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Question

Coordinate Geometry.
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.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) ?

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 ----------

Sine Wave

Sine Inverse Curve
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 ?

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)

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.

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Prof Scott Thank you. Thanks & Regards, Prashant S Akerkar

Volunteer

#### Scott A Wilson

##### Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

##### Experience

Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.