In plane coordinate geometry the numerical expression in terms of X and Y does not specify the slope at the point (X,Y), what ever value we may assign to the cordinates X and Y; coordinates (X,Y) and the slope or the Tangent AT (X,Y) are/remain independent variable. Therefore the numerical expression (formula) does not reveal how the slope (Tangent) varies between any two points (x1,y1) and (x2,y2) or between (x2,y2) and (x3,y3). Therefore in coordinate geometry we have only logical ways of 'connecting' any two consecutive points: (1) connect (x1,y1) and (x2,y1) then connect (x2,y1) and (x2,y2). This way we construct 'curvature' of a 'curved' line in terms of infinitely small 'steps' in the shape of right angles. (2) connect (x1,y1), (x2,y2), (x3.y3) etc by a series of straight lines. In this case each of the points (x1,y1), (x2,y2), (x3,y3) etc. conceal within themselves infinite number of 'slopes' or Tangents, which should logically have benn distributed in the space between the points. Coordinate geometry is not what it pretends to be; it only generates a system of configuration of disconnected points. The problem with numerical expressions is that there are always 'numbers' between any two 'consecutive' (specified) numbers. Therefore, unless we eliminate numbers we cannor GET lines and surfaces. May the noble minded scholars kindly correct any error committed through dullness of my intellect.
> In plane coordinate geometry the numerical expression in terms of X > and Y does not specify the slope at the point (X,Y), what ever value > we may assign to the cordinates X and Y; coordinates (X,Y) and the slope > or the Tangent AT (X,Y) are/remain independent variable. Therefore the > numerical expression (formula) does not reveal how the slope (Tangent) > varies between any two points (x1,y1) and (x2,y2) or between (x2,y2) and > (x3,y3). Therefore in coordinate geometry we have only logical ways of > 'connecting' any two consecutive points: (1) connect (x1,y1) and (x2,y1) > then connect (x2,y1) and (x2,y2). This way we construct 'curvature' of a > 'curved' line in terms of infinitely small 'steps' in the shape of right > angles. (2) connect (x1,y1), (x2,y2), (x3.y3) etc by a series of straight > lines. In this case each of the points (x1,y1), (x2,y2), (x3,y3) etc. > conceal within themselves infinite number of 'slopes' or Tangents, which > should logically have benn distributed in the space between the points. > Coordinate geometry is not what it pretends to be; it only generates > a system of configuration of disconnected points. The problem with > numerical expressions is that there are always 'numbers' between any two > 'consecutive' (specified) numbers. Therefore, unless we eliminate numbers > we cannor GET lines and surfaces. > May the noble minded scholars kindly correct any error committed through > dullness of my intellect.
There're these new invention called "sentences" and "paragraphs". You might want to investigate them. Stream-of-consciousnes is inappropriate in the groups posted to.
> In plane coordinate geometry the numerical expression in terms of X > and Y does not specify the slope at the point (X,Y),
Right so far...
> ... what ever value > we may assign to the cordinates X and Y; coordinates (X,Y) and the slope > or the Tangent AT (X,Y) are/remain independent variable.
Do you know how "slope" is defined?
> ... Therefore the > numerical expression (formula) does not reveal how the slope (Tangent) > varies between any two points (x1,y1) and (x2,y2) or between (x2,y2) and > (x3,y3). Therefore in coordinate geometry we have only logical ways of > 'connecting' any two consecutive points: (1) connect (x1,y1) and (x2,y1) > then connect (x2,y1) and (x2,y2). This way we construct 'curvature' of a > 'curved' line in terms of infinitely small 'steps' in the shape of right > angles. (2) connect (x1,y1), (x2,y2), (x3.y3) etc by a series of straight > lines. In this case each of the points (x1,y1), (x2,y2), (x3,y3) etc. > conceal within themselves infinite number of 'slopes' or Tangents, which > should logically have benn distributed in the space between the points.
Do you know how "tangent" is defined?
> Coordinate geometry is not what it pretends to be; it only generates > a system of configuration of disconnected points. The problem with > numerical expressions is that there are always 'numbers' between any two > 'consecutive' (specified) numbers.
Do you know the difference between "describe" and "define"?
> ... Therefore, unless we eliminate numbers > we cannor GET lines and surfaces.
If you eliminate numbers, you cannot GET anything.
> May the noble minded scholars kindly correct any error committed through > dullness of my intellect.
We don't need no steenkin' "noble minds". Math is adequate.
|
