Mathematics

I think most know as two Fibonnaci numbers are divided together, dividing the smaller one by the larger one, you get closer to the golden ratio as the two Fibonnaci numbers get larger and larger. Here is the equation that I want to use for this example: (Correct me if this is an incorrect way of doing this). Since at the limit of infinity there would, in fact, be a fraction, but of immeasurable magnitude, that would exist, therefore making this not an irrational number? I am not saying it isn't an irrational number, but I want to be sure of my logic on irrational numbers. Or would this immeasurable magnitude of the fraction make this an irrational number? …

there is a guy named Niels Abel. he tried and failed to solve the quintic - polynomial degree five. find it, solve it. it is trivial.

If you theoretically had negative lengths, what are some ways they would differ from positive lengths?

What do sin∅ and cos∅ tells us in cross product and dot product I mean what is the significance of them & from where it came ?

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…

Hello everyone I've seen 2 definitions for [math]e[/math] (one on the internet, one I have proven myself): [math]e=\lim_{n\to\infty}{\left[1+\frac{1}{n}\right]^n}[/math] and [math]e=\lim_{n\to 0}{\left[n+1\right]^{\frac{1}{n}}}[/math] Now, is there a proof that these two are equal? (I'd first like to know if I can change the first expression to something in the form of [math]n\to 0[/math].) Thanks! Function

Hello everyone My book gives us a proof for the rule of de l'Hôpital and to do this, its first statement is: [math]\frac{f(x)}{g(x)}=\frac{f(x)-f(a)}{g(x)-g(a)}[/math] However, I don't agree with this... Or I have no idea where that comes from... e.g.: [math]f(x)=6x^3+2x^2+4[/math] and [math]g(x)=8x^2+3x+1[/math] [math]\frac{f(3)}{g(3)}=2,243...\neq\frac{f(3)-f(7)}{g(3)-g(7)}=5,951...[/math] What's wrong with this? Thanks. Function Nope, wait.. I oversaw that [math]f(a)=g(a)=0[/math] Sorry (...again..)

Why does a negitive times a negitive equal a positive

Hello! Well as the titel says, I need help with a math problem I can't get a grip of. I have thought of this problem for around 1-2 hours and just can't understand it. Some tips: Use derivate For which numbers on a doesn't the curve (y = x ^ 3 + ax ^ 2 + x) has any extreme points? The answer to this question is -√3 < a < +√3 Regards!

Question : 1.How to solve this question (steps) 2.How to analyse this question Please help me it is emergency, I don't know how to analyse this problem.

Why does a negitive times a negitive equal a positive

Here is proof that a+bi=-a+bi: Using the distributive proprty, we can write a+bi as i(a/i+b). a/i is also equal to ai, so then it becomes i(ai+b). That equals ai2+bi, and i2=-1, so therefore it makes -a+bi. Equation form of proof: a+bi=i(a/i+b)=i(ai+b)=ai2+bi=-a+bi Proof that a/i=ai: Because i2=-1, we can write a/i as a/-11/2. a is also sq.root(a2), or a2/2, so it is also a2/2/-11/2. Since a1/2/b1/2=(a/b)1/2, we can write this as (a2/-1)1/2, which is also equal to -a2/2. -a2/2 =a2/2i, or just ai. What do you guys think?

There is a website named tauday.com and it was mad by a guy who thinks τ should be the circle constant. I agree with him, but what do you guys think?

I've found an exact equation for e without pi e=(cos(1/2)+i*sin(1/2))^(2/i) does this mean that e is not a transcendental number?

Doing a project in excel to make a little form to plug in linear speeds and have it spit out some data on the speeds estimated by SR and all that... And working with cells instead of normal variables made me entirely forget the formula... What part did I miss here: (V+u)/(1+(vu)/c^2) ... What part did I screw up?

I discovered this equation with a proof through mathematical trial and error. Here's the equation pi=e^(2*(((ln(pi))^2+2*ln(pi)+1)/(2*ln(pi)+2))-1) Using ttmath's online calculator with 1024 bit mantissa the equation gave me the exact same value for pi as the constant value provided for pi by the calculator. When using the calculator with a 2048 bit mantissa the 2 values of pi were different, the last least significant digit there was a difference in 1 between the the 2 digits. If someone has access to a calculator that can calculate too more precision I am curious to find out if the discrepancy is due to calculating error or either the current value…

I know nothing about curved geometry but maybe I don't have to, after all. I want to evenly distribute an arbitrary number of points on a hemisphere. I visualized for example 1000 vectors starting from the same origin, on one side of a plane containing the origin. If they are normalized they'll resemble a hemisphere. Being evenly spaced means the 'tips" make for corners of equilateral triangles. I guess there are at least 2 possibilities: on the top of the "dome" there's a point OR the center of a triangle. Basically I want to find the vectors. Can it be explained with matrices at most? Quaternions are a little too hard for me and be it only if there's no other choice.…

I have no proof for it but just wondering if this equation is new? (-1)^(1/x) = i*sin(pi/x) + cos(pi/x) where x>=4 I've tested this equation and Google calculator gives the correct answer for every example.

Stop saying "maths." ... It's "math." I don't go to englands and discuss footballs while drinking teas. Because unnecessary pluralization is wrong. ... Only time it can be acceptable is if you're discussing different kinds of math... Entirely different systems of math.... Then it's optionally Ok. Like "peoples" ... But stop asking "a maths question." And don't make horrible excuses about a silly way to abbreviate "mathamatics."

Im curious to know the relation between sin and cos on a ratio basis. Sin(45) and tan(45) both give approx 0.7071, how do they relate in ratio terms of incremental degree's? The gap decreases? im guessing its something to do with working from 90 as base and then scaling it to 0.1/0.2/0.3 etc as used on a polarized circle graph. The linear ratio would be 1 / 90 * theta; sqrt(2) / 90 * theta gives "close" result upto Sin(45) so the reverse could be used for tan. Is this the right track?

Hi there, So we know that some number [math]b^n[/math] is [math]b[/math] multiplied by itself [math]n[/math] times. What about roots? The logic would imply that we take [math]b^\frac{1}{n}[/math] as being [math]b[/math] multiplied by itself [math]\frac{1}{n}[/math] times. I'm a little vague on the underlying mechanisms of taking roots and fractional exponents. I am aware that fractional exponents and roots are computed using logarithms but how? As an example: [math]10^\frac{5}{2} = 10^{2 + \frac{1}{2}} = 10^2 10^\frac{1}{2} \approx 100(3.162) \approx 316.2[/math] I can see that breaking the exponent apart gives a sum of a whole power [math]2[/math] and a square …

Why is it not possible to have the log of a negative number? Examples would be greatly appreciated. Furthermore, is it the base that cannot be negative? Like log-bx or is it that when you have a number and you log it, the number cannot be negative. log(-x)

Oh my god I don't believe I am asking this>>> Rather how do you add a number and another number that has an exponent? That sounds more clearer. YES! I am scratchy on this, or just need to make sure... So we have, example here: 9.98857^34 + 4.777... 4.777 has no exponent. But should I take a log scale and see what the exponent for 4.777 ?? Such like this: 4.777^ 0.67915524128 here is the link I used for this: Logarithm of 4.777 Base 10 http://www.1728.org/logrithm.htm In all, I think I will always be confused on this, it just does no make any sense whatsoever.

Hi! According to this site http://www.intmath.com/applications-integration/11-arc-length-curve.php the arc length of the curve y = f(x) from x=a to x=b is given by: length_ab = Derivative_ab( Sqrt ( 1 + (dy/dx) ^ 2 ) dx) So, we got a sine wave function which is y = A * sin (F * x + P) from x=a to x=b the length of this is length_sine = Derivative_ab( Sqrt ( 1 + (A * F * cos (F * x)^2 dx) Example of this is in first link or here: http://www.wolframalpha.com/input/?i=tell+me+the+arc+length+of+y+%3D+1.35*sin%280.589x%29+from+x+%3D+0+to+10.67 Now, my question is what is the algorithm to compute length for specified x=a to x=b. For example, l…

The Next Operator Beyond Exponents: I was looking into operations greater than exponents when I discovered a few properties of nested exponentiation. I'm not claiming that I am the first to discover these properties. I am well aware of work that has been done on tetration and the Ackermann function. However, I have not found these properties of nested exponentiation anywhere. Also, according to Wikipedia, nested exponentation is not even listed as a hyperoperation: Another clue is that my version of Mathematica does not have any of these properties listed as operators and does not know how to simplify equations using the new operations I have derived. I fully un…