Mathematics

So I'm reviewing my rules of radicals prior to teaching it to students, and found out I'm a little rusty on them. Suppose you hit an answer that ends with a prime number as your radicand. Provided you used mathematically valid reasoning to get there, does this prime-number radicand now suggest that you arrived at the most simplified form, or are there "dead ends" distinct from the right answer?

Discrete examples are easy enough. Toss a coin, 1/2, toss a die, 1/6. Continuous examples, Probability of a nucleus decaying during observation, 1-exp(-λt), Probability of a neutron moves x without interaction, exp(-Σx), where Σ can be assumed to be the inverse of the mean free path i.e. the distance a neutron travels without interaction on average. My point is that I don't really have an idea as to how these continuous probabilities are derived. Any assistance?

Probably the most accurate method of dividing any angle into three equal parts. Simple and accurate

For those who haven't used a rubix cube there are certain patterns you simply cannot achieve, for example if you flip exactly 1 corner to the right or left, either by taking it out or by simply twisting it you can not solve it without either twisting it back or twisting all other corners relative to it, or you can turn all but one other corner in different directions and then be able to solve it. Or you can turn all of the corners and try to solve it and you will only have one corner turned wrong. I can not figure out the math behind this. Can someone explain if you can.

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.

So I was recently thinking about the similarity in formulae between spheres' volume (4*pi*r*r*r/3) and their surface area. (4*pi*r*r) Firstly, I noticed that the surface area looks like it's the derivative of volume with respect to radius... which come to think of it makes sense as the rate of change in volume at a point in time is that outer spherical shell being added times its thickness. But secondly I also noticed that the ratio of the two is r/3. As in, as if the average particle in a sphere were only a 1/3 of the way to the outside. More generally, V/A is in length units. Am I figuring this right? Does V/A represent average distan…

I discovered an improved method for finding large prime numbers by ignoring the prime numbers alltogether and only focus on the wavelike patterns of prime factors which is loosly related to the Sieve of Erasthonenes. Figure 1: The Sieve of Erasthonenes By noting that prime factors occur at regular intervals. ie multiples of 2 reoccur every other number, multiples of 3 reoccur at every third number, etc. we can leverage this periodicity of prime factors to identify all non-prime positions within a predifined large range of natural numbers arranged in an array. This periodicity of prime factors means that we can apply the concepts of Standing Wave Harmonics …

What is the use of Calculus in Computer Science?

I know the value of dn/dt (e.g. dn/dt = 123). a3 = 345 / n2 Is there any way to calculate da/dt?

This issue is offtopic in a thread about electrons so I have started a new thread for discussion. https://www.scienceforums.net/topic/115443-electrons-how-do-they-work/?tab=comments#comment-1062243 Finite is often used to mean a non-zero number https://en.wikipedia.org/wiki/Finite_number "In mathematical parlance, a value other than infinite or infinitesimal values and distinct from the value 0" I prefer the definitions of Dedekind : not infinite Russell : Able to be counted using a terminating sequence of natural numbers. Consider the equation x2 - 2x + 1= 0 Is the …

This statement is where we could use my own new type of maths I am trying to bring into secondary education through my company "Hydra." I have spent a lot of time planning new approached to maths, at secondary and tertiary levels, so, please bear with me and observe where the strengths are of my new system? This is just an example of how it can be applied, of course. [9H] * [6K] * [2X] * [1Q] = [108A]. This is because the powers can be applied to the symbols and then taken as '[X1]'. This leads to a simple set of symbols to multiply. Then, we take the [108A] divided into the symbols on the left that we recognize, being [H], [X] and [K], coming to [HXK] = [108]. …

This would be [infinity] * [2n] = [3] * [2] = [6] * [x] Then, [5] * [2] = [10] * [x] Then, [7] * [2] = [14] * [x] So, the answer is double prime times by [x]. Or, [N] * [2] *[X].

Is there an easy straightforward way to produce a mathematical model for anything that I can imagine? The more that I think about it the more and more that I see that maybe everything could be written as a function with distinct variables. I just want to know how I can make mathematics seem extremely intuitive so that if I see a leaf fall on the ground I could fully model that falling in all case scenarios with either a simple algebra equation or with a more complex differential and multi-variable calculus equation. I have had the urge for years so if anyone could help that would be great.

What is (unless there is more than one definition,perhaps?) the mathematical definition of a surface in a general sense? I am interested to know in the context of intrinsic curvature but feel I need to get this concept well understood first. For example must a mathematical "surface" in a 4-D space be 2-dimensional (like a skin) or is it 3-dimensional (like a volume)? If it is 3-dimensional,what defines it as a surface?

Every second, a green marble has a chance to appear. You are not told what the probability of this occurring is - instead, you are given a number which is equal to the average number of seconds it takes for a green marble to appear (let's call it 'mean time to happen'). Now let's say you want there to be a chance of a red marble appearing instead of a green one. In order to make this happen, you must define a separate 'mean time to happen' for the red marbles. But you do not want to change the overall chance of any marble to appear; the combined probability of a red or green marble appearing must be the same as the previous probability of a green one appearing. …

I know that the area of an ellipse is 1403761773.43497 and its circumference is 145485.418131498. Is there any way to calculate from those numbers that the semi-major axis is 26534.9039306654?

I started to study about diff eq for this summer class. And I already have trouble with it. The professor lecture is also probably too fast and I couldn't get anything to my brain. Is there any site exclusively for this matter? Please tell me.

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 = …

The Australian philosopher colin leslie dean points out Godels theorem is invalid because it uses invalid axioms ie axiom of reducibility it is the biggest fraud in mathematical history everything dean has shown was known at the time godel did his proof but no one meantioned any of it http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf look godel used the 2nd ed of PM he says note he says he is going to use AR but Russell following wittgenstien took it out of the 2nd ed due to it being invalid godel would have know that russell and wittgenstien new godel used it but said nothing ramsey points out AR is invalid before godel did his …

Hi all. I am new here. What actually are two dimensional objects? Do they really exist in material world?

Hello! I am stuck with a relatively simple task. I am doing some coding and need a certain kind of motion to apply to an object. The motion graph should look something like in the picture. It may look like sqrt(x) at first but this isn't the case, I am wondering if there is some function that actually reaches a slope of 0 relatively quickly (or a VERY tiny slope) ? Thanks!

Numerus “Numerans Numeratus” Let all abstract numbers be defined exactly as concrete numbers. Concrete number: A numerical quantity with a corresponding unit. Let the corresponding unit exist as an abstract dimension notated with the use of (_). Let the length and width of all dimensional units remain abstract and undeclared. Let the dimensional unit be equal in quantity to the numerical quantity it corresponds to. Let all numerical quantities inhabit their corresponding abstract dimensional units. Let zero be assigned a single dimensional unit. Classic Isomorphic 0 = …

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! Stupid question in the topic. Obviously, radius is perpendicular to a tangent at a point of intersection, but can it be said that radius is perpendicular to the circle itself? Does such statement even make sense?

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