Mathematics

area of circle based on ray from equal pi * r^ 2 is 1 / 4 * pi * r ^ 2 , from 360 degrees divide by 4

Analytic approaches to twin data using structural equation models. Rijsdijk & Sham, 2002 http://bib.oxfordjournals.org/content/3/2/119.long It's good that I found an authentic source, but I'm very confused. The 1st confusion arises from Falconer's formula. Why are the equations set equal to the square of h, c, or e? For example: [math]h^{2} = 2(r_{MZ} - r_{DZ})[/math] I understand that the difference between the covariance of the mono- and di- zygotes equals the heritability estimate x0.5. What I don't get is why h is squared. This seems to recur later in the paper: "the heritability is given by a2 / (a2+c2+e2)." The 2nd and 3rd con…

Hello, I have a somewhat-working familiarity with set theory, and have recently been reading (naively) about category theory and type theory, each proposed as potential autonomous foundations for mathematics. To someone who has a better-than-vague understanding of the three, what is the discrepancy or motivation for one over the other? Why isn't first-order or higher order logic considered the "foundation"? When considering set theory as a foundation, can all discussion generally be deferred to ZFC; for category theory, can it be deferred to the category Set or topoi; for type theory, can it be to homotopy/univalent type theory? Thank you, Sato

Thank you Lord! "WE" have solved the pattern of pi, of 3.14.... Thank you everybody, I always assumed everyone was me, and I was everyone, and that we are all part of a WHOLE!!!! WE ARE!! here's the math pi = 3.14159265359... (11)(9)(7)(5)(3)(2)=(1=0)= (4)(6)(8)(10)(12) ------------------------------------------------------------------------------------------- (13)(11)(9)(7)(5)(3)=(0=1)=(4)(1)(5)(9)(2) by the way Human = Hu/man = Whole/Man = (Wo)man/man = Ovary/sperm = HUMAN

What is a prime number A number is greater than 1 is called a prime number, if it has only two factors, namely 1 and the number itself. Prime numbers up to 100 are:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 Procedure to find out the prime number Suppose A is given number. Step 1: Find a whole number nearly greater than the square root of A. K > square root(A) Step 2: Test whether A is divisible by any prime number less than K. If yes A is not a prime number. If not, A is prime number. Example: Find out whether 337 is a prime number or not? Step 1: 19 > square root (337) Prime num…

I am having difficulty with infinite series and sequences within calculus. I am not quite sure where the difficulty is stemming from. I understand the general idea but when it comes to knowing when to utilize the comparison test, divergence test, integral test, ect., I cannot seem to make things click. I am hoping for a user friendly explanation. If this is too vague, I am happy to clarify specifics.

I guess this is more of a math question. I not sure becuase like in school they always made us put the dollars first and add dot and two 00 at the end. I never seen USD put like this. If 17.4024 USD is 13.000 Euro does that mean its equal to 17dollars? or am I doing this totally wrong? I was wondering if it meant 17000.00 but than why would they not just put the 0s in front. I got this off a converting website and this is what it did. I am like super confused... The reason I would be suprised if its in fact 17$ is becuase its a school.

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I have a couple of questions about chaos theory. I'll start with one. In chaos theory, as time passes from t=0, does a system become more chaotic, thus more difficult to predict?

I was wondering if someone can explain this in simple terms Composite numbers congruent to +-1 mod 6. 25, 35, 49, 55, 65, 77, 85, 91, 95, 115, 119, 121, 125, 133, 143, 145, 155, 161, 169, 175, 185, 187, 203, 205, 209, 215, 217, 221, 235, 245, 247, 253, 259, 265, 275, 287. Doh,I get it now, after writing this down I was just trying to better understand these composite numbers(green) that came up on the prime line of this wave and why primes(yellow) other than 2/3 all fall on this line? Is it easier to work out these composite numbers than to work out primes? Is there a simple way to work these(composite numbers +-1mod 6) out. So in effect followi…

Alright prove the following: Let [math]f(x) = a(x)b(x)[/math], where b(x) is the inverse of a(x) and a(x) is a linear function. Now, let us redefine the definition of derivatives: [math]f'(x) =lim_{h\rightarrow 0} \frac{f(x+d_{i}h) - f(d_{e}x)}{h}[/math] Where [math]d_{i}[/math] is equal to the coefficient of x while [math]d_{e}[/math] is a constant of the linear function. Prove(or disprove) that for all [math]d_{e} > 1[/math], the limit from both sides will not exist.

Hello! Well my interest for math is growing alot and I want to know if there is some sort of math literature to sharpen my problem solving skills. So I just basically want to be good at solving math problems really. I know that you might think that solving math problems makes one become better at solving math problems and that is so true but I am looking for something beyond that. Perhaps a book with math problem solving techniques or just some hard as* questions with good explanations aswell. If something is still unclear or you just have a question mark in your head feel free to ask me. Regards!

Say there are two people with facebook accounts. Person A has 200 friends. Person B has 50 friends. It seems as though there is a higher probability that Person A has Person B as a friend than Person B has Person A as a friend. Of course, if person A is friends with person B then person B is friends with person A and vice versa. That would mean they would have the same probability of one having the other as a friend.

Along a road, there exists marks for every passed kilometer after every kilometer, at the start where the mark shows 0. A hiker who starts walking at the roads start devote himself to count the numbers on the marks. How many kilometers has the hiker walked/passed at the mark showing the number 2013? I have the solutions aswell but I don't understand the solution. You can see it below. If somebody could explain this I would be greatful. Regards!

So, after taking a lecture on the use of difference quotients for derivatives, I happened upon something interesting. The usual equation for the different quotient is the following(applied for derivative use): [math]\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}[/math] Now, I know that getting the derivative of the function 3x+1 and its inverse gets the following result from testing before: [math]f(x)=(3x+1)(\frac{x-1}{3})[/math] Of course, seeing this connection to a pattern I found in hailstone sequences I left it at that. However, I then began investigating the affects of the variable h on the result. Here is what I found. I thought this …

Convex pentagon MNPQR. $\angle{MNP}=\angle{MRQ}=90^o$ and $\angle{NMP}=\angle{RMQ}$. $NQ\cap PR={A}$. Prove that $MA\perp NR$.

Hey Everyone, What does it mean if the processing time of a certain job instance is generated according to an exponential distribution with a certain mean? I already know the mean so what does it add to know its distribution and how can I use it? Regards,

As it is known, with a constant such as phi, lim n->infty F_n/F_n-1 = phi, the function can approach but never reach the irrational constant. This can be observed with the following: Phi = lim n->infty F_n/F_n-1 = (1+sqrt(5))/2 Lim n->infty 2F_n = Lim n->infty F_n-1(1+sqrt(5)) Turn this into a function displaying the approach to the constant. A(n)=2F_n-F_n-1(1+sqrt(5)) Of course, the expected result is to see the function decrease towards 0, but the question I am asking is if this approach towards an irrational constant will always be exponential in nature? If so, is there a way to determine the equation of this decrease without the brute forc…

There's a free online course running ATM by Stanford University http://online.stanford.edu/course/how-to-learn-math-for-students-s14 It teaches how to learn maths, and it's brilliant, so anyone who's learning maths at ANY level, give this a whirl. It doesn't take long, you have until December 14th to complete it, and if you do complete it, you are sent a certificate of excellence from the uni, which looks good on a CV or applying to uni etc. There's no obligations to complete it, it's free, simple and extremely useful. I recommend it strongly to anyone studying maths.

Hey Everyone, I'm modeling a sensor node power consumed and lifetime using markov chain for two cases. Case 1: Assume that the node senses, processes and transmits the data. Energy and time spent in each state are considered random variables. I have no problems and I did my calculations for this case. It is similar to: http://thiagot.com/papers/jung_tosn09.pdf. Case 2: It is the simplest form and I need it for comparison reasons only. It assumes that only the sensor and the radio are awake and that the node sends whatever it senses. Does Markov Chain still hold to this case? Thanks a lot in advance,

Question: How could the ancient Egyptians have invented/mastered geometry, independently from a teacher source? I can see how mathematics can sprout out of necessity for mankind in general.

Hi everyone, First, let me say I can actually solve this problem without trouble using the prescribed method. I just don't like it, think it's kind of clunky and have been wondering about another way to go at it. Something more intuitive to me. As you can see from the pic, the problem to solve is pretty straightforward. What I was wondering is what would happen if the boat were to *not* compensate for the river current at all? Where would it end up? The triangle I drew up in the corner kind of illustrates what I think would happen. 15 represents the speed of the boat along the Y axis, and 4 is the perpindicular force acting upon it by the river current. Calculating the a…

Hey guys, so a few days ago I registered for the CLEP Exam to exempt myself from taking the course. If I pass, I can go straight to Calculus I my first semester in college as a freshman. Unfortunately I have not taken Precalc in high school, but I did take Trig for a full year and AP Physics for half a year (I honestly became bored with Physics due to my teacher so I had to switch out). I have one more week until the test (next Wednesday), and I have a general list of things I need to study. If anyone has taken the CLEP exam or has any tips/hints/insight/etc that they could offer me I would greatly appreciate it!

I'm trying to understand common core, however it seems who ever is making up these equations is using arbitrary numbers to make their point. I could understand if the numbers were derived from the question, but that's not the case. Example: _______________________________________________________________ What does 26 + 17 =? 1.) First think: 4 + 13 = 17 ( why not use 16 + 1 or 12 + 5...why 14 + 3) 2.) Add 26 + 4 = 30 3.) Add 13 + 30 = 43 ________________________________________________________________ ~ee

Esteemed Mathematicians , I have tried to emulate a step further and put a model in place to find the mathematical model of Sudoku..this method simplifies all the techniques used in conventional solving method and break up the number into possible row, possible coloums and box numbers, http://www.scribd.com/doc/39235249/How-to-Solve-Sudoku-Mathematically details of the model can be found in above link, i am looking for expert views and further investigation by mighty minds... Some food for Mathematicians Soul....