Category : Research Papers
Sub-Category:
Mathematics and Applied Mathematics
Language: English
Title: MIRACLE EQUATION-CAN BE USED TO SOLVE 3 VARIABLES IN A SINGLE EQUATION
Date Published: 27-9-2013
Keyords:
NumberTheory, Theorem.
Abstract:
Before 2013, you required 3 equations to solve 3 variables. Now it isnt necessary.
PROOF
MIRACLE EQUATION-CAN BE USED TO SOLVE 3 VARIABLES IN A SINGLE EQUATION.
Seems Impossible.
But here is the proof.
MIRACLE EQUATION:
[(NX )² ― {(N―2) X }² ] =[N―(1―X²)]²―[N―(1+X²)]²
The above equation which is true for all real values of N and X,is actually analogous to the equation
[A²―B²] = C ²―D ² where A = NX ,B = (N―2) X , C = [N―(1―X²)] & D=[N―(1+X²)] where .A,B.C & D are four variables. One way of analyzing the same is, if anyone chooses one of these variables either A,B,C or D,the remaining 3 variables can be found out,by applying suitable values to N and X,in the considered variable and the other variables turn out correspondingly to the same.
The second case or application is given below.
Now ,there is an interesting application wherein ,we can utilize this equation to solve 3 unknown
variables in a single equation.
Assuming the 3 variabled equation is of the form
ax + by + dz = k where a ,b ,d are coefficients x , y , z are variables and k is the constant . Solution is given
by x = A²/a, y = B²/(-b) and z= D ² /d , since equaton is of the form A²―B²+D ² = C ²
Hence the solution to the equation 2x + 3y + 4z = 16
HERE C = 4 . Arbitrarily selected values of N = 1 , X = 2 to satisfy C=[ N―(1―X²)]
Ergo , x = 2, y = - 4/3 and z = 4. Alternatively. let us substitute X as any rational number .X can assume infinite values.Albeit, if X is real we get only approx. solutions. We could generate different values of N = C + 1 - X² ,corresponding to X equal any rational number)we can threreby get infinite solutions to this equation.We could resort to algorithm and programming at this stage,since a general equation is involved and a trinitarian aspect could be proved. Please note that C = √k
PN: When k is a perfect square , calculations are simple. Otherwise,multiply k by itself.For the equation to remain unchanged multiply each term of LHS by k and then resort to the steps like below
Suppose one need to solve
2x+3y+4z=13 Taking the necessary steps,the equation becomes ie multiplying each term in the given equation by k = 13,it transforms into
26x+39y+52 z= 169,therefore x= A²/a,y= B²/(-b) and z= D ² /d
HERE C= 13, If selected value of X=2, N = k+1 - X²=13+1- 4=10
Therefore x= 400/26=200/13, y=256/-39= -256/39 and z= 25/52
Take another value of X = 25,then N= k+1 - X²= 13+1-225= -211.
A= NX= 5275
B= (N―2) X= 5325
D=[N―(1+X²)] = 837
x= A²/a= 1070216.345
,y= B²/(-b)= - 727067.3077 and
z= D ² /d =13472.48077
Verification 26x+39y+52 z= 169
26(1070216.345)- 39(727067.3077+52(13472.48077)=169 (hence verified)  Category:Research Papers
Sub-Category:
Mathematics and Applied Mathematics
Language:
English
Title: Revoutionary analysing and interpreting the 2500 year old Pythagoras theorm
Date Published:
21-9-2013
Keyords:
NumberTheory,Pythagoras Theorem,Right Triangles.
Abstract:
It is astonishing to note that the 2500 year old,Pythagoras Theorem could be revolutionarily
analysed and interpreted, in a two variable case and in a one variable case ,with the aid of
axioms that have been deduced by me.
PROOF
Revoutionary analysing and interpreting the 2500 year old Pythagoras theorm.
Understanding the Pythagoras theorm,is essential or played a very great role in my analyzing the
Special Theory Of Relativity.Now,what I have deduced regarding the Pythagoras theorem
.If the hypotenuse of a right triangle,is the average of two numbers say .A and B ie (A+B)/2,then
the legs are (A-B)/2 and √(AB)
.
Another way of stating the Pythagoras theorem is,if the hypotenuse is product of two real
numbers N and X ie (NX),then the legs are,the smaller leg is {2 X √(N-1)} and the longer leg is
{X(N-2)},for large values of hypotenuse,where definitely, X<1.
Earlier,I reduced it to a two variable case.Now,I have reduced it to a single variable case.In that
case X is any real number and need not be less than 1. The hypotenuse is A and the legs are(n-
2)(A/n) and {2(A/n) √(n-1)} what I have done is substitued N=n and X= A/n and removed the
condition X<1.Also,note here n can be any whole number we substitute
.
One could also,have the hypotenuse as [(N-1)+X²] and then the legs could be [(N-1)-X²] and {2
X √(N-1)}
Putting suitable values in the above Pythagorean triplets can be generated  3. Domain of Relativistic Mechanics.
Abstract : .It is astonishing to note that ,the Special Relativity Theory Equations
are incongruous beyond one-third the speed of light, by mere Number Theory
considerations ,specifically time dilation and length contraction equations.
Nevertheless, there is an exception to this theory,for particles of masses less than
1kg, or time intervals between events which are less than 1s or length
contraction less than 300000km ,where it could be absolutely accurate as
Einstein predicted and therefore it implies,these could change upto only
6.07%,approximately.
Keywords: Relativity,time dilation,length contraction,mass variance,
number theory,algebraic formulae.
Proof
Introduction
Since the mathematicians invaded Relativity,I do not understand it anymore--- Albert Einstein.
This statement by Einstein,gives the general feeling that he was not convinced that the Theory of
Relativity was absolute.The onus is on me,therefore to prove that the Special Theory of
Relativity,has limitations and domain of relativistic mechanics is one-third the speed of light.,for
particles of masses greater than 1 kg, time events greater than 1second as well as length
contraction greater than 300000kms(approx.)
If you cant explain it simply,you dont understand it well enough.
Time travel is therefore an illusion. Science is really about demystification.The crowning glory of
my achievement is merely Number Theory and Miracle Equation are utilized to achieve
this. Miracle Equation is an equation,capable of solving 3variables in a single equation
Incredulous isnt it. Abstract:
Before 2013, you required 3 equations to solve 3 variables. Now it isnt necessary.
.
PROOF
MIRACLE EQUATION-CAN BE USED TO SOLVE 3 VARIABLES IN A SINGLE EQUATION.
SEEMS IMPOSSIBLE.
BUT HERE IS THE PROOF
MIRACLE EQUATION:
[(NX )² ― {(N―2) X }² ] =[N―(1―X²)]²―[N―(1+X²)]²
The above equation which is true for all real values of N and X,is actually analogous to the equation
[A²―B²] = C ²―D ² where A= NX,B=(N―2) X,C=[N―(1―X²)] & D=[N―(1+X²)] where .A,B.C & D are all variables.One way of analyzing the same is,if anyone chooses one of these variables,the remaining 3
variables can be found out.The second case is given below.
Now ,there is an interesting application wherein ,we can utilize this equation to solve 3 unknown
variables in a single equation.
Assuming the 3 variabled equation is of the form
ax+by+dz=k where a,b,d are coefficients,x,y,z are variables and k is the constant.Solution is given
by x= A²/a,y= B²/(-b) and z= D ² /d
Hence the solution to the equation 2x+3y+4z=16
HERE C= 4 . Arbitrarily selected values of N=1, X=2 to satisfy C=[ N―(1―X²)]
Ergo , x=2, y = - 4/3 and z=4.Substituting different satisfying values(any real number) to N and X to make C = 4,(for instance you could generate different values of N = C+1- X² ,corresponding to X equal any real number)we can threreby get infinite solutions to this equation.We could resort to algorithm and programming at this stage,since a general equation is involved and a trinitarian aspect could be proved.
PN:When k is a perfect square,calculations are simple. Otherwise,multiply k by itself.For the equation
to remain unchanged multiply each term of LHS by k and then resort to the steps like below
Suppose one need to solve
2x+3y+4z=13 Taking the necessary steps the equation becomes
26x+39y+52 z= 169,therefore x= A²/a,y= B²/(-b) and z= D ² /d
HERE C= 13,Arbitrarily selected values of N=10 and X=2
Therefore x= 400/26=200/13,y=256/-39= -256/39 and z= 25/52 We should also be educated in the Pythagoras Theorem to achieve the same. Abstract:
It is astonishing to note that the 2500 year old,Pythagoras Theorem could be revolutionarily
analysed and interpreted, in a two variable case and in a one variable case ,with the aid of
axioms that have been deduced by me.
PROOF
Revoutionary analysing and interpreting the 2500 year old Pythagoras theorm.
Understanding the Pythagoras theorm,is essential or played a very great role in my analyzing the
Special Theory Of Relativity.Now,what I have deduced regarding the Pythagoras theorem
.If the hypotenuse of a right triangle,is the average of two numbers say .A and B ie (A+B)/2,then
the legs are (A-B)/2 and √(AB)
.
Another way of stating the Pythagoras theorem is, if the hypotenuse is product of two real
numbers N and X ie (NX),then the legs are,the smaller leg is {2 X √(N-1)} and the longer leg is
{X(N-2)},for large values of hypotenuse,where definitely, X<1.
Earlier, I reduced it to a two variable case.Now,I have reduced it to a single variable case.In that
case X is any real number and need not be less than 1. The hypotenuse is A and the legs are
(n-2)(A/n) and {2(A/n) √(n-1)} what I have done is substitued N=n and X= A/n and removed the
condition X<1.Also,note here n can be any whole number we substitute .
.
One could also,have the hypotenuse as [(N-1)+X²] and then the legs could be [(N-1)-X²] and {2
X √(N-1)}
Putting suitable values in the above Pythagorean triplets can be generated
TIME DILATON EQUATION
t = t′ /[√ (1― v²/c²) ]
where t is the time measured in S frame is slower than the time t′ measured in inertial frame S′
by time dilation equations.In all these cases, c stands for velocity of light and equal to it,whereas
v is the velocity of the frame S′ with respect to S. On rearranging the relativistic
equation ,simplifies to( t′c)²=(tc )²―(tv)²,which finally leads to
(t′)²=(t)²―( tv/c)²
Note that each term in the modified form of the TIME DILATION EQUATION has the same
units.Units have no relevance and it can now be considered part of Number Theory.Comparing
both these equations,MIRACLE EQUATION and modified form of TIME DILATION
EQUATION.vital observations
Miracle Equation reduces to
[(NX )² ― {(N―2) X }² ] =4(N-1) X², tv/c corresponds or is equal to(N―2) X and t corresponds to(N) X
Ie( tv/c)/t =(N―2) X /(N)X
Ie v/c=(N―2)/N Therefore Ie v/c=(N―2)/N ie c stands for 3 meaning 300000 kms/s,N=3 therefore v= 3-2=1 meaning 100000kms/, therefore the Special Relativity Theory Equations
are incongruous beyond one-third the speed of light, by mere Number Theory
considerations ,specifically time dilation and length contraction equations.
Nevertheless, there is an exception to this theory,for particles of masses less than
1kg, or time intervals between events which are less than 1s or length
contraction less than 300000km ,where it could be absolutely accurate as
Einstein predicted and therefore it implies,these could change upto only
6.07%,approximately.For proof to the exception go to the journal link attached below Domain of Relativistic Mechanics - IJSER Journal Publication
points.Firstly,presently we see ,highest common factor of (t′),(t)&( tv/c) is 1.This has to be
understood in its context.Secondly,the Miracle Equation both sides has to be multiplied by
k,where k stands for any positive number,whatever possible values it can assume,so that it
becomes fully identical to modified form of TIME DILATION EQUATION and therefore(t′),
(t)&( tv/c) can attain any variations of values that may be possible.
(hence concluded.)
11.References
University Physics by Sears,Zemanski &Young.
The Feynmann Lectures by Richard P.Feynmann,Matthew W.Sands &Robert B.
Leighton.
Special Theory of Relativity by Resnick.
Fundamentals of Physics by Halliday,Resnick &Walker.
Author
Independent Researcher,
Cochin, Kerala, India
Mob:+91-9895854062
Email:koshy68@gmail.com
Domain of Relativistic Mechanics - IJSER Journal Publication
IJSER is an open access international journal online facilitating the publication of scholarly, peer reviewed journals in the field of science & engineering.
IJSER.ORG  4. Dear 07CAUCHY'S,

May I ask you a question? What is the purpose of this thread? Do you wish to ask a question, start a discussion or state the existence of a few papers?  5. I merged these posts, from, three different threads, into this one thread. The title of each post was the titles used above, i.e. "MIRACLE EQUATION-CAN BE USED TO SOLVE 3 VARIABLES IN A SINGLE EQUATION", "Revoutionary analysing and interpreting the 2500 year old Pythagoras theorm" and "Domain of Relativistic Mechanics"  Posting Permissions
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