Applied Mathematics

Does this thought experiment posit that BETWEEN the monkeys the complete works of Shakespeare can be compiled from individual words they type? Or does it posit that ONE monkey, given infinite time, will produce an error-free complete works. If it is the first scenario I can see this happening and I could actually imagine it working with just a large number of monkeys and a long time. If it's the second scenario I have a problem. Not just that it is totally counter-intuitive or that infinite time is impossible to comprehend. I realise that monkeys and typewriters are (fun) devices used to help think about complex theories pertaining to pro…

Greetings: Before anything, I am a 50 year young man with Aspergers and ADHD that considers himself a free-thinking Catholic. This question is in two parts. And my sincere apology for the length of the second one, it might seem like a wall of words, but i saw no other way to properly post it without changing anything in the question's content, interpretation or meaning. 1) First, a personal question, this is to see just how far math and science is related, in your person: "How important is mathematics to you, what place has mathematics to you, and how far does mathematics have an impact on your thinking/accepting?" 2) Here we have the actual math quest…

How many sides does a shpere have? One or infinite? PS: how does a mobius band work??

Let's take symmetry of functions as an example of regularity, others may be their periodicity, etc. If one analyzes it, one can conclude that even functions, which are by definition those for which f(-x)=f(x), examples of these are polynomials consisting of even powers of x, and odd functions, for which f(-x)=-f(x), examples of these are polynomials consisting of odd powers of x, are actually exceptions, rather than a rule, ie that functions are generally speaking asymmetric objects with respect to the x=0 axis (or plane in 3D), that do not necessarily have anything to do with those that are symmetric (even and odd). However, the fact is quite the opposite, every asymmetr…

This article was started as more of a debate than an answer to the question. According to Chaos Theory, any number, n, is defined as being higher than anything with lower value, or higher than any value from 0 to n, and lower than anything with a higher value, or lower than any value from n to infinity. Now, this may seem quite obvious, but also according to Chaos Theory, infinity cannot exist as a number. Both of these are stated in Chaos Theory, and are noted as a flaw in the number system, as how can a definite number be described as being below infinity, yet infinity is not a number in itself? Chaos Theory also states that any number has no definite point of "…

Hi friends I am a high school student from india and have been trying to prove the collatz conjecture. Physics and maths have always been my favourite and recently I have been able to develop a proof for this conjecture. What should I do? Whom should I send it to? What is its value? Please do help me out.

Why don't they use rectangular prisms for dice?

When you have to multiply two quantities with different units together, how do you interpret the meaning of the combined units? Take the formula for momentum, p=mv, for example - you have (say) kg times m/s. I know how to interpret m/s - for every second that passes by, so many meters are traversed. But what does kgxm mean? For every second, there are so many kilogram-meters. But what is a "kilogram-meter"?

I recently watched the movie again and was curious if anyone has studied John Nash's theory more in-depth. Can anyone explain exactly what the theory predicts and/or how it works?

For the two attached pictures below, let [math]{P_n}[/math] denote the proportion of the big circle covered by the small circles as function of the number of the small circle in the outer layer. Find the expression for [math]P_n[/math] and compute [math]\lim_{n\to \infty} P_n [/math]. Would you answer this question in details? **Author's answer to this question as follows:** Let R be the radius of the big circle, [math]r_n[/math] be the radius of the small circles in the outer layer, and \(R_n\) be the radius of the circle encompassing all small circles except those in the outer layer. Then in both cases \(P_n R^2\pi = n r^2_n \pi + P_n R^2_n \pi (\star)\) and…

“I constructed a circle by tracing around the shape of the base of a good cylinder(such as Milk Tin): How can the centre of such a circle be obtained, in order to measure its radius? IN SUMMARY: How Can an Unknown Center of a Circle be Located? NB: With only a straight edge and a pair of compasses.

I came across a bit of a snag when I was working with permutations of things in a circle. The problem is that I have 8 particles, 4 negative, 4 positive(the particles are indistinguishable except by their charge) arranged in a circle. When I asked the question how many ways can I reorder these particles? I came up some interesting results. According to the formula I was taught: (8-1)!/4!*4! But this equals 8.75 permutations! Is this a special case? Is the formula wrong? Please help me out!

While some say that pi goes on and is infinite, much like e (Euler's Number), but not square root of 2, and other mathematical sums as it may stop, are they similar to infinity? I know that infinity cannot be counted or regarded as a number, but what if we regard infinity as or equivalent to 9999999999999999999999999999999.... So on, and so forth. Or for you brilliant mathematicians prefer to this formula: ∞ = 9999999999999999999999999999999999999999999999... So what do you think? Guys, what are you opinions of infinity and mathematical constants? Are they equivalent to quantities, as they both go on? (Hard eh?)

My book says on average the sampling variance [math]\dfrac{\sum (x- \bar{x})}{n} [/math] is biased because it usually gives estimates smaller than the actual variance of a population. We fix this by dividing the sum by n-1 instead of n: [math]\dfrac{\sum (x- \bar{x})}{n-1} [/math] Is there a more intuitive or formal explanation of this?

A sphere has _____ side(s). Fill in the blank, thats all. a) one b) no c) infinate d)

I understand that anything other than zero to the zero power equals one. But this doesn't seem to make sence to me. Could someone explain how this is, rather than that it is? I'd like as much feedback on this as possible. Thank you.

This thread paraphrasing an old interesting one in this same forum. As always fascinated by the power of units and after a post of dear Swansont, here are some thoughts: _as an Architect, I use quite commonly a method to measure the slope of a piece of land, or the slope of a ramp, expressed as a percentage. For example say you have a ramp 10 meters long going one meter up, that gives a slope of 10% What did you do? You took the eight divided by the length (the horizontal projection), that is: 1m/10m=0,10 or 10% In fact you divided meters by meters and ended up with a unitless number. This unitless number represents something physical thoug…

When u flip a coin . there are three possible events E1= Head E2=Tails E3=landing on its side now P(E3) must be really small. but even if its small, imagine the number of times coins have been flipped!!!. there must have been a coin landing on its side. Just wanna know if there is any record of that ever happening.

The question is simple why is it 360 deg in a circle and not a number that is easier to work with. More importantly were does the number "360" come from when was it chosen why was it chosen and by who? P.S. What other units of mesurement are used to mesure angle?

on the homepage of SFN, I clearly see that we have 3121 members, but only 1 member's birthday is today. of course there are many users that didn't enter their birthdays to their profiles, but this number is still very impossible. could anyone give a mathemetical explanation?

When a probability question says 'what is the chances of getting at least one or at least two', how many does it mean in accordance with its stated amount..

This thread is an attempt to quantify the methods used to communicate a mathematical concept to another person for the purpose of applying the concept. Each response should ideally contain: A single math concept, as you would present it to an inexperienced colleague in your field, who asks for help. Any additions that you would include for the average person. Optional comments. Provide as many examples as you like, including historical examples, but please send each as its own post for ease of evaluating responses. There are no restrictions on field or complexity. The only restrictions on length and format are the practical limitations…

I need help with understanding this question.

There is an axis for Imaginary numbers, and there is an axis for real numbers. So we can just use the X and Y axes, what is the difference? They can do the same thing.

First time posting so apologies if this question is in the wrong section. I've recently gotten into the cryptocurrency market and so I've spent a lot of time online studying market analysis. When i got started i though it was the study of how stable a business or commodity is, outlook on productions, etc... instead I find that "Market Analysis" is the study of previous market movements to determine future market movements. some examples can be found here: https://optionalpha.com/13-stock-chart-patterns-that-you-cant-afford-to-forget-10585.html I've studied this hard and deep and then came to a sudden realization - This seems an awful lot like horoscopes.…