بسم الله ارحمن ارحيم                                 

​        "mathematics is the Black woman of the sciences"
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                  Measure of a sphere:         measure- قدر (qadara)

                    - volume: (4/3) x (3.14) x (radius ^3)

                      - surface area: (4) x (3.14) (radius ^2)



             axiom: the ratio of two natural numbers never equals zero



            theorem:   there is a ratio of two numbers; b /  such that h never equals zero 


                             a  =  b h  ;   h  =  0


                             a x  0  = b  ;   


                 b is not equal to 0  ;  there is no number 'a' multiplied by zero that equals b 


                           

                       example:       =   7 / 0  ;


                                              a x  0   =   7  ;


                                              there is no number 'a'  multiplied by 0 that equals 7












      angular velocity:   m  =   j / k                                                                     -  j (radians) 

       -  k  (time; seconds) 


       time (seconds)  =   radians / angular velocity                                                                                         =  (radians) / (radians s^-1)

                                 =  seconds

      

 angular velocity   =   radians per second ;   radians / s  =   (radians)  x (s^-1)

        - angular velocity is also called angular frequency ;   frequency  =  1/ s  =  s^-1

                                                                                

          - the geometric; circle (planar), is equal to 6.28 radians (360 degrees)

          - circle diameter is 3.14 radians (180 degrees)

          - 1 radian  =  57.30 degrees


            frequency   =   (speed of light) / (wavelength)

                   - speed of light  =  3 x 10^8  m/s

                  when using the speed of light as the value, frequency becomes a type                         of frequency

    


           natural numbers  =  { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ,  . . . . }








Numbers in a set  (a 'set is a group of variables; numerical, that can be defined from common characteristics; function activity. possible origin: kamit; set/ seth)

axiom:  if  m ,  then   p  = r - m   is not equal to  0 .  if    =  r  , then   p  =   r  -  m   is equal to  0  . (maity, ghosh;  analysis differential calculus, 1960)

grouping - organize of variables from common characteristics.  a group of variables define a  set .  the  set  is the manipulative of the system activity/ function activity;

        list of numbers -  1, 2 , 3, 4, 5, 6, 7, 8

further study shows that it is a list of what is called natural numbers .  from the list of natural numbers, we group/ organize the following variables:

             { 2 , 4 , 6 , 8 }

the group of variables are organized from the common characteristic; even numbers.  once a group has been identified for manipulation, the function activity (mechanism) can be observed (experimental).  grouping is significant because it defines the boundaries of your system (as a student, you have to learn that you can create the system; creation - creator, Creator of the heaven and the earth.  as a student, you have to learn how to create the system; you are creating the system, defining the boundaries for what you want your system to do.  your system can be infinite- a system with no boundaries within the universal boundaries of the Creator/ the creation of the heaven and the earth or your system can be finite; the universal boundaries of the creation of heaven and earth are your system boundaries. 


from the above  set  of numbers; { 2, 4, 6, 8 } , you create a function, numerical;  s(m)  =  4 m + 3 , to describe the earth's rotation on its axis.  the variable  m  can represent any of the values in your  se.  this function is describing system activity (planetary).  the values of your function  s(m)  will not be correct because universe boundaries define the earth's rotation on its axis; approximately 24 hours . 


Kamitian Ruler of Measure: notice the infinite measure characters



number analysis: natural numbers {1, 2, 3, 4, ....}


Equality Construction;

- manipulation of magnitude (number value) from increase/ decrease of independent variable


in general, numbers (natural) have a finite/ discrete value (specific).  the value of the number is the magnitude of the number, which can be described in micro-environments (10 ^-9 m - 10^-16 mas the nth dimension spatial position of the value (magnitude) on a number line (the position of a finite object/particle in space/ maatu مات ) from an origin (source/ cause).

مقدار - magnitude (maqad'aara)1. maximum spherical distance; n dimensions, of impact (effect) from origin (cause);{particle physics}  2. number value (manipulation of number value; increase/ decrease); {arithmitic, algebra}

   

 equation 1.          s  =  h   ;          s = 10          =  ?


if variable s is equal to h, and the magnitude of s is 10, than the magnitude of h is 10.   


the understanding of number relations, and construction of equality solutions from variable representations begins with the understanding that different numerical values (natural) for equality are multiples of a coefficient value ; arithmitic expression of multiplication, for equality


  coefficient  س  ;  variable multiple of a numerical value/ magnitude

            

                  s = h                                       sس h ;                                 s س h                       * variables are not numerically (magnitude) defined; non-discrete/ infinite;

           10 x 1 =  1 x 10  = 10                       10 = 1 x 10                              10 =  2 x  5                               values /solutions have to be solved for/constructed


function;      r (س)   =  س  h   =  s ;


                       s   =   h       ;       s   =  س h