Mathematics

Why do we teach our kids that 6 ÷ 3 = 2? If I divide 6 oranges in 3, what I get is not 2 oranges, but 2+2+2, without subtracting 4 oranges. So why don't we teach 6 ÷ 3 = 2+2+2, 1÷2 = 0.5+0.5, etc etc? If I say "I would like a quarter of this cake", then I am not dividing, but I am dividing and subtracting, I am doing a fraction, 1/4. Don't you think divisions shouldn't be confused with fractions?

I know how to write regular essay-type paper, but I know these type of papers have a different format(I think). Can someone show me how I would format the paper or direct me to references about how to do this?

It is probably a too long of title, but this question loomed in my mind. We all know that 3 dimensional geometric volumes have a finite size(unless told otherwise), and 2 dimensional shapes are made up of lines that are infinitely thin. However, 3 dimensional volumes such as cylinders are made up(theoretically) of 2 dimensional circles that are stacked upon each other until a given height, yet 2 dimensional shapes with lines that are infinitely thin are able to make up a certain height. How is this possible? I mean the formulas for determining surface area and volume are based on these principles, though I could be wrong.

Ok, thinking in radians just makes my head hurt, but I need to get a grasp on this for something I am working on. So, let us assume we have a stationary object, object A. For the purposes of this exercise, we can consider it to be a point. Orbiting this object we have another point object, object B. Object B orbits at a distance 5,000 meters with a fixed velocity of 100 m/s. So the question is, how many radians per second is object B's orbital velocity. I already know: [math]V_o = 100 m/s[/math] [math]C_o = 2\pi \times 5000 m[/math] So would it just be a matter of finding the angle subtended by the arc traveled in one second, and converting that…

I work at a small investigation firm and I have a problem that may or may not be possible. I have some numbers that indicate a list of possible suspects for a crime we are looking into. The list is encrypted or coded somehow. I went to the business where the numbers came from and was able to (out of the dumpster) piece together some shredded documents that have the number and the coded version of the number together. What I need is the key to decoding these numbers so that I can present it as evidence to my client. I am not smart enough but I was hoping for some possible help. Here are the numbers I recovered from the dumpster. Original Number Coded Number …

hi first sry for my bad english. I'm a computer science major and Im looking for some articles about relation between mathematics and computer sciences, Im looking for something like linear algebra in computer graphics or surface integrals in robotics, Iv searched alot but I didnt find what Im looking for ! and I dont khow where to seek, I want some articles that really shows how computer graphics is based on linear algebra or other things line that. I am working with openGl now and I khow something about computer graphics but I want other articles too. I am interested in everything that shows the relation between mathematics and computer sciences. thank you

saw this very interesting video: and wanted to share/talk about it in a place without 500 character limit lol i personally believe the answer can be considered undetermined, or both 0 and 1. to have a definite answer, we gotta know the number of 1's we have, and the operation sign we start with. starting with a - sign and having odd number of 1's means you have the final answer = 1 (1 - 1 + 1 = 1) and having even number of 1's means you have final answer = 0 (1 - 1 + 1 - 1 = 0). infinite, by oxford's definition means "impossible to measure or calculate" which means there is an undetermined numbers of 1's involved. to want an definite answer is to collapse th…

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…