Mathematics

a vector is given by [math]\vec{v}=\sum_{j=1}^{n}a_j{\vec{i_j}}[/math] where i is the unit vector for a given dimension and n is the number of dimensions of the space in which the vector exists. the magnitude ([math]|\vec{v}|[/math]) is given by [math]|\vec{v}|^2=\sum_{j=1}^{n}a_j^2[/math]. the unit vector in the direction of the vector v is given by [math]\vec{u}=\frac{\vec{v}}{|\vec{v}|}[/math]. if theta is the angle between vectors A and B, then [math]{\vec{A}}*{\vec{B}}={|\vec{A}|}{|\vec{B}|}{\cos{{\theta}}}=\sum_{j=1}^{n}a_jb_j[/math]. [math]\cos{\theta}=\sum_{j=1}^{n}\frac{a_jb_j}{|\vec{A}||\vec{B}|}[/math]. the projection of A on B is [math]Proj_{\vec{B}}{\vec{A}}…

I not sure which maths forum to stick this in so I'm putting it here I don't mind if it gets moved though. I was thinking about this earlyer and its been bugging me for a while now. Say you have two numbers 1 and 2 isn't there an inifnate amount of numbers between them? Like 1.999' So how can we ever get from one to the other? Does that make sense I'm going crazy here!

I am a latecomer to this problem having watched the program about FLT and Andrew Wiles and I am no mathematician so I am looking for a bit of help understanding this. I have googled and read but most of the stuff is completely impenetrable for a layman. The thing that confuses me most is that the theorem seems fairly easy to 'prove' in descriptive visualisation terms so why is it so difficult to prove mathematically. How I visualise it is as follows: The basic premise is: an + bn = cn cannot be true where n is greater than 2. My starting point is to visualise pythagorean triples where a2 + b2 = c2 is true. In this case I can describe three squares of which square …

Hello everybody. This is my very first post and I warn you now it's going to be unusual. I have always been a very creative and imaginative person, I have ambitions of becoming an author someday maybe even producing my own animated TV shows. I have always regarded creativity as a realm of infinite possibilities, where anyone and everyone can bring something unique into this world. But lately I been feeling very depressed because of two scientific theories. The first one was introduced to me years ago by my father who has always been very interested in science. He told me that there is a finite limit on the number of books is possible to write. Not because hum…

It has been proposed that Pi should be replaced with the Tau for mathematical purposes. The Tau has twice the value of Pi. The reasoning behind this change seems to be that it would simplify many formulae since"2*Pi" is much more common in formulae than Pi on its own. This certainly seems to be the case in electronics and it seems some eminent scholars are convinced. What do you think?

I came across a formula derived by Ankur Tiwari, which he says enables division by zero. The website claims This formula enables us to divide in a unique way without using denominator. This formula is based on the principle that, If the value of X divided by Y (X/Y) is A than by using this formula we can find out A without dividing X by Y directly, that means without dividing X by Y we can find out its value. This is the reason why ‘Bhartiya New Rule for Fraction’ is capable of diving by Zero. The interesting points in regard of this formula are :- 1.‘Bhartiya New Rule for Fraction’ is based on present phenomenon and rules of mathematics. 2. It is ver…

Hi everyone Let me get to the point: in my opinion, the equality between "chance" and "probability" isn't very well chosen... Let me illustrate this with an example: Imagine a sheet of paper, of whatever area. On this paper, a part is covered with honey or some other sort of sweet stuff. The chance that a wasp, or a bee, a fly, whatever, lands on a very specific point of the sheet of paper, not covered with honey, is almost 0 (1/infinity). This chance is equal to the chance it will land on a point covered with honey. In my opinion, though, the probability that it will land on a point covered with honey, is much larger than it will land on a point which is…

Our maths teacher was explaining the other day limits and put an example of a turtle that advances half of the way each time The turtle runs one meter, then half meter, then a quarter of meter... so the turtle limit is 2 without never ever reaching it Several costudents were questioning the teacher lesson, most would say they thought the turtle would reach destination After the class a friend gave a solution to this: The turtle advances one meter, in one second, half meter, in half second quarter of meter, in a quarter of second... so obviously by second 2 will have reched destination and by second 3 will have traspass it Seems the same to me with…

Let us say you have a ruler laid out on the floor, with the spacings arranged such that 1 increment = 1 meter. You are standing at 0. You start flipping a coin an infinite number of times. When you get heads, you move 1 meter forwards (positively) on the ruler. When you get tails, you move 1 meter backwards. If you flip tails at 0, you stay at zero. Let's say that you flipped the coin once and it landed on heads, so you are now standing at 1 meter. With a potentially infinite number of coin tosses, what are the odds of eventually arriving at 0? How different would it be if the ruler was infinite as opposed to finite? --------------------------------------------------…

I have already made a post for this, but that was in early October, and would be hard to find in all of the more recent posts. I wanted to know what the uses of the mathematical constants [math]\pi[/math], [math]e[/math], [math]y[/math], and [math]\phi[/math] are for, and what there uses are. For example, I know that [math]C=\pi r2[/math], and that [math]A= \pi r^2[/math], and that [math]\pi[/math] is aproximatly equal to [math]3.1415[/math]. So, I guess I understand [math]\pi[/math] pretty well. But I have no idea about [math]y[/math] [math]e[/math] or [math]\phi[/math].

Someone please help...I'm stuck on these problems. The fenders (factor enders) of 156 are 1, 2, 3, 4, 6, 8, 9 and that 156 is a 7-fender (that is, it has seven fenders) {1},{2, 12, 52},{3,13},{4},{6, 26, 156},{78},{39} Q1 Find a 1-fender which is composite. Is the answer {1, 11, 121} Q2 Show that a number which has 0 and 9 as fenders has at least four more fenders. Q3 The smallest 10-fender is less than 700. Find it and explain why it is the smallest. Another 7-fender is 460 - its set of fenders is {0, 1, 2, 3, 4, 5, 6}, which is different from the set of fenders of 156. Q4 Find three 9-fenders less than 1000 with different sets of fenders.

Let's say the collection of numbers A contains all number higher than 3 and lower than 4, including infinitesimals. This group is infinite. Let's say that group B contains all numbers higher than 3 and lower than 5. This group is also infinite. My question is if group B contains more numbers than group A? Although B is a more ''extensive'' infinity, i.e. technically includes double the amount of numbers than infinity A, either one of them are infinite and therefore nothing can have a higher value than any one of them. I would imagine this has been asked a trillion times over the course of history but I don't know of a definite conclusion.

From your post #63: "I do not have the understanding of solid geometry and calculus it would take to figure if the length of the diamond's side is exactly r, when measured on the surface of the sphere, but it would be "neat" if it was, and would have implications as to what Pi is. That is, as to "why" Pi is. Just one of the things I care about figuring out. If it has already been figured out fine, I am just looking for the answer, one way or the other." Pi is an imaginary number. The result of attempting to describe the imaginary circumference of an object by the length of a line used to scribe that circle. The radius may be a real physical construct; a circle won'…

Why are numbers between 0 and 1 fractions? And what base uses this "rule"? Base 10??? As in % ??? Hopefully this question doesn't receive "scrutiny" It's ok if nobody doesn't know the answer..lol

Could someone explain, in as simple and non technical terms as possible, what integrating and differentiating are. Is there a simple everyday example where these two things are used. I've had a look in various places and they all tell you how to do it but not what it is you are actually doing i.e. the penny hasn't dropped for me yet. Your help would be much appreciated.

Stop saying "maths." ... It's "math." I don't go to englands and discuss footballs while drinking teas. Because unnecessary pluralization is wrong. ... Only time it can be acceptable is if you're discussing different kinds of math... Entirely different systems of math.... Then it's optionally Ok. Like "peoples" ... But stop asking "a maths question." And don't make horrible excuses about a silly way to abbreviate "mathamatics."

5 * 17 = 85 Prime Number + Prime Number = Product = N (in RSA) y = ((85/x) * 85 - x^2)/ x = ((85^2/x) + x^2)/ 85 p = ((85/x) * 85 - x^2)/ x * ( 85^2/((85^2/x) + x^2)) - 85; sol = NSolve[p0, x] {{x®-86.893},{x®-7.50438+19.0222 ä},{x®-7.50438-19.0222 ä },{x®16.9017}}

I was thinking about the quote "Nothing is impossible" and it brought up the idea of carrying out a specific task the same, but with a different set of restrictions or rules applied to that task needed to be done. Yes, certain things are impossible because of the rules of physics and the rules of mathematics, but some how we find a way to accomplish that task another way. I find it interesting how this can be done even within a different set of rules and restrictions. So, it got me thinking that these tasks being done in a different set of restrictions can be generalized by a function that if you have found the process of completing a task within one set of restrictio…

What is the code in mathematica for sigma?

My math teacher gave us this problem. You're selling stamps. One costs 3 cents and the other costs 5 cents. People can buy as many stamps as they wish. If x is how many 3 cent stamps someone buys, and y is how many 5 cent stamp someone buys, 3x + 5y represents the price of both of them. What is the lowest price of combined stamps, 3x + 5y, so that every price after that continues at an interval of 1 cent. The next problem is what if you have m cent stamps and n cent stamps. What is the lowest combined price so that every price after that continues at an interval of 1 cent? My English may be vague and incorrect, so tell me if you need clarification.

I`m sure all the maths guys know of this "rule" a simple question though, what does the `O` stand for in it?

The little I know about primes is that there is no any 'Systematic Formula' for obtaining prime numbers in either ascending or descending order.And the whole world is in a delima as wheter there is a limit to primes or NOT.That is whetther there is a HIGHEST PRIME NUMBER. I have Good, Better and Best formulae for generating Prime Numbers systematically. TRY THE GOOD ONE: P=7d-4 Where: P=prime number(Needed) d=odd number(Chosen) Example: At d=5, it means; P=7(5)-4=35-4=31 there are a few exceptions for the Good formula. Questions and contributions are welcome

I want to know why people have such a hard time dividing by 0. Basic concept: in A/B=C, when B gets larger, C gets smaller. When B gets smaller, C gets larger. So A/0.1=10A and A/0.0001=10000A.... Obviously when B becomes infinitely small (0), C is an infinite multiple of A. Logical proof: if I want to save $100 and I save $0/month, how long until I reach my goal? 100/0=inf, therefore an infinite amount of time will pass and I will never reach my goal. Objection A: But, if A is negative, you'll net "negative infinity". Answer: yea. What's wrong with that? -A/.0001=(-10000A). Still works. objection B: if a/0=inf and b/0=inf but a and b are different…

When calculating the circumference of a circle, we use 2πr. Since π is an irrational number, then for a unit circle, for example, the circumference must be an irrational length. However, the meter was origionally based on being one billionth the distance between the N. Pole and the Equator thus making the circumference of the Earth an integer in terms of meters. The meter was later changed to be based on the speed of light to again force the value of c in a vacuum to be an integer in meters/second despite an uncertainty of 4 parts in a billion. i.e. the uncertainty then becomes the length of the meter. It is the relationship of the speed of light to the cir…