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QUESTION: Dear Prof Scott

http://en.wikipedia.org/wiki/Analytic_geometry

http://www.mathopenref.com/coordintro.html

http://www.math.com/school/subject3/lessons/S3U1L2GL.html

http://c-schools.net/PPT/Coordinate%20Geometry.ppt

http://www.youtube.com/watch?v=7h74ad7IWiI

http://www.math.wisc.edu/~robbin/461dir/coordinateGeometry.pdf

http://www.wolframalpha.com/examples/CoordinateGeometry.html

What could be the Impact to different disciplines and applications

of mathematics if Point (x,y) is replaced with Point (y,x).

i.e. x coordinate = Horizontal axis

y coordinate = Vertical axis

Now instead of this standard convention, implement the following

given below

i.e. x coordinate = Vertical axis

y coordinate = Horizontal axis

For examples :

1st Quadrant Point A(3,2) will become Point A(2,3)

2nd Quadrant Point B(-2,3) will become Point B(3,-2)

3rd Quadrant Point C(-3,-4) will become Point C(-4,-3)

4th Quadrant Point D(2,-3) will become Point D(-3,2)

i.e. because the Points are now represented as y,x instead of x,y,

the Plotting of Points A,B,C,D on graph paper will be now different.

Can there be any impact while plotting Graphs viz Sine,Cosine, Tangent waves etc, vector algebra and other applications of mathematics similar to Coordinate Geometry if Point F (x,y) is represented as Point F(y,x) ?

Awaiting your reply,

Thanks & Regards,

Prashant S Akerkar

ANSWER: I'm sorry I don't have much time to read the articles that were sent,

but the only function I know that does this is saying f(x,y) = (y,x).

In other words, to get the value of the function, reverse the original values.

---------- FOLLOW-UP ----------

QUESTION: Dear Prof Scott

Thank you.

http://en.wikipedia.org/wiki/Sine_wave

Can the interchange of x - horizontal axes to y - horizontal axis and y - vertical axis to x - horizontal axes will effect the Sine, Cosine, Tangent and other trigonometric curves plotting ?

i.e. Will the Sine Wave plotted now will be seen in a different wave ?

This could be because the coordinates (0, 30 degree, 45 degree, 60 degree, 90 degree, 120 degree, 150 degree, 180 degree or respective conversion to radiant etc) will be plotted now on the Y axis ?

http://www.intmath.com/analytic-trigonometry/7-inverse-trigo-functions.php

Can the interchange of x - horizontal axes to y - horizontal axis and y - vertical axis to x - horizontal axes will effect the Sine Inverse, Cosine Inverse, Tangent Inverse and other trigonometric curves plotting ?

i.e. Will the Sine Inverse Wave plotted now will be seen in a

different wave ?

Awaiting your reply,

Thanks & Regards,

Prashant S Akerkar

ANSWER: It will flip the graphs by 90 degrees,

Note that when this is done, there need to be limits imposed to still have a function.

Once x and y have been switched, there needs to be one and only one x for each y.

---------- FOLLOW-UP ----------

QUESTION: Dear Prof Scott

Thank you.

What could be the Impact to different disciplines and applications

of mathematics if Point (x,y,z) is replaced with Point (z,y ,x).

i.e. Three (X,Y,Z) dimensional instead of Two Dimensional (X,Y Axis).

i.e. Point A (2,3,4) will become Point A (4,3,2)

Awaiting your reply,

Thanks & Regards,

Prashant S Akerkar

If the function is 1-to-1, the only difference between the dx, dy, and dz values would be that they were interchanged. If the function were not 1-to-1, mathematics could not be applied.

For example, even sin(x) on [0,2*pi] if a function, but the inverse is not unless the x range is restricted to a width of pi.

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Comment | Dear Prof Scott Thank you. Thanks & Regards, Prashant S Akerkar |

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