The point of E = mc^2 is that mass and energy are fundamentally the same quantity. The longer equation just uses rest mass to illustrate the connection to the classical concept of momentum; neither is more "right" than the other.

Also, E_0 = m_0*c^2, the rest mass being the rest energy, just as E = mc^2 when all the mass and energy are taken into account, since mass and energy are the same thing. Likewise, the equations with the momentum and the one with the Lorentz factor ("gamma") relate the *rest* mass to the *total* energy, which is why they've got more unknowns.

Removed the following:

"* T-shirts such as this. I mean, linear equations with tangent lines? Really?

- The equation next to the graph appears to be the equation of the tangent line, not curve from which the tangent is derived. The curve from which the tangent is derived appears to be a cosine function, not a linear function."

As far as I can tell, the shirt is completely legit. The linear equation is supposed to be the tangent line to the curve, not the other way around.

There was as Simpsons episode where Homer enters a portal into the "mysterious" third dimension. It's one of the Halloween episodes I think. He ends up floating in free space surrounded by formulas. These formulas all made sense and were very clever. I don't remember all of them, but one of them said "P=NP", which would answer The Greatest Question In Computer Science Ever. This could serve as one of the counterpoint examples, where the writers selected their formulas carefully.

Hide/Show RepliesI think that would just be a straight example. The formulas may have all made sense, but unless they had something to do with the plot, they were still just random formulas, and I'd be willing to bet that any significance wasn't intended by the writers.

Its not Enot, its m-> relativistic mass where the relatistic mass relates to the 'normal' mass mnot by the equation m = mnot times the lorentz factor, I would edit, but I obviously don't know how to use subscript.

Removed this example for inaccuracy:

Mandelbrot Set: the procedure described in the lyrics actually generates the Julia set, not the Mandelbrot set.The procedure describes the Julia set because the Madelbrot set is defined by the set of values for which the Julia set won't trend towards infinity, and Coulton describes the Julia set

in this context.