# Minkowski diagram

I have not well understood the picture of geogebra regarding the angle of time (t') that is inclined compared to (t) of 26.57°angle . In the picture we see that the velocity is setted at 0.5c, for which i belivied that if with c = 1 is represented by a 45° inclined line, and now we want draw a speed of 0.5c, all we have to do is divide 45° by 2 and we obtain an inclinatio of 22.5°... Somewere i have read that to have the correct inclinatio we have to do this calculation : new angle = arctan(0.5/1) = 26.57° This is the correct solution but i have not understood why...

Coordinates of the original frame as functions of coordinates of moving frame are given by inverse lorentz transform: $$ct=\gamma\left(ct'+\beta x'\right)$$ $$x=\gamma\left(x'+\beta ct'\right)$$ Now imagine point on the $$ct´$$ axis, lets say $$(ct´,x´)=(1,0)$$. This point will have coordinates in the original frame $$(ct,x)=(\gamma,\gamma\beta)$$ from which the slope is given by: $$\tan\alpha=\frac{\gamma\beta}{\gamma}=\beta$$