Mathematics

Suppose you are given the relation that [math] a^a= b [/math] . Then how you do you proceed to find a in terms of b ? Or, the solution doesn't exist.

(Disclaimer I am a very curious 14 year old so bare with me) I found an article saying glass with 2.5 g/cc would have to be 14 light minutes(Lm) in radius to create a black hole, I am now trying to find out how many Earths' that would have to be in a row to create a black hole. I just need help with the math. Would this mean 1 g/cc would have to be 23.333 light minutes(Lm) large to create a black hole considering 14Lm + (14Lm ÷ 1.5g/cc) = 23.333Lm/g/cc (Lm being Light Minutes)? 1 g/cc density would take 23.333Lm to make a black hole ? Considering this that would mean Earth (Which all together has a density of 5.513 g/cc) would be 5.513 g/cc 5.513 g…

From that other thread I wondered "hmm, how would I come up with that from scratch?" How would you go from a simple recursive series to that exponential formula? http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html#section1

Is there a quick and easy way of working out the nth number in the Fibonacci sequence when you don't know the values of the two preceeding numbers in the sequence?

For some reason I just literally can not figure this out, my brain has hit a wall even though I know it's so simple... So I have 25,000mg of binder and I have 250mg of active ingredient. All I need to know is what is the ratio, how do I figure out how much active ingredient is in x amount. Lets assume I wanted like 3 mg worth of active ingredient, how much would I have to scoop from the mixture to get that?

I think I have my own methodology but I'm curious to see what the formal definition of this is. I'm looking for an x-value of a function where its integral is the same on both sides of the x-value over some interval [a,b]. With some testing it doesn't seem like the average value theorem directly relates to the answer, but it seems like the general answer should be something close to that. The answer I got is [math]x=F^{-1}(\frac{F(a)+F(b)}{2})[/math] where F(x) is the integral of f(x).

So what I thought I knew years ago for some reason I am confused with right now. How shameful! Wonder which marble I lost? I must have had a brain fart. Anyway, the identity goes (a - b)2 = a2 + b2 - 2ab Going from right to left, without knowing the left side, how would we know whether the negative term is a or b?

Before you roll a die, you could say there is a 1 in 6 chance that it lands on any of the numbered sides. After you roll a die, you could make the point that there is a 1 in 1 chance that it lands on a certain side. I know this is practically irrelevant and too complex for humans to calculate, but it is technically correct. If you were to assign a super-advanced machine to calculate odds, it would always give 1 in 1 odds for it landing on a certain side. It would be able to calculate this from the angle, force, direction etc. of the die throw. If you were to throw the die under the same conditions an infinite numbers of times, the same result would always come up. Th…

Dear reader; It seems that iam off target! And I beg your pardon: Withthe help of mathematical illustrations and explanations, may you please show me(step by step) on how to check an equation like E=MC2 in dimensional analysis? Please I beg.

As an addition to all current field axioms. "For every A in S there exists a z1 and a z2 constituting A. Such that any A in operation of a binary expression of mulitpilcation or divison is only representing z1 or z2. Such that z1 and z2 for all A's other than zero equal A. Such that z1 for zero equals zero. Such that z2 for zero equals 1. "

Hi, I am looking for a very special and unique mathematical solution which, from another direction of investigation not related to maths, I have reason to believe exists, which is to work out those phases of a "mobius light" configuration that will superimpose properly. For references about the recent experimental work in which "mobius light" was successfully demonstrated, see arxiv:1601.06072, and for the theoretical work dating back to 2009, see Isaac Freund's paper arxiv:0910.1663 Please bear in mind: I am a software engineer, I have a CV 15 pages long, I am not a n00b but my mathematical ability is that of an O'Level / A'Level student, whereas my knowledge-de…

My goal: Write a python script that will hold the left set, right set, and calculate the value of a surreal (if it is finite) and return it when called. As I understand it, a surreal number [latex]S[/latex] and [latex]S'[/latex] are equvalent so long as the the maximum of the left sets, and the minimum of the left sets are the same or simply: [latex]S=\{S_L|S_R\} \equiv \{max(S_L)|min(S_R)\} = S')[/latex] [i cut everything else out, because I wasn't making sense, please see below] For fuck's sake, I hate this unnecessarily complicated recursive numeral system. THIS is why more people don't understand surreals, because the numbering system isn't intui…

So there is this weird phenomenon that occurs when you follow these specific rules: If ODD 3x+1 If EVEN x/2 The theory is that if you take a number through these rules as far as possible you will achieve a never ending cycle of 4,2,1. So say for instance you start with 5 follow the ODD function to get 16 then even function for 8 again for 4 again for 2 again for 1 then 4, 2, 1, 4, 2, 1... As far as I am aware this has not been proven to work for every number and it is unsure if there could be other sequences like this that appear from numbers untried. I guess my point is for a discussion to see if it can't be proven.

check this diagram on different sizes infinity and maybe you could point me to someting similar i could study: i just did this work based on this concept:

Here the monty hall explained: So I was thinking if you could do that with cards so I tried. Soon I realized playing with just 3 cards meant that most probably you would eleimnate your pick or the price so this is what I did: I extended the option to 52 poker cards and the prizes to both red aces. I pick after shufle the first 13 cards and start elminating cards till I get a red ace. Now theres just one red ace left, thats the prize but there has been a change of variable so its in my interest to switch pick. I did a program that studies this startegy and it gives you an edge as it should matematically. http://sma…

Our maths teacher was explaining the other day limits and put an example of a turtle that advances half of the way each time The turtle runs one meter, then half meter, then a quarter of meter... so the turtle limit is 2 without never ever reaching it Several costudents were questioning the teacher lesson, most would say they thought the turtle would reach destination After the class a friend gave a solution to this: The turtle advances one meter, in one second, half meter, in half second quarter of meter, in a quarter of second... so obviously by second 2 will have reched destination and by second 3 will have traspass it Seems the same to me with…

How can a combination of a complex and a real number be plotted in a single graph ? How about merging the Argand and Cartesion planes in perpendicular orientation?

Below is from Wikipedia Not that long ago probability and statistics had different definitions of variance because of their different frames of reference. Probability is about future expectations and statistics is about past results. In probability, it used to be something like: the maximum amount something could change based on a single event. However, now I can't find any evidence of that old definition. My question has nothing to do with the merits of the change. Before thinking that hard about it, it seems like a more useful form in some respects but its also bad in other respects but then, perhaps there should be two terms instead of one. However, just …

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…

Counting number filed (1,2,3,....) results into consequences such as for example prime numbers. Prime numbers are located in the counting number filed (1,2,3,4,5,6,7,8,9,10,11,...). The bolded numbers are primes. So we can assume that the counting number field has a great relationship to PN that needs to study to know the deep nature of prime numbers. So for you, what could be there relationship?

The other day I was going through a post that said "Applied Mathematics involves mathematical models as well as creativity".

Hello all, I was practicing some problems and I come across this question : Is triangle ABC with sides a, b and c acute angled? Triangle with sides a2, b2, c2 has an area of 140 sq cms. Median AD to side BC is equal to altitude AE to side BC. Which one is the right answer? And How? Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. BOTH statements (1) and (2) TOGETHER are sufficient but NEITHER statement ALONE is sufficient to answer the question asked. EACH statement ALONE is sufficient to answer the que…

What does this symbol mean? I pointed to it using the red color. http://www5.0zz0.com/2016/12/22/18/706933985.jpg

Very Interesting Number Nine Two Numbers (10 a+b) and (10 x+y) For two digits numbers, numbers can be written in four ways like this 1. (10 a+b) and (10 x+y) 2. (10 a+b) and (10 y+x) 3. (10 b+a) and (10 x+y) 4. (10 b+a) and (10 y+x) Multiple with each other  (10 a+b)*(10 x+y) = 100 ax + 10 bx + 10 ay +by  (10 a+b)*(10 y+x) = 100 ay + 10 by + 10 ax + x b  (10 b+a)*(10 x+y) = 100 bx + 10 ax + 10 by + a y  (10 b+a)*(10 y+x) = 100 by + 10 ay + 10 bx + ax Subtract each one respectively 1.100 ax +10 bx + 10 a y + by - 100 a y - 10 by- 10 ax - x b = 90 ax + 9 bx - 90 a y – 9 by = 9(10 ax+bx-10 a y- by) 2.100 ax +10 bx + 10 ay + by – 100 bx – 10 ax-…