Mathematics

I thought you guys might find this interesting. Adding Time to a 2D Prime Factor Harmonic Matrix to demonstrate the “behavior” of standing vs moving prime factor “waves” Previously I had introduced the Prime Factor Harmonic Matrix which showed that prime factors behaved like waves or specifically 1 dimensional waves that either behave like moving waves or standing harmonic waves within a 2 dimensional matrix of natural numbers. A PFHM is simply any matrix of natural numbers that is dimensioned according to a primorial. Paul Ikeda's answer to What’s the significance of prime numbers in physics and nature? Finding large Primes …

I found an article with some equations and got some questions whether some of those equations are correct or not. On the picture you can see that matrix Tpi is on the left side, while matrix TR is on the right. Aren't they supposed to be vice versa? Link to the article: https://research.ijcaonline.org/volume113/number3/pxc3901586.pdf

Continuity and uncountability Discussion about continuity of line, how continuity is related to uncountability and the continuum hypothesis. The real line is made of real numbers which are points. Points are discrete objects, but lines are continuous objects. How does continuity arise out of discreteness when points make line? The idea of uncountability solves this problem. Rational numbers are countable, the line they make contains holes. Real numbers are uncountable, the line they make is continuous. So, continuity must be created by the uncountability of the points of a continuous line. One can imagine that uncountable points are so numerous on the real line that real …

Ok, you are going to laugh at this one. But I am seriously asking this question. I need to think outside the box if I want to break a one-way-function. In this case outside the triangle. My question is: Why can’t I combine the Law of Sines and the property of similar triangles to solve 2 different similar triangles of different sizes? And secondly why can’t I say the proportions in one triangle are not proportional to the same proportion in a similar triangle? I mean if all sides and angles are known in one and the other similar triangle all the angles are known, there has to be a method to solve the segments of the unknown, second similar triangle…

Hi, I discovered reverse Fibonacci sequence. Can you comment me what you think and what math value have this discovery? The article is in attachment. Thanks. Reverse Fibonacci sequence Short - Ondrej Janicko.pdf

I have been tearing my hair out over this lol. I am trying to work my holiday (vacation) entitlement out. Can somebody please tell me if I am right? I get 27 days holiday plus the bank holidays (public holidays). My work year is 1st of April to 31st of March. Due to Easter moving about that means this year I get 7 days as bank holidays. In total this year I get 34 days holiday entitlement If I worked full time I would do 7.5 hours per day and work 5 days per week = 37.5 hours per week. 34 holidays days x 7.5 hours a day = 255 hours holiday entitlement. If I was full time every time I take holiday day I would lose …

Hello, there are two circles in nature a real circle well defined in mathematics. And an imaginary circle in our head that can not be defined.

i have a question for any maths wizz here. something from my real life. i have a toolbox with a padlock that opens via a 4-digit sequence. so, for example 8734. and the padlock opens. so when i lock the toolbox sometimes im a bit lazy and i just move the 4 slot around a bit, without touching the 873. one of the other guys reckons its easier for someone to work out the code to open the lock if i have only moved 1, instead of all 4 of them. is he right? or does the law of averages mean there are still the same chances someone will guess it regardless of how many or few i move.

I am trying to find the maximum and minimum peaks of a function which goes as: y=x1 cos(f1+ teta) + x2 cos(2*f1); The peak values are straightforward for cases where the frequencies are equal or when they are non-multiples. I am having trouble to quantify the maximum and minimum values of 'y'. Note: teta, x1 and x2 all these vary from time to time. I am therefore looking for a generalised expression (accuracy <5%). Thanks in advance.

So I was recently thinking about solar angles. A fairly straightforward, everyday example of solar angles. Or so you'd think. However, recently one thing came to mind. Suppose it was 6 hours before or after noon during a fall or spring equinox (for our purposes it wouldn't matter) at the equator. Since it was "halfway" between sun-over-the-horizon and sun-overhead, I presume the solar angle would be 45 degrees, right? Now suppose at the same time someone else was, let's say, at 45 degrees latitude; (north or south for our purposes wouldn't matter) at the same time. How would one determine, then, what the solar angle there would be? Is t…

If the radius unit vector is giving us some direction in spherical coordinates, why do we need the angle vectors or vice versa?

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?