# What is the meaning of this (potentially humorous) mathematical equation?

The equation in the image shown below (outlined in blue) was found on the cover of a magazine, along with several other "math equation jokes" like the "I heart pi" joke. My friends and I haven't been able to figure this one out, and I can't seem to identify the last part of the equation.

It's obvious that the first part (square root of negative one) is "I", and the heart symbol is self-explanatory. I suspect that "$mc^2$" corresponds to "e" (but perhaps this is intended to be purely phonetic, or maybe intended to mean "energy").

• After looking over this extensively, I have concluded this is completely meaningless. Maybe this is the discovery of a whole new type of artistic mathematics? – Asimov Sep 10 '14 at 22:46
• @LoganMaingi That is a very good guess for a random guess. – Lord Soth Sep 10 '14 at 22:55
• @LoganMaingi It then becomes "I love MC Squareo," where MC Squareo is somebody like MC Hammer. – Lord Soth Sep 10 '14 at 22:56
• @LoganMaingi Ah! I think that might solve it! The magazine is from Edmund Optics, so "I ♥ E O" seems to be logical (and clever, I suppose). Gosh, now I feel like the message just ended up being "Be sure to drink your Ovaltine"... – Evan Wondrasek Sep 10 '14 at 22:57
• @LoganMaingi Want to promote your comment to an answer? I think you earned a green checkmark for this one. – Evan Wondrasek Sep 10 '14 at 23:04

• $\sqrt{-1}$ is referring to $i$, the imaginary unit. $i$ satisfies the equation $i^2 = -1$. This is sometimes written as $i = \sqrt{-1}$, though this is abuse of notation in some cases depending on your definition of $\sqrt{}$.
• $E = mc^2$ is Einstein's formula for the rest mass-energy of a massive body. $m$ is the rest mass (or invariant mass), and $c$ is the speed of light.
• $\frac1f=\frac1i+\frac1o$ is the thin lens equation, which describes the distances of an object and the image of that object (which may be real or virutal) relative to a thin refractive lens in geometric optics. $f$ is the focal length of the lens which is defined by this formula in the limit $o \rightarrow \infty$.
Those number 1's are sloppy -- or is the bracketed amount on the right actually $-2$ instead of $-1$. I will assume $-1$.
Then, the item in brackets can be rewritten as $$\frac{if}{f-i}$$