in wikipedia,but did not understand it. Also, i am studying physics and not math,so please don't complicate things with symbolisms that i might not understand. Also, i want an intuitive answer,because i know the maths behind categorizing critical points.

Can someone help me on the problem: Assume the probability of each relay being closed is 'p' and that each relay is open or closed independently of other relay. What is the probability that current flows from L to R? See the circuit diagram below. The relays are just like switches. If closed current flows else if open current does not flow. This problem is from the book of Meyer : introduction to probability and stastical applications.

This guy is trolling me at school, he keeps saying that "You're a Senior, you should know that", but I find this kind of statement to be invalid. Because if Advancing to the level of Senior = Knowing a specific piece of information was indeed true, then why didn't I know that? So now, I want a to put it into a mathematical equation to shove in his face. Any ideas how to write it?

Why is it that a negative * by a negative equals a positive. Especially given that if I add to negatives I get a negative. Multiplication being addition and all.....

Why is it that 1 is not considered a prime?

I am looking for in depth reasons for why division by zero must remain undefined.

The Not Integer Line ~-5 ~-4 ~-3 ~-2 ~-1 ~0 ~1 ~2 ~3 ~4 ~5 Author: David Elkins

Give an explicit form each of the terms: a(1) = 1 a(2) = 3 a(n+1) = [a(n) + a(n+1)]/2 I just started with this topic. How can I calculate what a(n) is? Should I replace a(n) by 1 and a(n+1) by 3 and divide the result by 2? Would that give me de?

I have little math, But i came across this fact about prime numbers which i thought was interesting and worth a share, Most properly old to those with math, 23X23=529 =(24X22)+1 29X29=841=(24X35)+1 31X31=961=(24X40)+1 37X37=1369=(24X57)+1 41X41=1681=(24X70)+1 I was wondering if there is any sequence to this? Between the multiples of 24? A little find like this to me, brings a new interest and lets me explore where i would otherwise perhaps never go. So my first thought was 3x24 -1=73, So i googled 73 , 73 is an emirp, m…

Hi all, My brother is getting married next week and he and his wife to be are school teachers. They had a bit of a theme going on the wedding invites etc that was the square root of R + V = "heart shape" and I would like to turn this around in a clever maths way of taking the piss. Not to clever though as many guest including myself wouldn't understand!! Can anyone help?

does anyone know this puzzle and has seen a solution like the following before: https://www.facebook.com/profile.php?id=100008303142425 i hope it's ok to post it in this subforum. i will not try defend the puzzles ideological background nor comment on crowley himself, i'd just like to treat it AS IF IT WERE an actual puzzle. the original cipher / puzzle / riddle as found in the "liber al vel legis", respectively as it is traditionally multiplied (4638ABK24ALGMOR3YX2489RPSTOVAL) is "translated" into letters only, then into numbers only. i think the most important step is the "double translation". it brings up the question of how to treat the number 24 (as either the le…

In this integral (error function), what is d and what is t? This stuff is hard to find for math noobs

I recently watched a pretty neat youtube video about a theorem that one of the writers of Futurama made up for one of their episodes https://youtu.be/J65GNFfL94c The professor has invented this mind switching chair that lets two people who sit on it switch their minds. But once two bodies have sat on the chair the same two bodies cannot switch minds a second time. In the episode the characters end up with their minds all over the place. They bring in two extra mathematician/basketball player characters who prove that they can sort out any mess using their two bodies as storage space (the Futurama theorem). Here are a few problems which I think would be fun to puz…

Hello, my name is Fred I am trying to predict the outcome of competitive counter-strike global offensive matches by using data that I stored. Matches are 5v5 and there are 30 rounds per match Entry kill ratio: the ratio at which the players manage to make the entry kill (kill the first enemy without dying) The data that I have: TEAM 1 : allu 1.81, get_right 1.18, forest 1.17, friberg 0.8, xizt 1.27, AVERAGE 1.246 This is the entry kill ratio for each player for this team on this particular map. Round win % after getting first (entry) kill: 77.22% TEAM 2: maniac 0.95, x6 1.01, kennys 1.48, rpk 0.97, apex 0.91, AVERAGE 1.064 This is the en…