Mathematics

To get the inner dimensions right one have to see to it that overblowing produces the overtones in tune and that require one get the tapering right. Could some Math person help me set up the 1732 tapering. suppose the music instrument is 600mm long and the inner tube start as small as 6mm diameter and in the end it is about 30 mm. How is the 1732 related to all the other numbers how does one set it up? I ask because I want to build such an instrument say a Horn in wood or a Sax without mechanics just fingerholes or a oboe without mechanics just fingerholes so would love to get how one set up the equation. I am an old retired person and I have never un…

Okay so here's the problem floating around in my head. Everything we see, and do is 3D. Everything. And mathematics was a medium to create the 2D, and 1D world. But how can we percieve anyrhing but the 3D world? Our brain makes a image with the data model its given from the eyes. And the eyes catch light bouncing off objects. The 1D is made up of lines. And the 2D is made up of overlapping lines. And according to the progression of mathematics, the 3D is comprised off overlapping 2D planes. Which creates depth. But all we see, or do will be 3D. The datamodel for a 2D plane is an illusion from seeing it on a drawing board or chalkboard, ect. We get the image in our …

It says that a 'system' cannot be understood (or 'described') without the 'rules' of a 'higher' system. 1. Give me a better, but equally short definition. 2. Well.... I guess '2' depends upon 1. I want to know.

If you have a circle in the complex plane, say, |z| = 1, and you have a function of z, f(z), after one continuous anticlockwise circuit of the circle, how many laps about the origin are made in relation to f(z)? I just want a general method. I thought you would transform into polar coordinates and increase the angle theta by 2*pi. But I can't get anything from it.

Hi Below is a sample of a type of problem I'm struggling with. I’d be enormously grateful for a step-by-step worked solution to it in simple terms. I’m embarrassed to admit that I’m Bayesianly challenged. During a free trial period, an Internet horse race tipster has given out 100 tips as to the winner in each of the same number of races. 25% of these won, and the associated starting odds were high enough to enable his followers to turn a profit. Based on his success, he now decides to charge for the service. During his next 60 predictions his success rate drops to 10% winners, and his customers now lose. At this point how do they calculate the a posteriori probabi…

Hello, Does the Price Equation, when it comes to explain how the altruism trait can spread throughout the population, break down if a group has only one individual who has the trait? In other words, when applying the Price Equation to altruism, is there a lower bound beyond which the Equation doesn't work? If the Equation needs more than one altruistic individual (and actually many individuals) within the group, is it not the case that the Price Equation is a non starter when is comes to explain how altruism can spread within the population? Here's a link to Wikipedia: http://en.wikipedia.org/wiki/Price_equation BTW, I also posted the question in the Biology Sec…

Fermat's proof. Fermat's Last Theorem.pdf

Trig functions with arguments a rational multiple of π are algebriac numbers. Are ALL others trancendental (almost all are)? If you know the answer, please prove it or supply reference.

hello. I have a doubt about my thought process on this exercise. we have 3 sets: A,B,C. A intersection B intersection C = 10% A intersection C = 20% B intersection C = 20% A intersection B = 40% A = 70% B = 55% C = 30% what is the complement (A union B union C)? first I determined that: U = 100% then I cut the problem in order to calculate A union B first. A union B = (70+55)-40 = 85 (adding A and B minus common elements, to find the true content of A union B) (A union B) union C = (85+30)-20-20 = 75 (same procedure, removing the common A intersection C and B intersection C) then I add A intersection B intersection C to the last …

So I was reading this article that talks about how just because we are unable to explain something now, doesn't mean its unsolvable. Perhaps we are just taking the wrong approach. Link removed What do you guys think?

hello, I'm studying mathematics by myself, and following some books I came across this exercise: "in a class of 28 students, 12 practice swimming, 8 practice soccer, 7 practice both swimming and soccer. how many students do not practice any of these sports?" so then I extracted the data: Universe = 28 Swimming = 12 Soccer = 8 Sw intersection So = 7 Universe - (Sw union So) = complement (Sw union So) = ? then I calculated arithmetically: (12+8)-7 = 13 (Sw union So) 28-13=15 (complement (Sw union So) ) <- solution of the exercise I don't know if it is the right approach to solve the problem, even if the solution is correct. how can I solv…

Why is it, that the simple equation "a = bc" explains so many functions/behaviors in our world? It explains Newtons Second Law, the partial pressure of a soluble gas (Henrys Law), the force of a spring, ph of an acidic/alkaline solution, motion and static equations, it goes on continously...So why does this simple equation explain so many workings in our world? How can the multiplication of two numbers so universal to so many different systems?

I was just wondering; is there any way, within the realm of what is practically possible, to write out the number 'googolplex' in its long form? I mean, writing it down on paper is obviously impossible; it would probably take more than a googol years to do so, no to mention that the universe isn't even close to being large enough to accommodate the amount of paper that would be required. But modern computers are capable of extraordinarily rapid calculations and the like. Is there any way for a computer to render the googolplex in its full form? Even in principle? Oh, for anyone who doesn't know, a googolplex is 10^10^100; 1 with a googol zeroes after it.

i want to know about fermi's last theorum and ABC conjectur

Although the set of real numbers and the set of natural numbers each contain an infinite numbers of elements, the set of reals has a higher cardinality than the set naturals. Why is that?

I've been trying to figure this out for a while. In the F-Zero games the cars are able to travel over 1000 km/h, which would obviously end the race much faster if it was a real sport. The games only depict each race as lasting 3 laps, so obviously that wouldn't be a long enough race to satisfy the audience. Now, let's consider these factors: -Each car is driving at over 1000 km/h. -The track is at least 500 meters. -The race is 30 laps long. With those factors in mind, what total time would the race accumulate?

Suppose a>9 is odd and b is the cycle length of a as defined below. Then I conjecture that if (a - 1) / b = 2 ^ c for some positive integer c then a is prime. Cycle length: a is an odd number > 9 and Od is the odd part function, Sloane's A000265. Let a(0) = 1 and a(n) = Od(a(n-1) + a) for n > 0. If a(n) = 1 for 0 < n < N/2 - 1 then the cycle length is the smallest such n, otherwise it is a/2 - 1. For more information see A179382. Example: 11 = 5*2^1+1 11 (1,3, 7, 9, 5) 97 = 24*2^2+1 97 (1,49, 73, 85, 91, 47, 9, 53, 75, 43, 35, 33, 65, 81, 89, 93, 95, 3, 25, 61, 79, 11, 27, 31) if c = 1 that's OEIS A001122 if c = 2 that's OEIS A155072 if c = 3 …

hello everyone, this is my first post. I have decided to refresh my math, all by myself, following some old high school books. anyway I like to understand what I study, but with this example I have severe difficulties understanding it. I attempted solving the example without looking at it, but I failed miserably, entering in an endless loop of wrong assumptions, since this book seems to be written only as a textbook to be accompanied by live lessons, it lacks several explanations of what's being done, IMO. "in a class of 25 students, 7 students play basket, 13 play soccer, 9 none of the above. how many students play both basket and soccer?" the demonstration fol…

From the Wikipedia article on Pythagorean means, a geometric construction... where [math]a[/math] and [math]b[/math] are two numbers represented as line segments. Their arithmetic, geometric, harmonic, and quadratic means are shown expectedly. Now, the harmonic mean is a sector of the line segment from endpoints of A and G. What is the significance of that angle, i.e. is it a right angle? Because otherwise I can see H taking on any other value. Also, the Wikipedia article also gives the following properties for the Pythagorean means: [math]M(n,n,...,n)=n[/math] [math]M(bx_1,...,bx_n)=bM(x_1,...,x_n)[/math] [math]M(...,x_i,...,x_j,...)=M(...,x_j,...,…

Hey all, I'm working on a project right now and Im going to skip right to the point. I count occurrences for probabilistic training. Sometimes my program generates a string like this 'eres your stuff' Should I leave it the way it is, which is approximately 80% grammatical, or should I prettify it? Should I even waste my time on prettifying its output? Another question is this. If I make a variable for strength that counts every sequence of occurrences, certain sequences are going to emerge as more probable, namely, sequences of 1 or 2 occurrences. I don't want to arbitrarily assign a number, but I'm thinking that if I add one occurrence, the most probable one…

Let's say I want to group numbers between 1 and 50 with 4 columns: 1 2 3 4 1 2 3 5 1 2 3 6 ... 2 3 4 5 2 3 4 6 ... 47 48 49 50 To find the total possible combinations,we do: 50*49*48*47 __________ 1*2*3*4 This formula gives the maximum possible combinations. My question is,what would the formula be to find maximum of how many combinations of these numbers include number 1 and 2(for example)?

Hi!!! I need some help... I want to write a code in matlab for the backward euler method. How can I solve the equation to determine y^(n+1)??? Are newton's method, fixed point iteration, fsolve, fzero equal???

Hi all, thanks in advance for any help. This is the question: Solve the following recurrence relation by forward substitution and then verify the result by mathematical induction: T(n) = 2T(n/7) for n > 1, n is a power of 7 T(1) = 1 My answer: T(7) = 2T(7/7) = 2T(1) = 2 T(14) = 2T(14/7) = 2T(2) = 2^2 T(21) = 2T(21/7) = 2T(3) = 2^3 T(28) = 2T(28/7) = 2T(4) = 2^4 (I'm not sure if going up in 7's is correct) Solution for recurrence relation: T(n) = 2^log n T(1) = 2^log 1 = 2^0 = 1 T(2n) = 2T(2n/2) = 2T(n) = 2^1 x 2^log n = 2^ log 2n Check answer for T(14) = 2^2 2^log n = 2^log 14 = 2^7^2 (two to the power of 7 squared) = 2^7lo…

Richard Feynman on The Pleasure of Finding Things Out said something about how when he was tutoring his cousin about algebra and said that his cousin was to find the value of 'x'. Feynman went on to the answer and then his cousin said 'but you did it with arithmetic, you have to do it in algebra'. The following was then about how algebraic rules were invented so kids could pass a class even though they didn't know what they were doing and that it didn't matter how you got the answer so long as your answer is correct. My question is, apart from the 'traditional' rules of algebra, in what other ways could you 'do' algebra and also what did it mean when it was said that…

Hi, I am trying to apply Hidden Markov Model to improve my detection accuracy. In my program, there are two states, 1 and 0. I used Bayes detector to generate the probability for each instance to be in class 1 and 0. For example, I have a sequence Actual states: 1 1 1 1 0 0 0 0 probability in class 1: 0.5 0.6 0.7 0.8 0.9 0.2 0.3 0.4 0.5 0.5 probability in class 0: 0.2 0.3 0.4 0.5 0.5 0.5 0.6 0.7 0.8 0.9 I tried to "use probability in class 1" as the "seq" and "Actual states" as "states" in function hmmestimate ([estimateTR, estimateE] = hmmestimate(seq,states) But it seems that "seq" must be integers, and I do not understand what is the requirement for the inp…