# Lorentz transformation

Dark_knight90
Hello
This is a part of a simple paper about special relativity

[PLAIN]http://img15.imageshack.us/img15/8789/91001769.jpg [Broken]

I don't understand the assumption in the red box .. why are they all squared ?

thank you

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Mentor
Do you remember the Pythagorean rule? In two-dimensional space, $\Delta x$ and $\Delta y$ are the lengths of two sides of a right triangle, and $\Delta r$ is the length of the hypotenuse:

$$(\Delta r)^2 = (\Delta x)^2 + (\Delta y)^2$$

What you have is the three-dimensional version.