Mathematics

Hello everyone In a dissertation for maths, I've mentioned once "quadratrix"... Can't really explain what it is, but I think I know what it is, and I've discovered what seems to be a pretty beautiful property of the quadratrix of a circle (commonly known as the quadratrix of Dinostratus) So I thought: what if I 'completed' the quadratrix? (i.e. completing the circle and the quadratrix, resulting in a horizontal flip of the quadratrix over x=0, a vertical one over y=0, and a horizontal one of the vertically flipped one over x=0) The result: an eye-shaped geometrical figure. If you're eager to see this 'completed' quadratrix, you can ask me and I will try to up…

hello everyone Let me get straight to the point: [math]p[/math] is prime, [math]a\in\mathbb{N}[/math], [math]p\nmid a[/math]; [math]A=\{a,2a,3a,\cdots ,(p-1)a\}[/math] Let [math]ra\equiv sa\pmod{p}[/math] Then: [math]ra=mp+R[/math] and [math]sa=np+R[/math] [math](r-s)a=(m-n)p[/math] So [math]p\mid (r-s)[/math] So [math]r\equiv s\pmod{p}[/math] The elements of [math]A[/math] must thus all be different and congruent with the elements of the set [math]B=\{1,2,3,\cdots ,(p-1)\}[/math]. The sequence is not important. I found these steps of the proof (which continues after this) on the internet, and I don't really get the statement I put …

Hello out there, I am a long time lurker of this site, but this is my fist post. When I was in primary school, I never particularly cared for mathematics. I used to think it was boring and was not given any context for the work I was doing. Years later, in college, I would read the work of Rene Descartes and it really revolutionized how I thought about mathematics, geometry, and the world around me. I might be a bit of an eccentric, but I spend a lot of my free time studying maths and get a lot of enjoyment out of it. This enterprise wound up leading me into finding this website and spending a lot of time on it. I started studying from the ground up on all the stuff …

So whats the relationship between an angle and its sine? I typed out all the degrees between 0 and 89 into a spread sheet and wrote out the answer then made a graph. Using the mighty powers of excel I got equations for the graph. I had the option of choosing how many polynomials I wanted in my function. here is the one to the order of two: y = -0.0001x2 + 0.0208x - 0.0227 Here is the one to the order of six: y = 2E-13x6 - 4E-11x5 + 6E-09x4 - 1E-06x3 + 5E-06x2 + 0.0174x + 1E-05 each one of these will allow me to put in lets say 10 degrees and get an answer of 0.1753 or 0.17357 or 58 degrees and get an answer 0.88018 or 0.8473 These are app…

What would you say is the validity of statistics? Also, if you're going to support your argument with definitions please don't, as I think you must ask yourself why you have so much confidence in the definitions in the 1st place I believe the uncertainty just encourages people to not search for the *real* relationship or variables / constants, and it also encourages pointless studies that emphasizes on correlation when the true relationship (if existent at all) is *not* proven. This also goes for probability, however, I heard that probability is quite applicable in quantum physics.

Hello everyone I have a rather odd question for you this evening. Yesterday I posted a topic on the quadratrix (you should read it if you'd like to know more about it) and now I'd like to know if there's something special about the number 6.37, or a number that's really close to it, because, that's the place that the quadratrix of a circle with radius 10 intersects the x-axis... I've tried using square root of pi, pi squared, square root of 10, and much more... I've even used the constant e... But I can't to find an expression, using methematical constants and 10, which results in about 6.37... The closest point I find is 2*pi... Could someone help me…

what is the difference between euclidean and non euclidean geometry-thankyou

I have been busy putting together a guide to the new HP Prime graphing calculator: url deleted Hope you enjoy, Like and subscribe please, Regards MC

Well, this is probably thought of already, but might as well give people the concept. This work is a small fraction of Collatz Theory So, basically, the idea is that it is an "equation" that lies on multiple dimensions(two dimensional). It is an evolving equation matrix, meaning on an infinite scale it involves infinitely. Here is the notation of a Collatz Matrix equation: [math]C(x)_{k\times d}\begin{Bmatrix}a_{f}&b_{f}\\u_{f}&v_{f}\end{Bmatrix},s(k_p,d_p) = A_{k\times d}[/math] In this case, the four variables that end with the subscript f are the formulas used in the equation to calculate the matrix. In each case, if the number were to be moved up the m…

Hi folks, Here's an armchair question... A significant figure (sigfig) is the number of figures (a.k.a. digits) to which a number is meaningful, even if the numbers are zero. For example, 10.000 has 5 sigfigs if indeed one has that much precision. But how about in the instance of degrees of a compass, when measuring it as a full 360 degrees... if the current measure is 5 degrees, how many sigfigs does this have? I would think it effectively has three. Or maybe it's simply a question of semantics. Your thoughts? Mike P.S. My first post here! ScienceForum.net looks like a nice active place.

This is not to say that there were will be times when this happens, but what if it does happen? Would it show Mathematics to have flawed axioms? Or would it simply reveal loop holes within assumed axioms of mathematics? What other consequences would occur?

Let's take a look at the following picture: Of course, a^2+b^2 = c^2 has infinite primitive(I think) Pythogorean triples where a,b, and c are whole numbers, proven by Euclid. However, are there infinite primitive Pythagorean triples where one of the elements, when square rooted, is also a whole number? I am asking this because, for example, let us take the primitive Pythagorean triple (3,4, 5). Notice how the square root of 4 is 2, obviously. Let us apply this to a geometric visual. This means that it takes a real whole number sided square to get two squares that have irrational sides. In interesting phenomena, I say.

Is the summation below true? [latex] \sum_{a}a * Pr[R=a] \leq \sum_{a\leq b}b * Pr[R=a]. [/latex] Where R is a random variable and Pr[R=a] means that the probability that the random variable is equal to some number 'a'. You can ignore that part and replace Pr[R=a] with x: [latex] \sum_{a}a * x \leq \sum_{a\leq b}b * x. [/latex] The first summation provides all 'a' values, so the summation is over larger amount of terms. The right hand side sums only those a<=b, so the right hand sums over less amount of terms. But at the same time the right hand is multiplied by b>=a. So it is not clear which one is bigger. I am not extremely familiar with Riemann sum, so …

Hello, This is a question for the professional mathematicians on this board. I want to become a mathematician. My background is in law. I would most likely be able to begin studies in the spring semester of next year. I am 25 years old. From your perspective, am I coming to mathematics too late in life? Do you have any advice to someone wanting to make the transition to math? A few other questions: In law, we approach problems using "legal reasoning". Legal reasoning is an approach to problem solving taught in legal schools, and learned with practice. Is there an analogous process of approaching mathematical problems along the lines of "mathematical reasoning"…

Hello again folks. Is the following of any interest if it can be proved? P: Relative to any finite set of primes there are infinitely many pairs of consecutive twin primes. Note 1. In case it's the wrong word - by 'relative' I mean that none of the primes in the set are factors of the pair of twin primes. Note 2. This is nothing like a proof of the TPC. Thanks for any replies.

While looking for a modular building block for a sieve of Eratosthenes, for example, an 8-bit block of zeros with composite multiples of 2 and 3 already marked as ones,I noticed something bazaar. If I grouped the digits from the sieve into groups of 8 and marked the composites, it takes the same number of groups of eight to form a repeatable block as the prime who's composites i was marking. For example, here are some primes and the groups of eight digits for the sieve. 2 == 10101010 3 == 10010010 01001001 00100100 5 == 10000100 00100001 00001000 01000010 00010000 7 == 10000001 00000010 00000100 00001000 00010000 00100000 01000000 11 == 10000000 00010000 00000010 00…

Of course it hasn't been solved yet, but it would be significant to consider other properties of Hailstone sequences after it has been solved(or the properties brought in this post will be solved with the solution to the problem). Before introducing these problems, here are things to be defined: A Collatz number is defined by a number in a Hailstone sequence that is represented by [math]c_{x}=6x-2[/math] where x is the index of the number. This is a result of [math]c_{x}=3(2x-1)+1[/math]. A Hailstone sequence is a sequence of numbers resulting from the Collatz conjecture rules. A Hailstone exception is a number that does not follow the pattern of a Collatz number …

So, something I've been doing lately is reviewing driver safety. I got my license in 2008, and I have reviewed driver safety the past few months. I think I'm a much better driver than in 2008, but I've been reviewing skills to prevent myself from ever getting into an accident. One of the mathematical models that I came across lately in driver safety is the Solomon curve. http://en.wikipedia.org/wiki/Solomon_curve It's a mathematical model describing the relationship between speed between drivers and the probability of getting into an accident. What I don't understand about the curve, and perhaps some mathematician here could do research and give me insight, becaus…

Hello everyone Here's a question from the acceptance exam for Med school: 6,000 people undergo an ABO-bloodtest. 1,846 are not positive for antigen A, nor B. 2,527 are positive for antigen A, while 2,234 are positive for antigen B. How many are positive for both antigens? First thing that came up in my head, was to substract First thing that came up was Boolean algebra, where: [math]6 000 = \neg(A\vee B) + A + B + (A\wedge B)[/math] (O, A, B and AB) [math]1 846 = \neg(A\vee B)[/math] (O) [math]2 527 = A\wedge (A\wedge B)[/math] (A and AB) [math]2 234 = B\wedge (A\wedge B)[/math] (B and AB) But there's a problem: [math]A\wedge (A\wedge B) = (A\wedge…

Thanks to iNow, I was able to make this finding(unless this was already found before I found it). I was meaning to post this sometime or other, but now I have the time to do so. When I saw the equation for the prime test, I decided to mess with it. When I took it's derivative, I found that the equation, when solving for x when y = 0, would come up with complex numbers, where the real part is 1/2. I modified the equation(only the exponents) so it would fit the characteristics of the Riemann Zeta function(though an unorthodox method, I thought it would be important). [math]\zeta (x)=(x-1)^{s}-x^{s}[/math] Where s = p+1 and s must be an even number. Now, in t…

Hello everyone In class, we saw some stuff in probability and I wondered if they could also be written with these symbols: [math]P(A \; \text{and}\; B)=P(A\cap B)[/math] [math]P(A \; \text{or}\; B)=P(A\cup B)[/math] And so I also wondered if they could also be written with proposition logic symbols [math]P(A\wedge B)[/math] and [math]P(A\vee B)[/math] For the chance of 'not A', we saw this notation: [math]P(\bar{A})[/math], but I wonder if this: [math]P(\neg A)[/math] is also good, and which one is the 'best' (best known, most correct one). Thanks. F

Recently I'm learning about complex networks and I'm interested in similarity functions that give how similar two nodes are in a network/graph. I found couple similarity functions/indices that were described in the sense of undirected networks. However my concern is with directed networks. For example Preferential Attachment similarity between two nodes in an undirected graph is the degree of the first node multiplied by the degree of the second node. But what about directed graphs? Which degree should one use? In-degree or out-degree? Another index is Salton index which is defined as the number of common neighbors between two nodes divided by the square root of the m…

For the second derivative, why is (d/dx)(dy/dx)= [(d/dt)(dy/dx)]/(dx/dt)? I don't see the logic. Am I supposed to apply the quotient rule of differentiation on dy/dx? If I do that I get the second derivative is 0 because dy-dy=0. Am I allowed to use algebra on dy and dx?

So, I found something that was interesting that could related to the Collatz conjecture. Here is what I found. Take any regular function f(x) and multiply it by its inverse. take the derivative of that product. Repeat this step until you reach a pattern of 2x repeating. Here is an example: [math]f(x) = x+1[/math] [math]\frac{\mathrm{d} }{\mathrm{d} x}\left ( (x+1)(x-1) \right )= 2x[/math] [math]\frac{\mathrm{d} }{\mathrm{d} x}\left ( \left (2x \right ) \left ( \frac{x}{2} \right )\right )=2x[/math] (This is just a simple example) I have tested this with other functions and it seems to check out. I haven't seen this before, so if someone knows if …

I came across a formula derived by Ankur Tiwari, which he says enables division by zero. The website claims This formula enables us to divide in a unique way without using denominator. This formula is based on the principle that, If the value of X divided by Y (X/Y) is A than by using this formula we can find out A without dividing X by Y directly, that means without dividing X by Y we can find out its value. This is the reason why ‘Bhartiya New Rule for Fraction’ is capable of diving by Zero. The interesting points in regard of this formula are :- 1.‘Bhartiya New Rule for Fraction’ is based on present phenomenon and rules of mathematics. 2. It is ver…