Mathematics

Let me first (loosely) define both synthetic and analytic geometry. Synthetic geometry- deductive system based on postulates. The geometric objects are endowed with geometric properties from the axioms. This is includes the "high school" geometry of drawing lines and measuring angles etc. and from there making deductive statements. A geometry can be defined as a set plus a symmetric, reflexive relation. (Does it really need to be a set?) Analytic geometry-represent geometric objects using local coordinates. This makes much use of algebra (and in the differential case, calculus). I will also include algebraic geometry here (so sheaves, affine varieties etc …

Why 2 multiply 2 is equal 4?proof?

http://www.dimensions-math.org/Dim_regarder_E.htm I recently found this amazing recource. The whole of the first series is on one subject but I like that in that it starts simply and dosn't move to quickly. It builds up to verry complex stuff.

There was some discussion as to whether maths could be considered art. I was sent home from work today, due to a rather nasty infection, so I decided to plot some simple functions through mathcad, that shows you can manipulate an equation to obtain a desired shape. For anyone who uses mathcad, I've supplied the functions at the top of the pics. Not particularly special, but I hope it illustrates you can be creative with maths if you wish...I've added pretentious names, to make the images more arty Hmm, having problems uploading pics... Right...Dark Knight, and Valley of the Icey Math People. Note the functions are very simple, but plotted on a surface.

I've tried distributing etc but cannot get the correct answer of 60.1N My book doesn't give the steps. Tsin37 + (1.33T)(sin53) - 100N =0 I never know what to do with the (1.33T)(sin53) Any assistance would really be appreciated.

Correct me if I'm wrong, but is the difference between Euclidean geometry and non-Euclidean is that the latter includes the former but simply added the idea of doing measurements along the curved surfaces of multi-dimensional spheres and objects?

Hey guys. I'm really interested in learning discrete mathematics and logic. What math should I already know before buying a discrete math textbook?

Hey there all, this might be a pretty stupid question, but is there a method that allows one to extract the function from a graph? I know that one graph can represent many different functions, but if I didn't care which one, as long as that function would produce the same graph when plotted. Also, I don't mean functions that look like [math]f(x)=\begin{cases} \mbox{something} & \mbox{if } \mbox{something} \\ \mbox{something else} & \mbox{if } \mbox{something else} \\ \mbox{still something else} & \mbox{if } \mbox{still something else} \\ \mbox{\vdots}&\mbox{\vdots} \end{cases} [/math] ..and have a separate condition for every point. I know th…

Apparently mg + mv^2/r = mg(1 + v^2/rg) but does anyone know what is the name of the process?

Hey all, well, the title speaks for itself. Given a cube, what is the angle between the diagonals of two neighboring squares? Here's an illustration, just in case: It looks a little strange since it's a 2D picture, but I think you get the picture. Literally. My gut tells me it's either 45° or 60°, but...well, that's just my gut. the title almost speaks for itself. Given a cuboid, where [math]a \neq b \neq c[/math], how can I calculate the angle between the diagonals of two neighboring rectangles? Cheers, Gabe

Is it possible to create a logarithmic algorithm of prime numbers and a sequence of factors to produce a table in Exel.

Google docs gives the option to draw an orginisation diagram, it shows hyrachy in an orginisation. me parent son1 me son2 me son3 me Drawing this gives you a box at the top entitled parent with a line going down to me and then branching out to 3 sons. Moving on to another expample. 2n n 0 0 2 1 4 2 6 3 The values in the top row are lables, the second column is increased by 1 each row. The first column is double the second column. If we continue this chart up to n=40 and draw it according to the rules this is the result. http://img253.imageshack.us/img253/7651/image1kq7.png This allows you to see th…

Is it possible for something to have a negative number of dimensions? Or is that just meaningless? How about imaginary dimensions? The reason I ask is that there seems to be something missing in the table of simplex elements to make a complete Pascal's triangle.

Hey all, as some may know, I've been attempting to learn calculus lately, and despite the fact I though I had already mastered the part of the tutorial I was reading, I did encounter a slight problem for which I cannot find a logical explanation. Let us have a [math]f(t)=2t + 1, t\in N[/math]. Its graph would then be a line going starting at [math]A=[0, 1][/math] and going through [math]B=[1, 3][/math]. If we subtract two from the output, we will get [math]f(t)-2=2t-1[/math]. The graph will be a line starting at [math]A=[0, -1][/math] and continue on through [math]B=[\frac{1}{2},0][/math]. In other words, the graph will be moved down by two. It's minus, so it's do…

Can anybody help i have been reading up on goedels incompleteness theorem, and still am not able to grasp its true meaning and implication. Is there somewhere , where i can try and understand it , in its simplest form with a simple example or application. regards

Hey all,

Hey all, another post just reminded me about this, and I've been wanting to post it for quite some time. However, math syntax and me don't go together, so excuse the errors. Let us have a function (I'm using different brackets so they don't get confused with part of the interval) [math]N[x][/math], where [math]x[/math] represents an interval, and [math]N[x] =[/math] the number of real numbers in the interval [math]x[/math]. I know it will always be infinity, but bear with me. Let [math]a_n= N[ <n; n+1) ] \Rightarrow N[ R^{+}_{0} ]=\sum_{n=0}^{\infty}a_n[/math]. [math]\forall x \in R: x \in <1 ; \infty)[/math] [math] \Rightarrow 1/x \in (0 ; 1…

-------------------------------------------------------------------------------- I know how to differentiate F=Ma, so since integration is the inverse process to differentiation, how would one perform integration on the equation F=Ma? Thanks in advance Does no one know?

Hey all, Where am I making a mistake? [math]-i=(-1)\sqrt{-1}=\sqrt{(-1)(-1)(-1)}=\sqrt{-1}=i[/math] Cheers, Gabe

If it takes 1 calorie to raise the temperature of water by 1 degree Celcius, will it take 100 calories to bring the same amount of ice to a boil?

Are there certian postulated math axioms, that cannot be proven. Do these axioms ( if they exist) , constitute the basis of all mathematics. If so where can i get more info?

This is a question about the nature of Mathematics as a language. The question is very simple, as the thread name suggests, but I’ll expand my own perception of it here and so it would be helpful if someone can leave a few comments. Is mathematics relative or absolute? My insight developed as follows…; If Mathematics as language was invented by us it was definitely invented based on the observations of the physical space and laws on our planet. To simplify; we can find one thing in common between 2 yellow stones on one location and then 2 blue stones on another – the fact that there are 2 stones in each group. So number 2 is the commonality. If we add these 2 groups …

the maximum kinetic energy of a photoelectron, Ek,max , to the smallest amount of energy, E0, needed to free an electron from the metal, and the energy, Eph , of the incident photons of light: Ek,max = Eph – E0 In addition, you know that Eph = hf where h is the Planck constant and f is the frequency of the incident light. Which one of the following graphs represents the relationship between Ek,max and f ? please help answer due tomorrow. Carl1.

What is i to the power of infinity? As near as I can figure either the answer is the matrix [-1, 1, i , -i], or 0.

Does anyone know a good book, review article etc. on differential graded Lie algebras? I need to know some basic results/theorems from dg Lie algebras as I have what I think is a generalisation. Thanks.