Recent content by DarthPickley

uh, I think when it says "he decided to move his fingers... felt something on his shoulders... turned around to see who had done this" (paraphrasing) that there was some sort of portal / wormhole in front of him, like the part in front is glued to the part behind him.

Well, I created this thread (under Geometry/Topology) about the Law of Sines, specifically for the three kinds of geometries. http://en.wikipedia.org/wiki/Law_of_sines http://mathworld.wolfram.com/LawofSines.html The Law of Sines states that, for a triangle ABC with angles A, B, C, and...

here is an analagous situation: take the function given by the limit as a --> 0+ of the function f(x) = a*sin(x/a). Clearly, this converges to the function F(x) = 0. However, suppose that this is like physics, so you are going to talk about the energy of the wave (no quantum stuff here though...

Well, one thing I've been curious about is what would happen if a student who is learning about conic sections in precalculus just happened to ask what the circumference of an ellipse was. Now, I myself have too much of a history of asking questions that are revealing of my knowledge of higher...

well last summer before going into high school I just taught myself calculus and stuff, this year during school I'm not teaching myself the sort of stuff that I'm being taught, I'm teaching myself geometry stuff (my geometry class in middle school was boring... triangles are boring... I'd...

strange. it seems that it would be simple to have a set of all functions where a function is a collection of ordered pairs of an element of the domain and of the co-domain, so, given a set of which the domain and co-domain are subsets of, it should be simple to, for each element of the domain...

when I look into other people's eyes while they are talking to me, I become 'entranced' and highly distracted and cannot pay any attention to what the person is saying. Additionally, sometimes it causes me to spontaneously have a spasm or something, like I'll pass by a mirror and see my...

do you mean the one supplied by Euclid in his Elements book? that one... its so impossible to understand without staring at it for a long time! Its kind of confusing. I don't really like it, mainly because it is one of the least intuitive proofs possible for a pretty simple theorem. on...

I thought I had probably made a mistake. but anyways I just learned about Feynman's lost lecture so I have another way of understanding the Kepler stuff, but anyways, I think that here, for my derivations, I will redo things: having a vector v such that |v| = r, and then you have v + dv, with...

you have to prove that ( a*b + 1 ) is not divisible by a or b, and the same for like (a*b*c*d*e*f*g + 1) is not divisible by a,b,c,d,e,f,g. (and of course they are not equal to one) this is done really easily if you say that a*(...) ≡ 0 (mod a), then a*(...) + 1 ≡ 0+1 ≡ 1 (mod a). so if it is...

Well, that one you mention isn't really a proof at all, it just sort of shows that it works for the case of a triangle with side lengths of 3, 4, and 5.

I think it also means you can't have an integral or summation symbol of any sort, you have to have simple functions and algebraic operations and numbers. also, what would be a closed form of the roots of x^5 - x + 1 = 0 ? you can't get it by infinite process unless you define a recursive...

for some reason it reminds me of the definition of matrix multiplication...

make a square. make another square inscribed in it, with its vertices on the edges of the square. label edge lengths that are congruent. now, look for shapes and areas and triangles and stuff. . ._b_____a__ . | . ./ .\ . . . | a| ./c. . c \ . | b . |/ . . . . . . \| . |\ . c. . c. /| b| ...

There are about 4 pages of this stuff in my english notebook... (my physics notebook was full) This is what I got: θ' = (xy' - yx')/r r' = (xx' + yy')/r of course its possible that I made a mistake. most of my work from then on dealt with trying to derive formulas for θ'' and r''...