# Category Archives: Equations

## Q: How does “1+2+3+4+5+… = -1/12” make any sense?

Physicist: When wondering across the vast plains of the internet, you may have come across this bizarre fact, that , and immediately wondered: Why isn’t it infinity?  How can it be a fraction?  Wait… it’s negative? An unfortunate conclusion may … Continue reading

Posted in -- By the Physicist, Equations, Math, Number Theory | 14 Comments

## Q: What determines the size of the bright spot when you focus sunlight with a lens?

Physicist: This question really appeals to my ten-year-old self.  If you’ve never tried to burn something with a lens, collect three pairs of sunglasses, a magnifying lens, and something you dislike.  On a bright day, put on all three pairs … Continue reading

## Q: Why are numerical methods necessary? If we can’t get exact solutions, then how do we know when our approximate solutions are any good?

Physicist: When a problem can be solved exactly and in less time than forever, then it is “analytically solvable”.  For example, “Jack has 2 apples and Jill has 3 apples, how many apples do they have together?” is analytically solvable.  … Continue reading

Posted in -- By the Physicist, Computer Science, Equations, Math | 11 Comments

## Q: Is there such a thing as half a derivative?

The original question was: Another one of those questions of the type “does this make sense”.  You have first derivatives and second derivatives.  f'(x), f”(x) or sometimes dy/dx and d^2y/dx^2. Is there any sensible definition of a something like a “half” … Continue reading

Posted in -- By the Physicist, Conventions, Equations, Math | 13 Comments

## Q: How do I know my windmill is on straight?

The original question was: I got quite the challenge from my father in law. The problem is well defined, but I’m having difficulties finding a meaningful answer. The reason why he asked me is because I’m an engineering student and … Continue reading

Posted in -- By the Physicist, Engineering, Equations, Geometry, Math | 4 Comments

## Q: Since it involves limits, is calculus always an approximation?

Physicist: Nope!  Calculus is exact.  For those of you unfamiliar with calculus, what follows is day 1. In order to find the slope of a curve at a particular point requires limits, which always feel a little incomplete.  When taking … Continue reading

Posted in -- By the Physicist, Equations, Math | 2 Comments