Question

How can we represent the 3 space coordinates uniquely by one point that can be put on a single axis?

Answer 1

the Space-Time diagram (in the rest frame) we often take the Space axis as the horizontal axis and the time axis as the axis perpendicular to it as in the given figure.

While there are other models to graphically represent space-time, my question is:

What function f(x,y,z) on a 3 dimensional surface can we define such that no two distinct points (x1,y1,z1) and (x2,y2,z2) shall have the same value?

i.e f(x1,y1,z1)=f(x2,y2,z2) if and only if x1=x2, y1=y2 and z1=z2

That way every point in the X axis of the figure will represent a unique point in 3-D space.

Answer 2

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✔️✔️f(x,y,z) on a 3 dimensional surface can we define such that no two distinct points

(x1,y1,z1)

and

(x2,y2,z2)

shall have the same value

i.e f(x1,y1,z1)=f(x2,y2,z2) if and only

if x1=x2, y1=y2 and z1=z2 That way every point in the X axis of the figure will represent a unique point in 3-D space.

the presence of a coordinate system which allows one to ...

If every point in the space can uniquely be ... Page 3 ...

Simply put, it is the angular distance to the.


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