GRAVITATIONAL POINT OF A LINE IN A PLANE

GRAVITATIONAL POINT OF A LINE IN A PLANE

ARGUMENT

Most mathematical scientists argue that, since there are infinite many points in a line equation we cannot locate or predict a unique point in a line as our central of gravity.

They also argued that a line equation has an infinite ends. So we cannot locate or determine the ends of a line in a plane; unless a range of points are given that the mid-point of a line can be determined.

In fact, I have disagreed with that philosophy. A line equation has a unique point which I strongly believed as the central of gravity point of a line in plane using a concept called equal pairing concept which was discovered by me between the years 2007-2008.

MATHEMATICAL CHARACTERISTICS OF THE GRAVITATIONAL POINT

1)      It is a unique point at which the axial term of x is equal to the axial term of y in a line equation  Ax + By = C.

2)      At gravitational point of a line equation Ax + By = C in a plane, the value of the axial coordinates x and y is calculated as;

X_G = C / 2A

Y_G = C / 2B

3)      At gravitational point of a line equation Ax + By = C in a plane; the slope of a line equation is given as;

S_G = - ( Y_G / X_G )

ADONGO’S GRAVITATIONAL POINT VALUES INTERVAL THEOREM.

If  x_G Î X_G   and  y_G Î Y_G , where  X_G  contains the possible value of  x_G  and  Y_G  contains the possible value of  y_G. If  X_G  is a corresponding pair of  Y_G  and  x_G  is a corresponding pair of  y_G, then;

( X_G ; Y_G ) = [ ( x_G , x_G – x_G , x_G – x_G – x_G ,- - - - - -) ;( y_G ,y_G + y_G ,y_G + y_G + y_G , - - - - - ) ]

Or

[ ( x_G , x_G + x_G , x_G + x_G + x_G ,- - - - - -) ;( y_G , y_G – y_G , y_G – y_G – y_G , - - - - - ) ]

INTERCEPT OF A LINE

In fact, with the help of the gravitational point vales theorem the intercept of the line is calculated as;

( x_G ; 0 ) Î  ( X_G , 0 ) = (2x_G , 0 )

( 0 ; y_G  ) Î  ( 0 , Y_G) =  (0,2y_G  )

EXAMPLE

If  3x + y = 6 ,  find

         i.            The gravitational pairs, x_G and y_G of the equation.

       ii.            The slope of its graph using Adongo’s gravitations slope formula approach.

      iii.            The intercept of the line.

     iv.            The possible values of  x_G  and  y_G  to fourth interval.

SOLUTION

         i.            The gravitation pairs  x_G  and  y_G  is calculated as;

x_G = C / 2A

x_G = 6 / [ 2 (3) ]

x_G = 1

y_G = C / 2B

y_G = 6 / [ 2 ( 1)]

y_G = 3

       ii.            Slope of the line equation or graph is

S_G = - ( Y_G / X_G )

S_G = - ( 3 / 1 )

S_G = - 3

      iii.            The intercept of the line is calculated as

( x_G ; 0 ) Î  ( X_G , 0 ) = (2x_G , 0 )

                                          = [ 2 (1) , 0 ]  

                                          

                                         = ( 2 , 0 )

And

( 0 ; y_G  ) Î  ( 0 , Y_G ) =  ( 0 , 2y_G  )

                                   = (0 , 2 * 3 )

                                   = (0 , 6 )

     iv.            Applying the gravitational point values interval theorem (GPVIT), we have,

( x_G ; y_G ) Î [ ( X_G ; Y_G ) ] = [ ( 1 , 0 , -1 , 2 , -3 ) ; ( 3 , 6 , 9 , 12 , 15 ) ]

or

[ ( 1 , 2 , 3 , 4 , 5 ) ; ( 3 , 0 , -3 , -6 , -y )]

References

v  ‘’Adongo’s equal pairing concept’’

Developed by William Ayine Adongo.

Mathematical science student (option: Actuarial Science).

University for Development Studies (UDS) year: 2007-2008

v  Adongo’s Ayine William blog

Title: “Adongo’s mathematical profile”

Mathematical science student (option: Actuarial Science).

University for Development Studies (UDS) year: 2009