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2. **Naming**
 > "What's this phenomenon or behavior called?"

Sometimes we feeding one initial value into a function to get a first result, and then feeding that result into the same function to get a second result.

If the second result is always the same as the initial value,
no matter what the initial value is,
the behavior is called an ["involution"](https://en.wikipedia.org/wiki/involution_(mathematics)).

In cryptography, this behavior is called a ["reciprocal cipher"](https://en.wikipedia.org/wiki/Symmetric-key_algorithm#Reciprocal_cipher).

1. **Intuition**

 > "what's the intuition ...?"

       x columns

    o o o o o o o o o
    o o o o o o o o o  y rows
    ...
    o o o o o o o o o
    o o o o o o o o o
    

Say we have some total number of rocks C
and we line them up in rows and columns.

After we start placing C in x columns,
there's going to be some number y=C/x of rows of rocks.

If we take those same C rocks and start placing them in y columns,
there's going to be some number z=C/y of rocks per column.

It's relatively intuitive to me that we can rotate how we look at that rectangle without changing C, so we can see it as either dividing those C rocks into x columns, or dividing those C rocks into y columns,
so z must equal x.
(At least, it's clear to me when x and y are both integers; perhaps there's a more intuitive approach when x or y or both are not integers).