Mathematics

Hi everyone Imagine a horizontal line of length 1. Divide it into 2 equal parts. Now pick a random side of the 2 equal parts: left, or right. If you pick the left half, divide it in 2 and now focus on the 'new' right half (of length 0,25). Divide that into 2 and now focus on the 'new' left half. Divide that into 2 and focus on the 'new' right side. As you see, alternating between 'newly cut' left and right sides and divide that once again in 2. I find that using this algorythm approaches 2 values: 1/3 for the left side, and 2/3 for the right side. (1) Is this true and (2) how can this be proven? Thanks. F.

I want to make a golf ball launcher just beacuse it sounds like fun to see how far i could gat a golfball to go. anyway to make the golfball launcher i and going to get a 3000 rpm moter and make a wheel that will spin on the shaft of the moter. the top of the wheel will be inside a pvc tube so as the wheel spins a golfball will be droped in to the pvc pipe and be forced between a spinng wheel and the inside of the tube. this should force the golf ball foword. Like a soccerball launcher. If i use a 1 ft in cicumfernce whell than the ball will be moving at ruffly 22 mph. so i want to know how far the ball will be launched if shot at a 45% angle. how do i do this. at what ra…

Trying to understand the fundamentals of binary rather than just following steps, I wanted to know why do we multiply by 2 to convert a decimal ([latex]0.5[/latex], [latex]0.25[/latex]) to a binary and why do we divide by [latex]2[/latex] when we want to convert a whole number [latex](200)[/latex] by [latex]2[/latex]? Obviously, it works but how ? Take the following example: Convert [latex]200_{10}[/latex] to binary: Solution: D > B | Remainder ------------------------------------- 200 / 2 = 100 | 0 100 / 2 = 50 | 0 50/2 = 25 | 0 25/2 = 12 | 1 12/2 = 6 | 0 6/2 = 3 …

So, I saw the definition of the conjecture: A runner is said to be lonely at time t if he is at a distance of at least 1/k from every other runner at time t. The lonely runner conjecture states that each runner is lonely at some time. And then it asks "Can the Lonely runner conjecture be proved for k≥8?" What confuses me about the statement is it seems it is asking if it can be proven for smaller distances. Why would that be difficult to prove? I thought it would be more trivial that way(not saying it's a simple problem). Would it not be harder to prove it for larger distances?

I'm trying to write a function that where the domain is all whole numbers that returns only the values 1, 0, and -1. At first I made a peacewise function: [latex] f(x)=\left\{\begin{matrix} -1 & x<0 \\ 0 & x=0\\ 1 &x>0 \end{matrix}\right.\ [/latex] But I think I can be more clever than that. Would it be proper to combine the floor function and the sine function to make this? [latex] f(x)= sin \lfloor x \rfloor [/latex] Or would I need to do something else to make that work? Thanks in advance for the help!

I am looking for a mathematical theory that describes or explains causality dilemmas. I have come across causal decision theory but I don't think it covers the problem of dilemmas. It might be covered under Game Theory but I'm not sure. I am also looking for mathematical examples of such a problem.

FYI this isn't homework help, this is me teaching myself. I have a problem where the book tells me to solve for the inverse of the function. Then the book tells me to evaluate the inverse for: [latex] h^{-1}(9) [/latex] and... [latex] h(9)^{-1} [/latex] I can easily do the first one, but what the heck does the second equation mean??? And how do you do it, or is it the same thing just written differently? I've never seen that before! Thanks in advance for help

Scenario: Let us suppose we have a stationary Target T being orbited in a perfect circle by an Attacker A. The circle has the radius of R in meters. T has a weapon that can track A at a set rate, T1 measured in radians per second. Given those conditions, I want to find the minimum velocity (V) in meters per second at which A can move around the circle of the fixed radius (R) and still exceed the value of T1. Let us also suppose there are no outside influences to consider. So here's how I worked this. First, we know the circumference of a circle is [math] 2\pi R [/math] We can then write a formula based on the velocity that determines how long it tak…

Hi guys, I'm currently trying to do statistics to compare the variance of results in two different methods. However, my results are in totally different units. So I think I need a way of scaling my data so that statistical analysis can take place. The two methods are very different ways of measuring something, and the units cannot be converted to match. Is there a way of scaling, or perhaps a method concerning ratio? The data sets are BOTH dependant variables and here are a few of the equivalent data points: 183 - 7.8 173 - 7.7 173 - 7.7 175 - 7.6 166 - 7.4 174 - 7.4 Any help would be GREATLY appreciated! Thanks A x

I know it is a no solution problem, but I was taking a look at it through the use of a limit and wanted to see whether this approach was valid. Given that [math]\lim_{n\rightarrow \infty }\frac{x+1}{x}[/math]. We can apply this to 1^x = 2, which can be turned into [math]log_{1}(2) = x[/math]. [math]x = \frac{log(2)}{log(1)}[/math] Now, this is undefined. Therefore, we can take the limit by applying the above together. [math]x = \lim_{n\rightarrow \infty }\frac{log(2)}{log(\frac{n+1}{n})}[/math] [math]x = \infty[/math] Is this math wrong? I am assuming some of it is, though checked wolfram: http://www.wolframalpha.com/input/?i=limit+of+x+approac…

Hi folks. I am a student and i have to do an essay about a topic that intrigues me. I read the quote " The Unreasonable Effectiveness of Mathematics in the Natural Sciences" ( of E.Wigner) on the book "Is God a mathmatician" of Mario Livio, and that hit me. Maths in fact can seem useless or a mere tool of applied sciences, but in reality, often it has anticipated some evolutions of physical theories and every branch of it has been applied in some way. One example could be the knot theory that, from the theory of mathematics it has been applied to the study of DNA (for whom interested: http://www.tiem.utk.edu/~gross/bioed/webmodules/DNAknot.html). What do you think? Do…

I just wanted to learn some hyperbolic geometry by myself. And I found this YouTube channel which has many lectures on many different math topics: https://www.youtube.com/user/njwildberger Has anyone tried his lectures before? Is he any good?

Hi there, this is my first time posting so forgive any indiscretions on my part. I was wondering what the name of the attached geometric curve is? It was produced by a population of bots in a exploration simulation I am running using neural nets. To me it looks like a dimpled limaçon, but with two inner loops instead of one. If the curve has a name, or a defining formula, I would greatly appreciate it.

Ten samples are taken and an average reading of 6.1 resulted. The IQR was 0.6. Does this mean the sample readings were pretty close in range about the mean?

infinity^0=infinity^(1-1)=infinity/infinity equals any positive number.

It finite difference method is unstable?

Hello. Do you know the Monty Hall problem? It states: "Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?". The contestant should switch to the other door. Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their choice have only a 1/3 chance. After doing some research I found that there is a formul…

What unit of measure was used when the distance from the pole to the equator was being measured to later define the metre ?

If we assume that (-1) (-1)=-1 and (-2)(-2)=-4 but know that (0) (0)=0 Then (1+-1) (1+-1) must equal 1-1-1-1 =-3 and not the sum of (0) (0) which it should equal 0 unless we have assumed otherwise but have not. Likewise (-1+2) (-1+2) =(-1)(-1) must equal -1+-2+-2+4=-7 and not the product of (-1+2) (-1+2)=(-1)(-1) which should equal -1, which is inconsistent and does not equal -7 if we assume that (-1)(-1)=-1. But if we assume that (-1)(-1)= 1 then (1+-2)(1+-2) should equal 1+-2+-2+4=1 likewise (1+-1)(1+-1)=(0) (0)=1-1-1+1=0 which it does

The answer is yes! infinity*0= infinity (1-1)=infinity-infinity, which equals any number. because infinity-infinity-3 is absorbed in infinity like a blackhole. and still equals infinity-infinity, likewise infinity-infinity-5 equals the same thing.

Hello everyone In order to write a paper on the differences in epidemiology of pandemic influenza A(H1N1)pdm09 during that pandemic, between Europe and Africa, I need to understand a concept in a German article I'm using: "Der Altersmedian der Einzelfälle liegt bei 16 Jahren (IQR 10;28)." Which means as much as: "The age median of the individual cases is 16 years old (IQR 10;28)." Now, I know that IQR means inter-quartil-range, but can someone explain the meaning of this range 10;28 in this specific context? Would it just mean that Q1 = 10 and Q3 = 28? Thanks. F.

hello everyone I need help in this exercise. my attempts: i)resolved. ii) (t)=(1/n)=inf{s \in T: s>t}=1/(n-1) (t)=sup{s \in T: s<t}=1/(n+1) (t)= (t)-t = 1/(n-1) - 1/n =1/n(n-1). my answer for (ii) is right !! Thanks.

Isn't there a law that refers to the question of equations and how they are read, as far as forwards and then in reverse? In the simple 1+1+1=3, the ones can only add up to three, no debate. In the reverse order, three can be one plus one plus one, or a near infinite variations of numbers that add up to 3. This seems to have something to do with the 2nd law of thermodynamics, and why reality can only function forward in time. Thanks....

Hello! Suppose so you, mathematician, have such task: find whether point P (xp,yp) (2d) or (xp,yp,zp) (3d) is in triangle defined by vertexes A,B,C. Please show me your algorithms. The more optimized algorithm, the better *) Here is common stage needed for all below algorithms: (please note that this can be already calculated once at triangle initialization stage) min = Min( a, Min( b, c ) ); max = Max( a, Max( b, c ) ); if( ( p.x >= min.x ) && ( p.x <= max.x ) && ( p.y >= min.y ) && ( p.y <= max.y ) && ( p.z >= min.z ) && ( p.z <= max.z ) ) { [...more detailed check h…

Hello, Would someone be able to help explain the meaning of a term in a formula? The one in question is the deep learning weight adjustment formula from DeepNeuralNetworks. And here it is. So this shows the the iterative adjustment for the weights. Or is it the adjustment to the change applied to weights (as indicated by the delta)? But the main part I am unclear about is this. C is the cost function but what does this term mean?