Maths help?

[LessThanSatisfactory]

Sorry, I know this isn't a maths forum but I need help on my high school math problems. How would you wright the formula for a graph that extended in four dimensions? (3 conventional dimensions + time) I need to figure out how to write a formula for a point in 3 dimensions that corkscrews through the z axis as time passes.... Please help!

[Rashy]

Google....?

[ilikemacandpc]

your high school math is waaaaaaaaaayyyyyy beyond anything my highschool would ever teach...

[FloRolf]

you just add another line like:

X1             T1               S1

X2    +     t T2     +     S S2

X3             T3               S3

X4             T4               S4

 

And i think you need a third paramete too. dunno exactly.

[Rashy]

This thread is getting mathematical.. im abandoning this thread

[Scottonpc]

Think of the x and y axes as having a point on a circle that moves around as you move through the z axis

for a point on a circle with radius 1 the formula for any point on this circle will be x = sin(angle) and y = cos(angle)

x = sin ( a ) and y = cos( a )

a is the angle made between the point and the circle center, and the y axis

therefore if you substitute some multiple of z as the value of a, the point will rotate gradually through the z axis to make a corkscrew

x = sin ( mz ) and y = cos( mz )

a larger value for m makes a more regular corkscrew cycle then in order to make a sense of time you simply alter the phase for each value of t. This is so that the position of the point on each of the planes in the x and y axis have rotated to produce the effect of a rotating corkscrew

therefore you simply substitute a multiple of t into the two equations as follows:

x = sin (mz + nt) and y = cos (mz + nt)

a larger value of n will create a more rapid rotation of the corkscrew

 

if you wanted a different size for the corkscrew, or even an elliptic corkscrew, you just put a value for r1 and r2 in front of the sin and cos like this:

 

Final formula: x = r1 * sin (mz + nt) and y = r2 * cos (mz + nt)

[TideRower]

https://en.wikipedia.org/wiki/Parametric_equation

Look under 3-d example. I suppose that's what you're looking for.

 

However that's not a graph in four dimensions. I think you mean the image of a function going from an interval to the three dimensional room. The graph of this function would be four dimensional, but we obviously can't draw in four dimensions.

Edited April 16, 2014 by TideRower

[StingBull]

No, they don't. Screw maths.

[jezza39]

Use parametric equations to describe how each of the variables are varying with regards to time.

 

i.e. t1 = 2x

      t2 = cos(y)

      t3 = z^2 + 6

 

A corkscrew sounds like a 3d version of the r =  Ɵ which is a polar graph (2D)

[DarrenP]

What grade level math is this... I'm in 11 University math. Never seen this before...

[Jaybird]

Ive taken engineering math and Ive never learned this.