Mathematics

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…

Can someone explain to me mathematically, in terms of Axis, and or in word form what the 5Th dimension is? Please don't say its spiritual unless you are somehow speaking on biocentrism >.>

Hi, i have a very simple question (easy to state, i meant...) -Can someone explain, in the simplest possible way, why the complex numbers were chosen as a basis for the infinite series of the Zeta function? (in other words: why did Riemann build up his hypothesis of his Zeta function's non-trivial zero rational parts, in the idea of numbers which are partly imaginary too, ie x+iy)? I ask because, ideally, i would not want to spend huge amounts of time making a connection which probably is quite simple in regards to examining the hypothesis itself. I can suspect that Riemann formed the hypothesis as a (particular type of) series based on complex numbers due to the abili…

imagine a 3D flat space, embedded in a 4D flat space imagine a 3D object, in the 3D "hyper-3-plane" space imagine a linear vector through the 4D flat space, from the center of the 3D object in the 3D "hyper-plane"… hyper-dimensionally "out", to higher hyper-dimensional altitude, in the 4D space i.e. the center of the 3D object = (0,0,0 | 0) and the 4D linear vector = (0,0,0 | 1) with its "tail" at the center of the object (0,0,0 | 0) Now, please ponder spinning the 3D object, about the 4D linear vector, threading through its center, "out" to higher hyper altitude in analogy, a 2D object, in a 2D flat-land, rotating about a 3…

Let us say there is a formula [math]ax+b[/math], and a sequence of numbers is laid out. Let us say the formula is [math]3x+1[/math]. 4 7 10 13 16 19 22 25 28 Now, let us put these numbers into sets of 3 in order. {4 7 10} {13 16 19} {22 25 28} Then, add up the numbers in each set to get the following sequence. 21 48 75 The pattern can be describe as each number within the sequence of sets can be found with the following, where s is the size of each set. where c is some number related to the formula. Has this been looked into before? If so, can someone link the webpage about it?

Problem is to compute the ECDLP given: A finite integer field (Zp,+,*) as p ranges over primes y2=x3-5x+4 where P=(-1.65, 2.79) and Q=(-0.35, 2.39) I don't necessarily want the answer, i want to know where to start and how to get to it ...

Hi everybody. I want to find suitable range for four parameters: x(1), x(2), x(3) and x(4); in a way that: 326.705<x(1)*x(2)*(1+x(4))^2*(1-x(4))*x(3)^3<378.29 What should i do? Is there any way to find the answer by MATLAB?

I couldn't resist making this post because I [math]r=\frac{\text{sin}\,\theta\sqrt{\left | \text{cos}\,\theta \right |}}{\text{sin}\,\theta + 7/5} - 2\left(\text{sin}\,\theta - 1 \right)\,\,\,\,\{\theta\in\mathbb{R}\,| \,0\le\theta\le 2\pi\}[/math] math more than any other subject

In Lemma XIII of the Principia, Newton says "The latus rectum of a parabola belonging to any vertex is quadruple the distance of that vertex from the focus of the figure. And this is demonstrated by the writers on the conic sections". Well, Apollonius does not state this proposition. And I can't find any 'writer' who does. Hence, can anyone help ? Thanks.

I know this a topic which has been discussed to infinity, but I have a problem with this theory and would like other peoples' opinion on it. The 'proof' states that: x = 0.9999 10x = 9.9999 9x = 9 x = 1 I believe the problem lies in the second line already. Is it possible to do an arithmetic operation on a number with an infinitely repeating fraction? Let's take a finite number. x = 0.9999, then 10x = 9.9990. We have to know there are 4 digits after the decimal point, so each one moves one to the left, and the fourth digit after the decimal is replaced by a 0. I suppose the argument is with regard to the theoritical interpretation, but in practice i…

I've always been drawn to impossibilities, which is why I so enjoy the concept of I as the square root of -1... But I just thought to question what sqrt(I) is. Now, I've always loved math, but I never had the patience for the tedious homework necessary to make it into higher math classes... But when I searched for the answer, I was dissatisfied. According to the internets sqrt(I) is sqrt+/-(1/2). My problem is the insinuation that I=+/-(1/2). No? The thing about 1 is that if x>1, x^2>x. And if x<1, x^2<x. So "I" must be right on this magic Li'l circle where x^2=x, who h can only be 1.... If on some wonky imaginary number line. I could see if…

What happens when an undefined variable is .34 or larger?

could one please let me know how we write the equation of a conic passing thru two conics? for egs., the equation of a circle 'S' passing thru the points of intersetion of two circles S1 & S2 is 'S= S1+$S2' can we use this even for parabola and other conics? if no, then what is the general form of the above equation? please let me know the meaning of all the unfamiliar signs you use. and also the concept behind it. please help me.. thanks in advance.

1) Why are there so many notations for vectors and related operations? v, [math]\vec{v}[/math], [math]v^j[/math], [math]v_j[/math], [math]|v\rangle[/math], etc. I understand that there are conventions endemic to certain fields of math/physics, but is there any practicality to get out if it? 2) As for mathematical notation in general, do you think it would be practical to establish a universal set of notation that could be used across all fields of mathematics and science?

Many of us read the recent Guardian articles by Marcus du Sautoy and Alok Jha that described a potential new 14D geometric theory of everything. Unlike most such theories, Geometric Unity has a unique experimental prediction that can verify it or rule it out. CERN is capable of making this measurement with existing equipment. The mathematics and physics communities have been unable to judge the claims directly since they are looking for papers by Weinstein, and there are none. In fact, the theory was developed by another author and Weinstein's contribution has been to popularize the ideas. If you are interested in the truth, I highly recommend reading the following links.…

Consider this riddle. The result it claims is fairly remarkable, and yet the solution, although a bit difficult to digest at first, is logically sound, but based on axiom of choice. Just sharing it because I think it is really cool, and I figure this community would enjoy.

A friend posed a riddle. There are two boxes, one with ten tickets, and one with one hundred tickets. There is one lucky ticket in each. Do you choose one chance with the ten or ten chances with the hundred? I reasoned that with the ten out of one hundred, a person's chances are better because as you're picking tickets out of the box, there are less tickets in the box. Therefore the probability is 1/100 + 1/99 + 1/98 + 1/97 +... + 1/91 for a 10.48% chance of getting the lucky ticket. My friend says no, the probabilities are equal. Which one of us is correct? EDIT: I'm wrong because I know that this series doesn't add up to one, but I still have the fe…

So, two simple questions: Reading a book by terry goodkind called the law of nines.... So I'm in a math mood. He mentioned that the sale of his paintings fetched him 14,400 and I was like 0o, that's divisible by 9, maybe that's important... Then I went off on a tangent thinking it's also divisible by 10 and 3, obviously.... And 2, therefore 6, and 1, of course.... And 8.... and 4.... But not 7.... So I tried to think of the lowest number I could that would be divisible by 1-10.... So it would have to end in 560 to cover 7,8, and 10... So I think 7560 is the lowest one.... Anyone know of a lower one? Should this be the lowest one, it would entertain me enough …

I am assuming that since the amount of arrangements possible for a set of elements is equal to the amount of elements within the set to the factorial, that for a matrix it would be the area of the matrix factorial. Is this true?