This is my final work on the Prime product problem.
I know it is just x^2 * y^2 = PNP^2
However the terms would just cancel out. Instead I have decided to let x^2 equal a pattern of x and PNP. So I just substituted the equation which is more complex and will not equal the right side of the equation for x^2.
In calculus where you have a complex derivative where you let du/dx equal a portion of the derivative so you can understand and simplify the manipulation of the integral. I am instead taking a more complex pattern and leaving it so x^2 does not cancel x squared. By doing this I hope it solves the pattern.
So if you could solve this polynomial equation you would solve the factorization problem.
If you couldn’t solve the polynomial? Well you could just write an algorithm that plugged in Prime numbers from smallest to largest. And because the polynomial is set up to find PNP you would get a feel for the range x was in. I mean, that this time when you try a number how far away the computed value is from PNP is significant.
So if this works it is faster than using division to factor.
But of course I await any disagreeing opinions. I now this problem gets that. But it was my final attempt before moving on to a different problem to pursue.
(((((x^2*PNP^4 + 2*PNP^2 * x^5) + x^8)/ PNP^4 ) - ((1 - x^2/(2*PNP)))) * ((PNP^2/x^2 ))) == PNP^2 Above is the pattern of x^2 * y^2 = PNP^2 It is not to be simplified yet x put and tested in that place. It is faster than division since the equation approaches PNP as the proper x is used. Smallest to largest Prime numbers are to be used. PNP = 85 x = 5 (((((x^2*PNP^4 + 2*PNP^2 * x^5) + x^8)/ PNP^4 ) - ((1 - x^2/(2*PNP)))) * ((PNP^2/x^2 ))) 85 5 4179323/578 N[4179323/578, 14] Sqrt[7230.66262975778546712802768166089965397924`14.] 85.033303062728 ((((x^2*PNP^4 + 2*PNP^2 * x^5) + x^8)/ PNP^4 ) - ((1 - x^2/(2*PNP)))) 4179323/167042 N[4179323/167042, 14] 25.019593874594 ((PNP^2/x^2)) 289 Questions to ask: Is it unique to factors of PNP or does it just give a decimal to all real numbers? Does it work for other values of PNP and x? Is it faster than factoring (recursion)?. Is it just x = x and as so not a useful pattern? Can the error be programmed? Verify then post. That is what I need to do. But I actually believe there is a pattern here. The question is does it work for all PNP and x values. I have many patterns. Some answer some of the questions. But I haven't found a polynomial I can solve after these questions have been answered. For example if this worked, I would need to solve the given equation. And this proves to be challenging. PNP = 85 x = 3 (((((x^2*PNP^4 + 2*PNP^2 * x^5) + x^8)/ PNP^4 ) - ((1 - x^2/(2*PNP)))) * ((PNP^2/x^2 ))) 85 3 847772947/130050 N[847772947/130050, 14] 6518.8231218762 Sqrt[6518.8231218762] 80.739229138481]]>
On the other hand, mathematics shows us that there are an infinite number of real numbers between 0 and 1 and between 1 and 2. These infinities are the same "size" (but larger than the infinite number of integers).
On 2018. 01. 27. at 5:16 AM, OroborosEmber said:
if this is true why we need any numbers beyond 0 and 1? Feels like different scaling of the natural numbers.
What would be the difference between the infinite numbers between 0 and 1 or the infinite numbers between 0 and 1 000
]]>If I roll a fair dice I know I have a one in six chance of getting a "1".
What is my chance of getting a "1" if I roll it twice? (It could be either on the first roll or the second roll or both. I am just concerned with getting a "1" at some point.)
What is my chance of getting a "1" if I roll it ten times? (Same thing: I'm just concerned with getting a "1" (could be more than one "1") at some point.)
I realize this may be too basic of a question for this forum, but I'm hoping someone will have the time to help me out with this really simple question.
Thank you.
]]>
So I'll start off:
1) http://linuxfreak87.googlepages.com/
1) Covers a lot of stuff, Maths and some physics.
2) http://mathworld.wolfram.com/
2) Amazing maths resource, lot of advanced stuff.
3) Basic and advanced maths here. Good tutorials.
4) Again more good tutorias and weekly challanges.
5) http://mathforum.org/dr.math/
5) LOTS of question solutions here, examples too. This one has helped me a lot in the past and still does
6) http://www.ics.uci.edu/~eppstein/junkyard/
6) Lots of fun geometry, useful stuff and interesting stuff here.
7) http://en.wikipedia.org/wiki/Category:Mathematics
7) As always Wikipedia is a great resource for one and all.
8) http://www.research.att.com/~njas/sequences/Seis.html
8) If your interest is number sequences this is the place to go. Useful for research.
9) Equations, equations and yes you guessed - MORE equations. Very useful resorce for reference.
10) http://home.att.net/~numericana/
10) Lots of interesting stuff and some other useful links too.
11) http://www.mcs.surrey.ac.uk/Personal/R.Knott/
11) Lots of interesting stuff, the mysteries of the Fibonacci Numbers etc.
12) http://integrals.wolfram.com/
12) Very useful too, online integral solver!
13) Maths in music, what next?
If you have more to add pease share them
Cheers,
Ryan Jones
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I am trying to measure a curved profile of a surface(2D) to determine the surface availability at different rate of testing. I have attached an image for a rough picture. Actually I have a reference geometry and performed two tests to determine the behavior. They two had different profiles at top portion. So I considered an axis for reference geometry and drew radial lines with 15deg angle difference each and marked those points as 1 (15 deg anticlockwise from vertical axis),2(30 deg anticlockwise from vertical axis),3,... and measured length of the radial lines which gives the distance of the top profile at different points(L1 at pt1, L2 at pt2...). I did the same on my first test results and got the lengths L1',L2'...and with second test lengths L1",L2".... Now I estimated the deviation of the profile by calculating the error like this test1: Error = ((L1-L1')/L1)*100% test2: Error = ((L1-L1")/L1)*100% As the number of experiments increases it is a bit tedious to divide lines based on angles and measure the deviation of the top profile and hence would like to look for an alternative. One approach would be to eliminate the axis and split the complete area with square grids and get the coordinates (x,y) and find the error, but this seems not too good. Could any one please suggest an easy method to do find out the difference in the top profile? Thanks in advance |
What's a Piangle? Maybe this will make it clear.
The Piangle is an unraveled circle. Imagine cutting a radius, then draw some inner circles.
Next unroll each outline to the right.
This is a right triangle, so by the Pythagorean theorem the length of the hypotenuse is , which is or .
The Piangle is not distorted, it's just an unrolled circle. It even has the same area as its corresponding circle. Its area is 1/2*b*h = = .
Proof that I discovered this: the hypotenuse = ≈ 6.3622651. Googling that doesn't return anything about the triangle.
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[math]\phi^{(\displaystyle\frac{\pi + \phi}{2})}= \pi[/math]
which manages to roughly approximate [math]\pi[/math]. I then found if you did
[math]\phi^{(\displaystyle\frac{\pi + \phi}{x})}= \pi[/math] with [math]x = 2.000811416[/math],
the equation exactly reached [math]\pi[/math]. But [math]x = 2.000811416[/math] seems too random to me, is there any connection between [math]\pi and \phi[/math] that would produce [math]x = 2.000811416[/math]?
On the slight chance you understood what i said, do you know where [math]x = 2.000811416[/math] can be derived from?
Cheers,
Rob
]]>There is a relationship that occurs in R^{3} that I believe cannot be mapped to R^{2}.
The relationship exists between the sphere center and the surface curvature. I believe that because R^{2} has no third orthogonal plane or axis that this relationship does not exist in R^{2}.
This is best described as a relationship that exists between the tangent to a small circle on the surface of a ball and the gross position of the ball in 3-space.
The illustrations show how this relationship can be seen.
Mathematically, it is expressed as an identity:
[latex](\cos\frac{\phi}{2}\:\sin\frac{\lambda}{2})^2 +(\cot\frac{\phi}{2}+\cos\alpha)^2=1[/latex]
Does the fact that this mathematical identity exists and is not represented in the current mathematical approach to modeling spacetime have any significance? To me it seems that this isn’t an issue unless the spacetime is curved, at which point it appears that the whole idea of using R^{n-1} breaks down. Why isn’t this the case?
]]>
I could go on and on, but I'll go onto explain some of the basic syntax of LaTeX.
Syntax
Functions & General Syntax
Basically put, if you want to write a math equation in LaTeX, you just write it. If you wanted f(x) = 3, then bung that between to math tags and you're done, producing [math]f(x)=3[/math]. Don't worry about extra spaces or carriage returns, because in general LaTeX will ignore them. It does get a little more complex than this, but don't worry about that for now. Remember that any letters you type in will be presumed to be some kind of variable and hence will be italicised.
We also have functions to display more complex things like matrices and fractions, and they have the syntax of having a \ before them, usually followed by some kind of argument. For example, \sin will produce the function sin and \frac{num}{denom} will produce a fraction with a specified numerator and denominator. More on these later.
Also remember that LaTeX is case sensitive, so \sigma is NOT the same as \Sigma.
Subscripts and Superscripts
This is perhaps one of the easiest things to do in LaTeX, and one of the most useful. Let's, for the sake of argument, say you wanted to write x^{2}. Then you'd write x^{2}, producing [math]x^2[/math]. Notice that you don't necessarily need the { and } in cases where you only have 1 thing in the index, for example x^2. But it does care if you want to write something like [math]x^{3x+2}[/math]. Subscripts are done similarly, but you use the _ operator instead of ^. If you want both subscript and superscript, then use the syntax x^{2}_{1} - which is equivalent to x_{1}^{2}.
Fractions and functions
As I've mentioned, fractions are generated by using the function \frac{num}{denom}. For example:
[math]\frac{1}{3}[/math]
[math]\frac{7}{x^2}[/math]
If you want smaller fractions, you can use \tfrac, to produce things like [math]\tfrac{1}{2}[/math] which will fit into a line nicely without having to seperate it.
LaTeX has some nice in-built functions like \sin, \cos, etc. I'm not going to write them all down here, but I'll point you to a website at the end of the document that contains them. Likewise, you can write symbols (such as infinity by using \infty) and Greek letters (e.g. \phi, \Sigma, \sigma, etc)
Bracketing
You can get all your usual brackets just by typing them straight in; for instance, (, |, [, etc. However, sometimes they won't be the right size, especially if you want to write something like (1/2)^{n}. You can get around this by using the \left and \right commands, and then placing your favourite brackets after them. For instance, to write (1/2)^{n}, we have:
[math]\left( \frac{1}{2} \right)^{n}[/math]
Integrals, Summations and Limits
Integrals can be produced by using \int, summations by \sum and limits by \lim. You can put limits on them all in the right places by using the normal subscript/superscript commands. For instance:
[math]\int_a^b x^2 \,dx[/math]
[math]\lim_{n\to\infty} \frac{1}{n} = 0[/math]
[math]\sum_{n=1}^{\infty}\frac{1}{n^2} = \frac{\pi^2}{6}.[/math]
Summary
There's a lot more things you can do with LaTeX, and I'll try to add to this as time goes by. Have a look at:
http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/'>http://www.maths.tcd...ns/LaTeXPrimer/ - the LaTeX primer
http://omega.albany.edu:8008/Symbols.html'>http://omega.albany....08/Symbols.html - some symbols that you might find useful.
If you have any questions about the system, send me a PM and I'll try to help
Cheers.
Scenario: Under the previous process when purchasing goods for the values of $0 to $2,000 we were required to obtain one verbal quote. Now under the new process when we purchase goods for the same values we are required to obtain two verbal quotes.
Example: Under the previous process one quote was obtained for $1,200, under the new process two quotes were obtained for $1200 and $980
Is there any way to quantify the benefit to the organization by following this new process. As under the previous process it would have cost $1,200 but by seeking another quote it cost $980.
]]>
In every R there exists an integer zero element ( -0 )
( -0 ) =/= 0
|0| = |-0|
( -0 ) : possesses the additive identity property
( -0 ) : does not possess the multiplication property of 0
( -0 ) : possesses the multiplicative identity property of 1
The zero elements ( 0 ) and ( -0 ) in an expression of division can only exist as: (0)/( -0 )
0 + ( -0 ) = 0 = ( -0 ) + 0
( -0 ) + ( -0 ) = 0
1 + ( -0 ) = 1 = ( -0 ) + 1
0 * ( -0 ) = 0 = ( -0 ) * 0
1 * ( -0 ) = 1 = ( -0 ) * 1
n * ( -0 ) = n = ( -0 ) * n
Therefore, the zero element ( -0 ) is by definition also the multiplicative inverse of 1 .
And as division by the zero elements requires ( - 0 ) as the divisor ( x / ( -0 )) is defined as the quotient ( x ) .
0 / n = 0
0 / ( -0 ) = 0
n / ( -0 ) = n
0 / 1 = 0
1 / ( -0 ) = 1
1 / 1 = 1
( 1/( -0 ) = 1 )
The reciprocal of ( -0 ) is defined as 1/( -0 )
1/(-0) * ( -0 ) = 1
(-0)^(-1) = ( 1/( -0 ) = 1
(-0)(-0)^(-1) = 1 = ( -0 )^(-1)
Any element raised to ( -1 ) equals that elements inverse.
0^0 = undefined
0^(-0) = undefined
1^0 = 1
1^(-0) = 1
Therefore, all expressions of ( -0 ) or ( 0 ) as exponents or as logarithms are required to exist without change.
Therefore, division by zero is defined.
Therefore, the product of multiplication by zero is relative to which integer zero is used in the binary expression of multiplication.
]]>However, the meter was origionally based on being one billionth the distance between the N. Pole and the Equator thus making the circumference of the Earth an integer in terms of meters.
The meter was later changed to be based on the speed of light to again force the value of c in a vacuum to be an integer in meters/second despite an uncertainty of 4 parts in a billion. i.e. the uncertainty then becomes the length of the meter.
It is the relationship of the speed of light to the circumference of a circle and therefore the length of a sine-wave (2π) that I am interested in confirming my understanding is correct as I am trying to verify that there is a link between wavelength and relativistic effects.
Thanks.
]]>
One teacher described a graph with a decreasing y-axis value and increasing x-axis value as an indirect relationship, wihle another teacher calls this inverse relationship.
What's the difference, what the correct relationship, what do the graphs look like?
]]>I discovered a way of why this is the way it is. Primes and their locations are cause by this multiplicative-odd-number series process:
First the odd numer 3 is multiplied to itself and above 3 odds:
3*3=9
3*5=15
3*7=21
3*9=27
and so on...
Second the next odd of 3 which is 5:(same process like above)
5*5=25
5*7=35
5*9=45
5*11=55
and so on
Third, fouth and so on.This process will continue unto infinity.
let's find out using the above process why 2,3,5,7 are primes below 10.
3*3= 9
5*5=25
here, the odd numbers except 1 are automatically primes below 9 because there is no other way the odd 3 can be multiplied except to itself and above it. Since 3*3= 9 therefore all the odd numbers except 1 are prime numbers. 5*5 also can't accomodate that because it equals to 25.
Note: Below 10 is only an example. Actually it can explain all prime numbers. Sorry for my bad English if you don't understand what I'm saying.
]]>Im new in this forum and in advance I would like to apologise for possibly posting this thread in a wrong place.
I am learning mathematics and I came across this problem that I can't find a solution for:
x^2 - 4^2 = 1000000 , find all possible integer solutions for x and y.
Being an amateur mathematician I tried to understand this problem using system of equations technique and instead of million i used a prime number (5) as an anwser and turned this equation into difference of squares:
(x+2y)(x-2y) = 5;
5 is prime, has two divisors -> 5, 1;
(x+2y) = 5
(x-2y) = 1
2y - 2y = 0 (y is out)
2x = 6
x = 3;
3+2y = 5
2y = 2
y = 1;
Anwser : x = 3, y = 1;
I tried to do similar thing with a million:
(x+2y)(x-2y) = 1000000
let's say (x+2y) = 1000 and (x-2y) = 1000
(x+2y)= 1000
(x-2y) = 1000
2x = 2000
x=1000
y = 0;
But how do you find other solutions to this equation ?
I found these anwsers using brute force algorithm in java:
[[31258, 15621], [12520, 6240], [6290, 3105], [2600, 1200], [1450, 525], [1000, 0]]
is there a formula for finding all of the Integer possibilities? Where should I look ?
Thank you
]]>If you tripple any odd number and add one the result will always be an even number.
If you divide any even number by two, then half of the results will be odd while the other half will be even.
Since every odd number will be changed to an even number by 3n+1 then we know a divide by 2 will always follow. ⇒ for any odd number we can instead apply:
i.e. half of the results for all operations will be odd and the other half will be even.
⇒ half of the time the number will expand to slightly more than 3n/2, while the other half of the time, the number will contract to n/2.
⇒ 3n/2·n/2 = 3n/4
or for the long term average the number will be reduced by 25%.per operation on the series.
For any given positive integer, n, such that all integers < n have already been proven to converge to 1, then any series that drops below n will then converge to one.
Since the long term average is -EV to about 3n/4, then all series must drop below n eventually.
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?
]]>
QUESTIONS:
Does anybody here have good knowledge of supermathematics or related field, to give any input on the above?
If so is it feasible to pursue the model I present in supermanifold hypothesis paper?
And if so, apart from the ones discussed in the paper, what type of pˆdata (training samples) do you garner warrants reasonable experiments in the regime of the model I presented?
No axioms change (except) when involving zero.
The following projection operators allow for no further axioms......
[math]0 = \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) [/math]
0.z1 = 0
0.z2 = 1
[math] P_1 0 = (1, 0) ~ \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) = 1 \cdot 0.z_1 + 0 \cdot 0.z_2 = 0.z_1[/math]
a = 1, b = 0 , c = 0
1 * ( 0 + 0 ) = 1 * 0 + 1 * 0
1 * (0 + 0) = 1 * (0.z1) = 1 * (0.z1) + 1 * (0.z2)
a = 1, b = 1 , c = 0
1 * (1 + 0 ) = 1 * 1 + 1 * (0.z1)
a = 0, b = 0 , c = 0
0 * (0 + 0) = 0 * 0 + 0 * 0
a = 1, b = 0 , c = 1
1 * (0 + 1) = 1 * (0.z1) + 1 * 1
1 = 0, b = 1, c = 0
(0.z1) * (1 + 0 ) = (0.z1) * 1 + 0 * 0
(0.z2) * (1 + 0 ) = (0.z2) * 1 + 0 * 0
]]>
Let every number be arbitrarily composed of two numbers.
Let the number table exist as such…
0=(0,1)
1=(1,1)
2=(2,2)
3=(3,3)
4=(4,4)…and so on
Let no "ordered pair" be represented by another "further" ordered pair.
Let the first number of the number chosen be labeled as z1
Let the second number of the number chosen be labeled as z2
Let multiplication exist as follows…
(A x B) = ( z1forA x z2forB ) = ( z2forA x z1forB ) = ( z1forB x z2forA ) = ( z2forB x z1forA )
Let division exist as follows…
(A/B) = ( z1forA/z2forB )
(B/A) = ( z1forB/z2forA )
]]>