Mathematics

I'm trying to learn how to do mental math in base-16. I understand how it works and I can do it on paper if I think for a long time, but the biggest problem I'm encountering is what words to say in my head as I read the numbers from the page. I can't call 1716 "seventeen" when I know it equals 2310. And I have no clue what to call 1C16, 20016, 400016, etc. Usually I hear anything besides base-10 being spoken one digit at a time, so that 4D2F would be read "four-dee-two-eff." This feels very awkward and totally useless for mental math. I was wondering if anyone here has experience with this and knows of a widely accepted and intuitive spoken system for hexadeci…

Putting powers upon powers aren't taught in school. But this problem is interesting. The problem is to find x. x^x^x^x^x^x... = 2. Find x. This was in the book The Art of the Infinite. Now the question is whether or not there is such a number x. If there was, it'd have to be greater than 1. But it'd have to be less than 2. The idea is that because x^x^x^x^x... = 2, it is the same as x^x^x^x... = 2 and so you can have x^2 = 2, and x is the square root of 2. Now the steps seemed logical to me, but I was skeptical so I tried to check it on the calculator. But x can't be the square root of 2 because this diverges. I tried it on the calculator different ways, pressing …

I understand this type area = width*height e = (m*c)^2 As a programmer I use these type of equations all the time, although they are not always as simple as the ones stated above. However this type Utterly confuses me Coding isn't just equations, there will be commands and stuff backing my equation's up as they means noting to a compiler on there own, I guess in wider maths an equation does stand up on it's own as being meaningful therefore it needs to be expressed in a more complex way. Can someone explain or point me in the direction for stuff about understanding those sort of equations. Until then I will continue with my current "observe, under…

so I need to get a laptop for college, most of what I'm going to be doing involves mathmatics and physics so I'm wondering what kind of hardware should I get in order to be able to do things on mathmatica and such in a timely manner. Most importantly is processing power important or memory capacity, and in terms of rendering capability for complex graphs and such do I need to worry about the graphics card?

1.Why if f(x) is not divisible by 4, then, it has no integral solutions? 2. If p l ab, then p l a or p l b. Does this mean that p could divide a and b at the same time ?

a though occured to me the other day, 200 years ago the highest level of mathmatics any mathmatician was educated to was calculus 100 years ago we started having to educate young mathmaticians to the level of linear algebra and vector calc (probably a couple others that I am unaware of) Learning these additional subjets requires several additional years of training. today a mathmatician requires 6-8 years of schooling in order to be trained to the level where they can do real work that actually effects the field that their in. My question is what will we do in anouther 100 years when it takes 8-10 years of training to be an effective mathmatician? or even fur…

are there any programs out there that draw vector fields for you?

a tree stands vertically on the bank of the river. from a point on the other bank directly opposite to the tree, the angle of elevation of the top of the tree is theta.from a point x meters behind this point on the same bank, the angle of elevation is 30.find the hight of the tree and width of the river. pls try solving:confused:

does anybody have the textbook vector calculus: linear algebra, and differential equations by hubbard and hubbard? if so, do you have any suggestions for the best way to work with it/ the rigor of it etc.

could somebody please tell me how to do this?? i am totally lost on this one. hgupta

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if one wanted to make a quick and easy demonstration that online poker cardrooms' shuffles are indeed random, i guess it would be pretty easy, right? just use a little probability to state how many times a given even should happen, then compare data to the theoretical outcome, right? the only part i'm iffy on, because its been so long since i've slept through a stats class is this: how much deviation from the theoretical outcome is considered acceptable error? for example, here's the little experiment that i did: while observing a texas hold'em game, i chose to observe how many times a flop (3 cards on the board) would contain no ace. in theory, the prob…

This is something my teacher did accidently whilst showing something else. [math]-i = -\sqrt{-1} = \sqrt{(-1)^{2} \times -1} = \sqrt{1\times -1} = \sqrt{-1} = i[/math] He said "that can't be right", rubbed it off the board and started again. Thing is, I can't see where the mistake was. Can you point it out?

What are the last two digits of a) 3^1994 b) 7^1994 c) 3^1994 + 7^1994 d) 7^1994 - 3^1994

I have made a 3D function plotter as a widget for Opera 9 users, you can find it here: http://widgets.opera.com/widget/4408 Please let me know what you think of it, I have never tested other 3d function plotters so am not sure what features are standard. Hopefully your feedback will help me improve it. Regards, Moosie

Tell me a number which when divided, multiplied, added & subtracted by a x number gives a same number, for example when 2 is divided with 2 it gives 1 & multiplied with 2 give 4 . Therefore the number is not matching.

This is not that easy problem but give it a try. Suppose triangle ABC is equilateral, and AF = BD = CE = 1/3*AB (D,E, and F are on BC,AC, and AB respectively). Compute the ratio of the area of the triangle ABC to that of the area of triangle made by drawing liens CF,AD, and BE.

Hi, A chap in the pub gave me a problem last night and I cannot solve it. As I really need to get some work done, can anyone throw some light on the matter ? A 6ft by 6ft box is placed against a wall, and a 20 ft ladder is placed such that it touches the wall, the ground and one corner of the box i.e (the ladder makes the hypothenuse). I need to calculate the opposite and the adjacent. Regards, Phil.

The function [math]f:x \to , x^2 - 10x + 29 , x \in \Re , x \ge k[/math] is one-one. Find the smallest possible positive value of [math]k[/math] and the range of [math]f[/math] in this case. My understanding of "one-one" is that there can only be one value of f(x) per value of x. So I'm thinking that maybe k=5 because that is the minumum point of the function. Although I was only just introduced to the concept of "one-one" verus "one-many" so I can't be sure. Am I on the right track? Thanks.

I'm amazed by how many people fail to accept repeated proofs of .999... = 1 utilizing multiple methodologies. Don't read the body of this blog, just read the comments: http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html There are some rather intelligent people making revprez-style bombasitc arguments towards the contrary. Why? What fundamental misunderstanding compels these people?

Hi, I'm unsuccessfully looking for the proof of some sums. I'm sure they are very well known, so I wonder if some mathematician could redirect me to useful resources on the web, or just give me a hint about where to start for solving them. The first is the famous binomial. If: PP(i) = p^i * (1-p)^(s-i) * s! / ( i! * (s-i)! ) with 0<p<1, i and s positive integers, then I know the proof for: Sum(PP(i), i, 0, s) = 1 But I can't work out the proof for: Sum(i * PP(i), i, 0, s) = s*p and for: Sum((i-s*p)^2 * PP(i), i, 0 , s) = p*(1-p)*s A related problem leads to the definition of: PR(i) = Product((n*p-j)*(s-j)/((n-j)*(j+1)), j, 0…

hi every1~! I was just curious that what is the point of studying only integar solutions of a problem. One reason that comes up to my mind is that some irrational numbers have infinite numbers after decimal, so therefore it would be a problem to write an exact solution. But are there any more reasons that prevent us playing with other numbers?

I have no experience of using MATLAB but I would like to learn it (part time) in 6 weeks, probaby to a respectable standard, for something I'm doing over the summer. I am keen to learn how to use it but is this a realistic aim in 6 weeks? I will have to teach myself. Can anyone advise/comment on this? Are there any books which are good and assume no previous knowledge? (I need to make a decision in the next day or so)

Where I work I have a patron who come in and picks my brain. Usually just politics, riddles or I.Q. Test type questions. Most I chew up and spit out rather quickly and haven't had a problem until now. I admitted to him I was no mathematician but he gave me this problem stating it was only a high school problem, but it took him 2 months to figure out. I took a look at it and it seemed fairly easy but I can't seem to find the right equation or series of to solve for the unknowns. It's been a month and I've been scanning over all my old texts for similiar questions but to no avail. Any help would be greatly appreciated, even just a general point in the right directio…

So, that's the question.