Heron's Principle of Reflection
Let a ray of light $L$ travel from $A$ to $B$ by way of a mirror $M$.
Let $B'$ be the mirror image of $B$ so that $M$ is the perpendicular bisector of $BB'$.
Let $P$ be the point where $L$ is reflected from $M$.
The total length of the path of $L$ is $AP + PB = AP + PB'$.
Then $AP'B'$ is a triangle.
But $AP' + P'B$ is longer than $APB$.
Hence $L$ does not pass along the line $AP'B'$.
The result follows by Proof by Contradiction.
However, first she wants to take a drink of water from a river.
She wants to walk as short a distance as possible.
To what point on the riverbank should she walk?
Source of Name
This entry was named for Heron of Alexandria.
While this was merely a deduction of his based on observation, he was completely correct.