Mathematics

for a dv volume cylinder we get dv=2*pi*r*dr*L but why to multiply this r with dr.please make it understand

I am a new member have a problem, the subject of which has interested me for years. The solution for a in the hyperbolic function (for a catenary) y = aCosh(x/a), sometimes with +c added as a 'curve shifter'. I have managed in the past by iterative trial and error if y & x are known, but very time consuming, ineligant, sometimes unsuccessful. The Casio calculator I use has a "solver", which is useful when it can find an answer, but often can't. I have a new all singing & dancing HP 50G with several solvers, which is far to complicated for me to use at all! The problem is me. I do not understand why sometimes a cannot be found? Surely every Cosh curve…

Hello! Well, It's another math question that I want to know the answer of. This is not homework, I just want to know how to solve this. Unfortunately I have no idea what to do so if you can solve this one for me I would really appreciate it because I just need to look at your equations to understand how to solve this, would be good if you wrote a few words aswell, as an explanation. Here it goes: Put together two parabola sections to a roller coaster with a steady shift in P. What are the equations of the parabolas. Just a tip; They are asking for the equations of the curves on the image, There are two curves that meet in the coordinate P Regards!

Can a point can exist in 0 dimensions and if so, does it mean it's wrong to say 0 dimensions is nothing. It seems logical to say nothing has no dimensions. But if a point can exist in 0D then is no dimensions the same thing. If we look at the geometric progressions from 3D to 0D, solid, sheet, line, point. Could we then say nothing has -1 dimensions. Why isn't the empty set included? Is the nomenclature of dimensions chosen for a mathematical reason. How would it alter maths if a point was said to exist in 1 dimension ie all dimensions were renamed as n+1? Doesn't it make more sense to say a point exists in 1 dimension, the first being existence, the secon…

I love science, and while I gather that I don't have to be better at math per se, as tough as it is for me, I would really like to be a dope mathematician. I'm pretty good at finding free educational materials including books online, if I'm understanding correctly if I want to brush up on my skills and really get a deeper understanding of mathematics I should revisit the basics first with arithmetic, algebra, and elementary geometry. After the basics I should go for some trigonometry and both integral and differential calculus. For my work with computers I should also revisit discreet mathematics. From there I won't be anywhere close to a master but I'll be in fit…

according to euler, the infinite series 1+2+3+4+5.... = -1/12. the "proof" is a bit complex, but basically revovles around letting the series 1-1+1-1+1-1 = 1/2 here's my problem with this. let S = 1 +1/2 +1/3 +1/4 +1/5 +1/6 ... multiply S by 2. 2*S = 2 +1 +2/3 +1/2 ++2/5 +1/3 ... subtract S 2*S -S = 2 + 2/3 +2/5 +2/7 +2/9 ... subtract S again 2*S -S -S = 1 +2/3 -1/2 +2/5 -1/3 +2/7 -1/4 +2/9 -1/5 0 = 1 +1/6 +1/15 +1//28 +1/45... which aproaches a finite value greater than 0.

I was reading a book on timeseries and all the obvious candidates were there but the fourier was briefly mentioned. Now i dont have a great deal of knowledge of calculus or geometry but i was just curious as to identifying the coefficients. I have what i think is the general formula but the guide i used starts using complex numbers as proof and seems to overcomplicate the equation. Apart from the coefficients do you think the transform would have use in a timeseries? I'm talking straight X and Y discrete data, from which there is no obvious or absolute "periods", although i would like to know if it could dissect that part for me. Regards,

Hello, I have been looking around lately for literature about a specific topic but have not found anything directly relevant to what I am looking for, so I was wondering if anyone had any "keywords" regarding this topic for me to try out. Basically if we have a polyhedron, and we were to join it to another polyhedron along an edge or face, does this change its euler characteristic? I would like to find some kind of proof that the euler characteristic stays the same no matter how many joined polyhedra you have, even with the joining possibly occuring sometimes between edges, other times between faces, maybe also between completely different polyhedra. Does anyone k…

If a two dimensional object that is 2 x 2 inches has four square inches and a 2 inch cube has 8 cubic inches how many would a four dimensional object that is 2 inches on each side hold? Would it be proper to assume it would have 16 cubic inches or would it contain another measurement like 16 tesseracts?

Hello, My knowledge of abstract algebra beyond linear vector spaces is very limited. My problem is inspired from the (not very well-known) triangular inequality between angles of a tetrahedron (see for example http://convexoptimization.com/wikimization/index.php/Fifth_Property_of_the_Euclidean_Metric): [latex] \left| \widehat{x,y}-\widehat{y,z} \right| \leq \widehat{x,z}\leq\widehat{x,y}+\widehat{y,z} [/latex] where x,y,z are three vectors and [latex]\widehat{x,y}[/latex] is the angle formed by the vectors x,y. I am looking for a way to abstract this into some algebra of vertices. Say a vertex is the tuple [x,y], we would need to define some "addition" opera…

Hi all, I am currently operating a piece of equipment that essentially collects particles and separates them based on their size. Essentially you have 8 stages, and each stage has a differing size of particles it collects. For example: Stage----Size of Particles (D) (um)-----Mass Collected (M) (mg) 1-------------0.1 - 0.2------------------------------1 2-------------0.2-0.5------------------------------0.1 3-------------0.5 - 1--------------------------------1 4-------------1 - 2----------------------------------0.5 5-------------2 - 4-----------------------------------1 6-------------4 - 5----------------------------------0.5 7-------------5 - 9------------------------…

Howdy all! I have yet another question, this time in the realm of mathematics. For a project I'm doing at work I need to create an optimal sampling method for a drill cone and so the basics of the problem are like this: We have 3 cones nesting inside one another or a cone with 3 "layers". They all have the same base angle [latex]\alpha[/latex] but different radii and heights. If we use V as the volume of the bottom cone, then middle cone is 2V and the outer (largest) cone is 9/4V. Based on this I need to calculate percentages of the total height of the entire cone for the following: h3 - from the top of the outer cone to the top of middle cone h2 - from the top o…

Hi. By its definition, the distance from a parabola to its focus and directrix are the same. Well, this is not a directrix as I knew; it is at the opposite side : Question is -- are the lengths of the paths Q1 - P1 - F and Q2 - P2 - F and Q3 - P3 - F The same ?

I make use of computer a LOT in my math studies. My PC helps me to reduce errors, research questions if I'm having difficulty, crunch numbers, create geometric figures, graph data and functions, and interact with a lot of smart, like-minded people like you. Anyway, can any of you think about the down-side of computers in math studies? Jagella

I wont pretent to fully understand the hpothesis itself because of lack of knowledge of complex numbers (though i have basic understanding of imaginary numbers i dont understand the "critical line" or why infinite 0's sit on it). However i grasp the concept of the zeta function and how generally exponents create a convergence. I specifically want to know how using the pattern 1-(1/2^s) + 1-(1/3^s) + 1-(1/5^s) + 1-(1/7^s) etc relates to the zeta function. The example i have doesnt clarify how the zeta function and this prime pattern relate exactly so any information would be gladly accepted. (Also any examples of complex numbers that sit on this critical line). …

On Fermat’s last theorem This theorem states that for any n except 2, the equation X^n+Y^n=Z^n is not true for any positive integer triplet X, Y and Z. Fermat’s “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” has fascinated mathematicians from 1637 but no one has found what his proof was. Let us try to understand this theorem better. Please read the article at On Fermat’s last theorem http://pengkuanonmaths.blogspot.com/2015/07/on-fermats-last-theorem.html or On Fermat’s last theorem https://www.academia.edu/13665056/On_Fermat_s_last_theorem

Hi, Hope this is in the right place, apologies if not. I've recently started a Maths & Physics Degree and am just about to embark on my first Maths module. I've been toying with the idea of getting myself a graphics tablet to use on my assignments alongside the Windows Maths Input Panel. I'm not planning on using it day to day as i find it easier to scribble with a pen and paper but thought it would save me quite a bit of time when writing up assessments etc. I just wondered if this is something any of you guys have experience of and if it was a viable idea. Additionally if you have used these before do you have any recommendations? Thanks in advance, …

I'm not sure I understand exactly the product in category theoretic terms. The book I'm using gives a very concrete example that is easy to understand. However, I'm not sure I get it generally. How does it work for the product of the reals? What's X in that case? What are f1 and f2?

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.