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So I was bored and decided to find some simple equations to deal with relativistic geometric edges and angles at an angle to the direction of movement.

[tex]L=L_0\sqrt{(\frac{\cos(\Delta\theta_0)}{\gamma})^2+(1-\cos(\Delta\theta_0)^2)^2}[/tex]

[tex]\Delta\theta=\tan^{-1}(\gamma\frac{\sqrt{1-\cos(\Delta\theta_0)^2}}{\cos(\Delta\theta_0)}[/tex]

Where

[tex]L[/tex] is the relativistic length of the edge

[tex]L_0[/tex] is the rest length of the edge

[tex]\Delta\theta[/tex] is the “relativistic angle” between the edge and the direction of motion.

[tex]\Delta\theta_0[/tex] is the “rest angle” between the edge and the direction of motion.

[tex]\gamma[/tex] is the Lorentz factor of the object, [tex]\frac{1}{\sqrt{1-\beta^2}}[/tex]

Tell me what you think.

[tex]L=L_0\sqrt{(\frac{\cos(\Delta\theta_0)}{\gamma})^2+(1-\cos(\Delta\theta_0)^2)^2}[/tex]

[tex]\Delta\theta=\tan^{-1}(\gamma\frac{\sqrt{1-\cos(\Delta\theta_0)^2}}{\cos(\Delta\theta_0)}[/tex]

Where

[tex]L[/tex] is the relativistic length of the edge

[tex]L_0[/tex] is the rest length of the edge

[tex]\Delta\theta[/tex] is the “relativistic angle” between the edge and the direction of motion.

[tex]\Delta\theta_0[/tex] is the “rest angle” between the edge and the direction of motion.

[tex]\gamma[/tex] is the Lorentz factor of the object, [tex]\frac{1}{\sqrt{1-\beta^2}}[/tex]

Tell me what you think.

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