Mathematics

I had wondered if looking for Pi in a different base other than "10" would produce finite or repeating decimals. So using the formula circumference/diameter I started with the normal base 10, as a control, putting 23.12/7.36 into the WolframAlpha engine, of course getting 3.14..... (infinitely non-repeating as usual). And then I changed it from base 10, entering "23.12/7.36 in base 5". I also tried it with all other bases from 1-20, also 100, and a few in between. Oddly, every single result had the numbers repeating after only less than fifteen digits. Cap'n Refsmmat advised me just input "pi in base (anything)" to see what happens. And of course doing that…

So, given enough time, a monkey typing random words on a keyboard will eventually type out Hamlet word for word. Let us calculate the expected time it would take the monkey to do that. In my intuitive (but limited) understand of probability, I think we only need to know: 1) The number of letters in Hamlet (or characters if you want it to include spacing, punctuation etc., but excluding capitalization) 2) The average time it takes someone to type one letter, or in other words, words per minute. We must be given some leeway here because we must agree upon whether the monkey is frantically mashing the button with its fingers (not whole hands, because then the probabi…

Hi everyone, I'm a little confused about positive & negative skewness. From what I've read, this is the picture I have, please tell me if it is correct: Positive Skewness This is when more data on a graph is towards the left of the graph (i.e. the lower values on horizontal axis). Even though the mass of the values are towards the left of the graph - the 'tail' is said to be greater on the right and the distribution is said to be right-skewed (if the majority of the data is on the left then wouldn't it make sense to think of the tail as being greater on the left and skewness to be left skewed?). Negative Skewness More data on a graph towards the right …

Me and a few friends at school the other day were wondering if pi and phi were somehow connected, After a while i managed to throw out [math]\phi^{(\displaystyle\frac{\pi + \phi}{2})}= \pi[/math] which manages to roughly approximate [math]\pi[/math]. I then found if you did [math]\phi^{(\displaystyle\frac{\pi + \phi}{x})}= \pi[/math] with [math]x = 2.000811416[/math], the equation exactly reached [math]\pi[/math]. But [math]x = 2.000811416[/math] seems too random to me, is there any connection between [math]\pi and \phi[/math] that would produce [math]x = 2.000811416[/math]? On the slight chance you understood what i said, do you know where [math]x = …

I've wondered this for a long time: Why the heck is the famous Monty Hall Problem even to this day so controversial? I mean, I'll admit that when I first heard the problem I was like "Give me a break; two doors left means there's a 50/50 chance, so switching your choice is pointless," but once I grasped it fully I was quite frankly embarrassed that I didn't get it right away, because it's pure common sense. For those of you that don't know the Monty Hall Problem, this is it. A game show host presents a game show contestant with three closed doors and tells her that behind one of the doors is a new car (i.e. one out of three doors is a winner), and behind the othe…

Just a very wild idea. It starts by defining a "point" as being a Plank length (there is some logic behind this idea) and then using this measur the circumference and to calculate pi by dividing the circle into triangles with the plank length on the circumference. A circle with a radius of one plank length has a pi = 3.0. Pi increases as the radius grows –but will it end with a rational number?

I know that to find the sum of an arithmetic series I'd use [math]S=\frac{n}{2}[2a+(n-1)d][/math] but what do I do if I want the product of an arithmetic series (all the values multiplied together nicely)?

Is anyone here interested in the Collatz Conjecture? If so I believe I have the solution, seriously, and I need to work with someone who knows how to write a formal proof better than I. There are some errors in my proof, but the underlying principle is right. I only have my minors in mathematics, so my proof writing skills are subpar.

I am simply not intelligent enough to dissect any meaning from this claim. Can any sharper minds here illuminate this concept for me as to whether or not it is truly significant? If not, can you articulate for me why it is arbitrary? (which it seems to be). https://www.youtube.com/watch?list=PLTlGAyi6v1bYm8lBwg4W9jU4ahz16UX8i&v=Stw316T0nQg#t=174 Here's some commentary from the post I got this link from: "This is what number 9 looks like! Zero Point Singularity..The God Mind, Mathematician. Nine is both the singularity and the vacuum...ZERO POINT ENERGY. Nine models everything and nothing at the same time. Nine seems to Govern TIME and SPACE !!! It i…

From now on, I will use this thread to inquire my math questions that I have. I don't want to create a new thread for everytime when I have a single, small math question. Waste of time in my opinion. Also, to let everybody know, those math questions will never be my homework. They are just some bogus math questions that I see around or on the Internet. IT'S NOT MY HOMEWORK. Awhile ago, I just found this old Fermat Competition booklet in my bedroom that I entered last year (A Canadian National Math Contest), and I have this question. When [math]a=\frac{1}{2}[/math] and [math]b=\frac{2}{3}[/math], what what does [math]\frac{6a + 18b}{12a + 6b}[/math] equals? I…

Hi all, would anyone be able to give me a little bit of help with this question. for part (a) i did this.... our sphere is given by [math] x^2 + y^2 +z^2 = 25 [/math] putting in z = 3 to find out part of the sphere gives: [math] x^2 + y^2 = 16 [/math] so we change to the parametric representation of the part of the sphere we are interested in sphere which is [math]\vec{r}(\theta,\psi) = (4sin\psi cos\theta) \vec{i} + (4sin\psi sin\theta) \vec{j} +(4cos\psi) \vec{k} [/math] then [math]\vec{r_\theta}(\theta,\psi) = (-4sin\psi sin\theta) \vec{i} + (4sin\psi cos\theta) \vec{j}[/math] [math]\vec{r_\psi}(\theta,\psi) = (4cos\psi cos\…

Does anyone know why a negative times a negative equals a positive? I have never been able to understand the reasoning behind that.

Apparently [latex]xe^{-x^2}[/latex] is an odd function. I found out the long way finding the integral sums to zero (btw, excluding trivial cases, is that a sufficient condition to conclude a function must be odd?). However, i am supposed to be able to tell this was odd by inspection (similarly for even functions). I'm sure they don't mean i need to be able to determine the parity of any function by inspection, but does anyone know of any hints and tricks for doing so? I'm starting to see a pattern where the parity of a Gaussian integral multiplied by a polynomial is equal to the parity of the polynomial. Any others?

If a/b is greater than 1 than b/a must greater than 0 but less than 1.<br><br> For every number greater than 1 there is a multiplicative inverse greater than 0 but less than 1. <br><br> Examples 3/4-4/3, 7/8-8/7, 9/10-10/9, 1/3-3/1, 3/5-5/3 <br><br> But is there a proof for this?<br><br>

Just like any other construction the Neolithic architects and engineers who built Stonehenge knew exactly what they wanted long before the foundations were dug. The stones were positioned in respect of a vision of their vision - a superb premeditated geometric structure. It was also largely prefabricated, just look for example at the complex jointing in the lintels, they can only have been created off-site and must have been trial fitted on the ground (which also indicates just how much thought and planning went into the design). As for all the so called alignments, it has only one, an axis of symmetry; that of the midwinter sunset and midsummer sunrise. Now where does t…

The little I know about primes is that there is no any 'Systematic Formula' for obtaining prime numbers in either ascending or descending order.And the whole world is in a delima as wheter there is a limit to primes or NOT.That is whetther there is a HIGHEST PRIME NUMBER. I have Good, Better and Best formulae for generating Prime Numbers systematically. TRY THE GOOD ONE: P=7d-4 Where: P=prime number(Needed) d=odd number(Chosen) Example: At d=5, it means; P=7(5)-4=35-4=31 there are a few exceptions for the Good formula. Questions and contributions are welcome

Is there a way to convert irrational numbers from decimal to binary? Has it already been done?

Does (a+b)1/2 equal a1/2 + b1/2 - (2ab)1/2? If you have ( (a+b)2)1/2, then because of the binomial theorem, then (a+b)2=a2+b2+2ab. Inserting this into the equation, then you get (a2+b2+2ab)1/2, which gives you a+b, since a2+b2+2ab=(a+b)2. If you set x=a2 and y=b2, then you have (x+y+2x1/2y1/2)1/2, which gives you x1/2+y1/2. This is also equal to x1/2 + y1/2 + (2x1/2y1/2)1/2 - (2x1/2y1/2)1/2, since (2x1/2y1/2)1/2 and -(2x1/2y1/2)1/2 cancel out. What if you removed 2x1/2y1/2 from the square root? Then, would you get x1/2 + y1/2 - (2x1/2y1/2)1/2?

It has been proposed that Pi should be replaced with the Tau for mathematical purposes. The Tau has twice the value of Pi. The reasoning behind this change seems to be that it would simplify many formulae since"2*Pi" is much more common in formulae than Pi on its own. This certainly seems to be the case in electronics and it seems some eminent scholars are convinced. What do you think?

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…

Necromancy! I searched the forum for 'Möbius' and this thread was the only one returned. And wonder of wonders you have mentioned just the concept I had in mind, i.e. squashing. Before I launch into squashed space I would just point out that above you say 'at the ends' and a Möbius band has no ends. So a few years back I got to wondering if there was a limit of L to W beyond which I could not join W's to get a Möbius band. I made paper bands as well as sewed some of canvas. Anyway, yes Möbius bands beyond certain ratios must be squishified. At some ratios the band squishes into a hexagon. After seeing it [the hexagon] and having recently read about the mysterious hexa…

Let us say you have a ruler laid out on the floor, with the spacings arranged such that 1 increment = 1 meter. You are standing at 0. You start flipping a coin an infinite number of times. When you get heads, you move 1 meter forwards (positively) on the ruler. When you get tails, you move 1 meter backwards. If you flip tails at 0, you stay at zero. Let's say that you flipped the coin once and it landed on heads, so you are now standing at 1 meter. With a potentially infinite number of coin tosses, what are the odds of eventually arriving at 0? How different would it be if the ruler was infinite as opposed to finite? --------------------------------------------------…

Density is 10.34 Flow is 1844 Nm3/h… Anyone know how to convert to Kg/h?

Hi, Hope this is in the right place, apologies if not. I've recently started a Maths & Physics Degree and am just about to embark on my first Maths module. I've been toying with the idea of getting myself a graphics tablet to use on my assignments alongside the Windows Maths Input Panel. I'm not planning on using it day to day as i find it easier to scribble with a pen and paper but thought it would save me quite a bit of time when writing up assessments etc. I just wondered if this is something any of you guys have experience of and if it was a viable idea. Additionally if you have used these before do you have any recommendations? Thanks in advance, …

I was just curious to know whether people think there is a definite dividing line between the two, because it would seem somewhat intuitive for a mathematician to be numerologists by default. One such line ive heard drawn is when you look for a specific number or pattern everywhere, because doing so is a somewhat self-fulfilling prophecy. Also certain patterns and numbers of significance i believe do repeat in nature everywhere so where is line the drawn? Primarily PI, Fib and the golden ratio seem to be recurring everywhere. However you also get people finding abstract relations in patters of stairs or such which is nonsensical in my mind. So where do…