Linear Algebra and Group Theory

Not sure what forum this goes under, so someone will have to move it to the right area. Could someone explain to me fibonacci numbers? I tried google, but all I came up with was a bunch of sites that show how cauliflower has rows that spiral outwars, and so do pine cones My calculus teacher mentioned something about the ratio between your forehead and your bellybutton, and belly button to your toes is always the same for every person. Fibonacci was in the same sentence, but I didn't catch what he was trying to say about them (distracted w/ the fine specimen of female beside me). From what I can gather they are numbers that commonly occur throughout nature??

I Love Math! My daughter, age 9, has a book of Mensa puzzles for kids. She hit me with this one: A guy recycles candle stubs and can make 1 new candle out of 7 stubs. How many candles can he make out of 679 stubs? The solution is simple: Stubs, Candles Made, Leftover Stubs 679, 97, 0 97, 13, 6 19, 2, 5 7, 1, 0 Answer: 113 So, I’m teaching myself calculus and I know that I can find a general solution for this problem. Well…not quite. I know that the answer is a series: f(x) = { (x/(7^1)) + (x/(7^2)) + (x/(7^3)) + ... + (x/(7^n)) } Testing the series with some actual values I get: x, f(x) 679, 113.120 15,139, 2,552.103 3,020,302, 503,…

I just want to let everyone know that I have won the USAA National Mathematics Award! I have never heard of the USAA before the other day, but believe me, I was honored. I think this is my first award ever!

It seems as though everyone has different ways of doing simple calculations in their head, like adding multiplying, dividing. I was just wondering if any of you guys have a good method of doing this, I have been trying to decide which is the most efficient; maybe you guys can help me out. When I come across simple addition, lets say 37 + 17 I first break down the two numbers into multiples of 5, so I would figure 35+15 real quick then take the remaining numbers and add them, then add the two sums together so for me it's like 50+4=54 I can do this pretty fast but sometimes people can calculate things much faster. I also have a method for subtracting, that I will…

I need some help with some relatively easy number theory problems, I'm just not sure how to go about them...

When someone says "A is inversely proportional to B, it means A=k/B", where k is some proportionality constant. Or 2 inverse is 1/2, or 0.5, or 2^-1 = 1/2. Why is that sin inverse, although written as sin^-1 is not 1/sin? Likewise for cosine and tangent.

I have been reading about the public key cipher where the encrption is squaring your message mod n where n=pq (primes = 3 mod 4). The decryption scheme here relies on finding roots mod p,q - namely on the theorem that states: x^(p+1)/4 is a square root of either x or negative x mod p, if p is prime=3 mod 4. It was not mentioned in my text why the -x case is not relevant. Since the number that needs to be rooted is known to be a rsult of squaring, it is implied that the way they know the -x will not happen is that there is some theorem that states the following: let p be prime and p=3 mod 4, then there is no x such that x^2= -1 mod p. My question is: is there indeed …

I dont understand this at all, i dont seem to get the logic in this, ive seen my helpful little rules to memorize but i dont seem to recognize it when i face a factoring problem, is there any tricks or some logical concept on this topic?

Eh, I saw this problem on a quiz today and couldnt' remember for the life of me how to do it. I'm sure its something simple, but I'm way too lazy to get my notes out of my car Inverse Cosecant (2) = csc-1(2) =

Could someone explain string theory to me? I've heard of it, but never read up on it. I just got a book called "The Elegant Universe". Havn't started reading yet. I just want a general idea before I start reading.