Relativistic Pythagorean Theorem

[jgrafton]

In physics today, while doing linear transformations with Lorentz transformations, we learned that the Pythagorean Theorem seems to not hold up - the hypotenuse is shorter than its legs.

Could math seriously be broken? Of course not - you just need to add the relativistic correctional factor. A little bit of scribbling in my notes reveals the following:



And so the world is still complete. Obviously this does not corrupt the original definition, since for relatively low v the correctional factor can be ignored.

(Yes, I know this is horribly broken, and probably not symmetric and probably doesn't make sense. But I can have fun anyway, right?)

Comments

[jgrafton]

I can explain it more fully in person sometime if you'd like.