Mathematics

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?

How did mathematicians come up with Area of circle = ( pi * r^2 ) ? Why did they choose r^2 as one of the products? Was pi found by brute forcing numbers until it worked?

In a chemistry book I saw the following calculation with regard to entropy:- S = 1.38 x 10^-23J/K x ln2^10^22 (or if it helps 2superscript10superscript22 or 2 raised to 10 to the power of 22) The answer is apparently 0.096 J/K So how would you calculate ln2^10^22 using a calculator? Thanks G56

I thought it might be fun to show you some elementary aspects of superanalysis and in particular how we might generalise two well known differential equations on the line to superlines. First what is a superline, [math]\mathbb{R}^{1|m}[/math]? We will define the superline as the space with local coordinates [math]\{t, \theta^{\alpha}\}[/math] where [math]\alpha[/math] runs from [math]0[/math] to [math]m[/math] and [math]\theta^{\alpha}\theta^{\beta} = - \theta^{\beta} \theta^{\alpha}[/math]. In particular, [math]\theta^{\alpha}\theta^{\alpha}=0[/math]. As we will be doing some elementary analysis, we won't worry about coordinate transformations or anything like that. …

I wanted to share with you some useful results concerning differential forms on a manifold. For those that know, the coordinate free definitions of differential forms and their derivations (de Rham, interior product and Lie derivative) are I feel quite complicated. I have very little feeling for them. If we turn to a "super" description in terms of local coordinates then the definitions are much more workable. What I am about to say is not new. Definition(ish) A supermanifold is a "manifold" with both even and odd coordinates. Locally, we mean that a supermanifold can be endowed with coordinates [math]z^{A}=\{x^{a}, \theta^{\alpha}\}[/math] such that [math]x^…

There is this problem from my textbook but I can't seem to figure it out. A rectangular swimming pool is to be built with the area of the pool being 2500 square feet. In addition, the owner wants 6 foot wide decks along the sides of the pool and 8 foot wide decks at the two ends. Determine the dimensions (to the nearest tenth of a foot) of the pool that allows the pool and decks to be built on the smallest possible piece of property. Thank you

I'm taking part in a course with the Open University and I have been given an assignment, which includes a question asking me to calculate the speed of someone diving off a diving board. The distance given is 4.6m and the acceleration due to gravity is 9.8 m s-2. I'm totally lost and have no idea where to start in trying to calculate this. The context of the question is in relation to solving equations by changing an equation round. If anyone can shine some light on this for me I would be forever grateful.

[ATTACH]1664[/ATTACH] As a practising geometist I was intrigued by the attached diagram which I drew a long while ago. I endevoured to draw eight circles around a larger circle so that all the circumferences touched. By rough measurement it appeared that the ratio of the diameters of the smaller circles to the diameter of the larger centre circle was very close to the Golden Section. A good friend and mathematician advised me that it was close but no coconuts were to be won. Well I have since wondered about the fact that it was so close. I have expanded my wondering to go 3 dimensional and to consider spheres instead of circles. So the question is gentlemen wou…

Just how small is a nanometer? Liked this guys analogy with the aircraft carrier... anyone got a better one?

Discrete Mathematics or Number Theory? I have never done discrete mathematics before but I'm interested in it. Number theory sounds fun, too.

I have over a 100 pages of attempts to find a pattern in Prime numbers. However you only have to read one of them. Go to the Homepage at www.constructorscorner.com and under the date of the updates click the link of the new work. A lot of work still needs done, but I believe I have found a way to find “x” on the Parabola. I am looking for feedback on my work. Let me know what you think. Can it work?

there are 40 balls in a bag, each numbered idividualy 1 through to 40. what are the odds of picking say 1,2,3, and 4? I know it`s 1 in 10 of picking at least ONE ball correctly, I`m stuck what happens after that though any help?

Simplify applyin' properties: [math](p\implies q)\implies[p\implies(\sim q\wedge p)].[/math]

Hi. Would polar coordinates be preferred for calculations on a heliostat mirror aiming? Get about a metre long piece of string, anchor one end to anything, call that T 'target' and also anchor about the middle of the string to anything else, higher or lower, being that point M -mirror- Grabbing the end of the string point S -sun- , a solar ray path can be visualized by moving the string along a plane. Now, what are convenient reference axis to use for calculating the azimuth and elevation the mirror M should aim so S always illuminates T ? Or, any other suggestions on how is it done ?

I never studied the curve algorithms; I just use 'em. So I really have no idea how to answer this question. Once again working in SVG. When using the cubic Bézier curve commands, I want to find out the coordinates of the actual peaks. For instance, c 3.75,20.0 5.00,-20.00 8.75,0.00 approximates (!) a one-cycle sine curve. I want to be able to figure out the curve's minimum and maximum (y-axis) values. How can I do this? Thanks!

...are computer using the Newton-Raphson method to evaluate square roots ?

Hey guys, I came accross this proof while I was studying this material but I am have a hard time with it. Does anybody know how to go about showing those too equivalencies?? Prove that log(n!) = Theta(n log n) by proving the following two claims: • log(n!) = O(n log n). • log(n!) = *omega(n log n). Thanks!!

Anybody here know how to compute pi factorial? Pi isn't an integer, or a rational number, so I'm at a loss at how to do it....