Mathematics

Suppose a, b, and n are positive integers and a + b = n. For what values of a and b maximize ab? The only way I know of maximizing ab is by drawing a table of values and comparing numbers. It seems though that if n = 2k, then the maximum is obtained when a = b = k. If n = 2k + 1, the maximum is obtain when a = k and b = k + 1. Is there an intuitive way of showing/deriving this though. I can't seem to think of anything.

Have your teachers taught you about the mod and absolute value? I want to know whether I will come across with the lessons of these skills. (Actually, I learnt them myself)

Please look at the attached pdf http://www.geocities.com/complementarytheory/Roots-Chain.pdf . By this model we can see that √1 is the "shadow" of √2 and √2 is the "shadow" of √3. I think that we can conclude that √3 is the "shadow" of √4 ... and so on. In short, I am talking about roots which each one of them is the diagonal of its dimension level, where each n_dim diagonal is the "shadow" of n+1_dim diagonal. We have a chain of "shadows" between infinitely many diagonals in |N| dimension levels. Do you think that this "Chain of Shadows" has any mathematical/physical meaning?

[MATH] log(x+y)/logx = log(x+y)/logy[/MATH] Can anybody show a calculation? I think that's a trick.

Today, I read some function book. And I drew a lot of graph, but due to the size and my hand-drawing, the output is very ugly. I want to have a very good graph drawing software. Can you suggest some to me which are free, simple?

Hello everyone, I am going to read some books in my summer holiday. Which region of mathematics involved in science the most? Or which part do you like the most? ( the most or most ???) Would you suggest to me?

I saw a program on tv about a professor that came up with a mathematical equation that says there must be other planets that hold life. I think he worked along with seti,,,but not sure,,,waas wondering if anyone knew what that equation was?

As a new user I haven't been able to see how things have progressed at ScienceForums.net but I believe the users in the Maths forums mostly fall into a few categories: . Varsity Maths Students . Interested High School Students . Interested Members of the general public What I'm concerned about is the possibility of some people who have non-standard/alternative theories that use these forums to debate with those that are still learning what Maths is all about. What do you guys think about adding an extra forum for these alternative theories so that people viewing them know that they are a bit less "mainstream". I think this would ensure that the less "knowle…

I was just curious to know wether the trignometric functions and the log / antilog functions are defined for imaginary and complex numbers....and if yes then how are they defined ?

I have a question, I forget what the symbol is for this set problem: {1,2,3,4,5,6,7,8,9,10} ??? {4,6,8,9,10}= {1,2,3,5,7} What is it???

I have a nice problem for you guys, just a funny problem to stimulate the mind. For each non-negative integer [math]n[/math], let [math]a_n[/math] be the number of digits in the decimal expansion of [math]2^n[/math] that are at least 5. For example [math]a_{16} = 4,since 2^{16}=65536[/math] has four digits that are 5 or higher. What is the sum [math]\sum_{n=0}^\infty \frac{a_n}{2^n}[/math] ? I evaluated machinally the first 299 (see attachment) terms a of the sum. The sum converges to 0.086617 numerically, what is the exact value ? What is the growth rate of a_n ? Mandrake a.txt

check here. http://www-groups.dcs.st-and.ac.uk/%7Ehistory/Day_files/Year.html no one famous was born on my birth day. so sad

Happy pi day everyone...yep its 22/7 meaning its national pi day...so celebrate by using pi

Alpha Day is May 17, the 137th day of the year. The constant alpha is the basic constant in all electro-magnetic interactions and determines among other things why we have the elements we do and what their chemical properties are. So its being the right size and not a few percent different makes life possible. And keeps the sea from blowing up in an H-bomb fusion reaction and makes it so there are stable elements heavier than helium, and so on. It is fundamental to the universe. Alpha reciprocal is about 137.036..., so very close to 137. So a good approximation for alpha is 1/137. Alpha is better than PI

What is the code in mathematica for sigma?

what happened? i thought you were going to put more of your calculus lessons.

[math]x^n+y^n=z^n[/math] This is fermat's enigma, where n>2. However, [math]\sqrt3^4+2^4=\sqrt5^4[/math] is true. Huh???

I am sending my friend an email, but I need to draw up the equation. It is a sigma equation! Anyone know the code for this???

Just changed the names around for some of the forums. This is a kind of guide as to what you should try and put in each: General Mathematics: Anything that doesn't fit into any of the other subforums. Analysis/Calculus: Any analysis problems (e.g. differential equations, questions with convergence/limits/continuity/etc). Modern/Abstract Algebra: Linear Algebra, set theory, equivalence relations, etc. Applied Mathematics: This is the old Stats and Geometry forums, and its use is now for any maths of a more applied nature. Hope you find it easier to choose where to post your stuff now Cheers.

OK, I know a few, like 'i', but I don't know 'e'. Can someone explain it to me> And tell me if there are any other imaginary numbers?

A pretty easy one just for kicks, and it's a fairly standard proof. Prove that [math]e^{i\theta} = \cos(\theta) + i\sin(\theta)[/math] and hence show [math]e^{\pi i} = -1[/math] (for the more adventurous, try showing [math](\cos(\theta) + i \sin(\theta))^n = \cos(n\theta) + i\sin(n\theta)[/math]).

I was looking through a book talking about the history of the number pi and it was talking for a few pages about the search for a way to find a circle and square of equal area. It talked about the Egyptians and their method and went on to the Greek ideas but never exactly explained what the problem is and why there isn't a solution. I ran out of time looking through the book, so maybe I missed this later on, but could someone explain a little about this?

I had to start a little work out of the old calculus book today. The teacher's want to make sure we understand how to calculate the slope of a line when given two points before we get into the really tough stuff like the slope of a curve and logarithms this fall. (I know I might not be the best at math, but come on). Ths is a question I came upon in the book that I just couldn't find a way around. Incidently, the only reason I saw it was because the teacher told us to skip over that section. So I naturaly tried some of the problems. One of them has me a little stumped though. It came with a diagram, but since I don't know how to paste pictures on here, I'll just des…

Could someone please tell me how to calculate pi in the windows program excel please? If you could post the solution under this thread, or just email it, I would be very grateful. THANKS!

Can someone explain these to me in the simplest way possible? Also the Absolute Infinite.