Mathematics

Hey all, first, apologies for the non-descriptive title, but I really couldn't come up with anything better. That said, I'll get straight to the point; we have the following numbers: [math]N_{1}=1[/math] [math]N_{2}=3[/math] [math]N_{3}=6[/math] [math]N_{4}=10[/math] [math]N_{5}=15[/math] [math]N_{6}=21[/math] [math]...[/math] [math]N_{n}=N_{n-1}+n[/math] Let me just give those numbers a name, for the sake of simplicity I'll call them Strange numbers (note, I wouldn't be surprised at all if this was a long discovered and frequently used series, such as the Fibonacci Numbers...so if it is, please correct me, since I am not aware of i…

Again, in Stephen Hawking's "A Brief History of Time" he states that he created a mathematical theorem that incorperated "imaginary" numbers to descible the possible expansion of the universe. The differance between "real" and "imaginary" numbers is that when one squares a real number, the result will always be positive(2*2 = 4 and -2*-2 = 4) but with imaginary numbers; the square is always negative. Hawking uses a variable to explain this(eg. "i") (i*i = -1 and 2i * 2i = -4 and so on). Please will someone explain the mathematics behind this.

Hi, I am looking to take a logarithmic spiral defined by [math]\varphi[/math] and calculate it's volume as a "cone". See: http://en.wikipedia.org/wiki/Golden_spiral I know it's effectively a fractal so it tends to [math]\infty[/math], but within a reasonable level of accuracy I should be able to calculate its' volume, but its' flat side I think always throws my calculations from the value I'm expecting by a small value.

I know this is a physics question but the answer is mathematical. In Stephen Hawking's "A Brief History of Time" he says that there is an equation that explains how a particle will not look the same if one rotates it 360 degrees but it will look the same if it is rotated 720 degrees. Can anyone explain this equation?

At work my friends sometimes gamble on this harness race web game. The game is simple - the odds are posted and the horses run (but the favourites seldom win). The game is single player so we use the odds to determine the payouts and play 'to win' bets - each of us picks a horse. Some must bet more than others depending on how their horse is listed. A long shot is a low bet that could win everything... get it? One of my buddies is now winning all the time. Esp after we play a few times - he has a system and at first it was a joke but now we are all curious as to how he has managed to figure out this simple racing game. Some kind of a probability equatio…

So I have finally decided to go back to school. Its been nearly 5 years since I was last in a formal educational setting. I dropped out of high school, but have made the choice to attend a county college and hopefully transfer to a 4 year school (Rutgers University). Major will be Computer Science. I've decided a little catch up work is in order as I never payed attention in school. As far as math goes, I'm starting at the basics. Just finished a basic arithmetic book. Adding, subtracting, multiplication, division, decimals, fractions, etc etc. Now, I know this is very basic, and thats what I was going for.... My question is, where do I go from here? If i remember, pre-al…

By chance, is anyone here familiar with the paper entitled "Efficient rounding of approximate designs"? By Pukelsheim and Rieder, it was published in Biometrika, 1992 (79, 4, pp. 763-70). I would like to discuss it with someone who understands it in order to determine whether or not my take on it is correct. It is a rather obscure subject; the paper's summary is as follows: "Discretization methods to round an approximate design into an exact design for a given sample size n are discussed. There is a unique method, called efficient rounding, which has the smallest loss of efficiency under a wide family of optimality criteria. The efficient rounding method is a multip…

I am looking to get a program that does something similar to the Latex except for typing papers and lab reports. I have read of a program called Abacus and was wondering if anyone used it and if so how did it work. Or does anyone use a similar program.

I spend a great deal of time wondering about the Universe and have in the last year or so become particularly interested in Physics and Astronomy (especially general relativety). I have a problem though. I don't understand math. This limits me very much in my study of Physics. I've looked at plenty of "maths made easy" type texts but all it takes is for one thing to become clear and i'm pretty much lost. They generally do not have a clear application to real life either. Anyone familiar with General relativity knows that it is based on the idea that time is relative to the individual. If I assume this is correct, then relativety makes perfect sense to me. Of c…

The two dimensional regular polygon series, triangle, square, pentagon, hexagon etc. is infinite. An observer of the entire series will not be able to observe individual members. As a result, the series must appear continuous. Suppose that the regular polygon series was finite rather than infinite. In this case an observer would always see the series as discontinuous. How would this affect our universe? Would one dimensional parameters like length and breadth become discontinuous?

Hey everybody! Hopefully someone has tried this without a computer sometime in the last 20 years or so. I want to draw a graph of cartesian equations, without using software. How does one go about doing this? Example: [math]x^4=x^2y-y^3[/math] I know what it should look like, as I can cheat and graph it online, but assuming my computer explodes tonight, how can I visualize something like this? Do I just plug in x = 0 and solve for y, etc...? Or is there some kind of easier path I should follow? Thanks in advance! Chris

How do you calculate pi using Base 16? According to Wikipedia it's 3.243F6A8885A308D31319… but how did they arrive at that number?

Does anyone know why a negative times a negative equals a positive? I have never been able to understand the reasoning behind that.

Hello all, i had a question to you all i am intressted in math but as i have never as i was growing up the intressed in learing it atleast not so much.. now that i am learning math. beacuse, i have an intressed for it now, so i was woundering could anyone answer this question, When i am studdying math i am constantly feeling my body wanna do something else, and also the lack of concentration and i don't have the will for it i don't get why i wanna learn and so on but my body and you can say my soul rejects it why ?.. is there some way i can focus better or etc... please all help would be great! sorry for my incorrect spelling i am in a hurry i will correct …

Ok here is the deal i need to solve this in gauss-jordan method: OK here it goes: 3x-y-z=4 x+2y+z=3 -2x+y+2z=1 Ok thank you very much. I need this fast.

...Should be known by someone who does not use math in daily life? I am relearning everything I have forgotten since I graduated from high school. In college I have only taken 4 math classes and out of all the classes I have taken, that is only a very small percentage. If anyone could give me a general ball park idea of where I should be, I would be very appreciative.

In PHYSICS, speed is a scalar, or 0-vector, measure of motion. Standing in the middle of a street, you see a car racing at (the speed of) 50 mph. But it makes a difference as to whether it is coming toward you or going away: DIRECTION was missing in that "50 mph" statment. Adjoining DIRECTION to SPEED creates a (1-)vector measure of motion</I>. I argue we've a similar problem in relating LOGIC to everyday speech. "It was raining at the Washington Monument, 4/12/08" is A POSITIVE SIMPLE DECLARATIVE SENTENCE CAPABLE OF VERIFICATION -- qualifying it as a STATEMENT (a.k.a. proposition) in STATEMENT LOGIC (a.k.a. 0-ORDER PREDICATE LOGIC). But "Was it rai…

Two neglected math concepts: EXTENSION, INTENSION. Easily explicated in set language. Say, in natural number system, N, numbers less than seven. An extension is {0,1,2,3,4,5,6}. An intension is {x: x in N, x < 7}, "set of any x such that x is in N and less than 7". Seems ok. But Problem: extension is univalent: one referent; intension may be multivalent: descriptive statement may fit many referents. Axioms are intensional. The familiar Peano Axioms invoke the standard integer system. But online is a nonstandard version fitting Peano Axioms such that its every integer is greater than any standard integer. (A "stolen identity" case?) Banach-Tarsky Paradox says Euclide…

I often read in books of the radius of a circle being expressed in units of degrees. What does this mean? I'm used to writing and measuring the radii of circles in units of length but not angular units. For example what does a circle of radius 22deg mean and how would you determine the radius of a circle in degrees? Thanks G56

I've been trying to find the exact definition of a CQF in many places, but I have not been able to actually find it. Does anyone know the exact definition of a conjugate quadrature filter? =Uncool-

Hello ! May be somebody send me his/her opinion about my work at : http://biologygeometry.blogspot.com BYE

Hi everyone. Im hoping someone can tell me speed, in MPH, of airflow from an extractor fan please. The extractor is 8inches (200mm) diameter. Figures says its 1600m3/hr. Any help greatly appreciated.

I notice there are a few subthread which take a reader through basic elementary subjects. Is it possible i can create a basic guide to algebra?