The (perverted) pleasures of computation

Lao Chen: The rectangle is 2 m by 1.5 m.
Senior Engineer: Yup, so the diagonal distance would be…

The Senior Engineer picks up a pencil and prepares to perform some squaring operations ala Pythagoras.

Lao Chen: 2.5 m. You scale the dimensions up to 4 by 3, and it becomes a 3, 4, 5 triangle. Scale it back down and you get 2.5 m.
The Senior Engineer: Oh, yes yes. You’re doing it using similar triangles. Very professional…


***

Lao Chen: How much tips did you get today?
Ruth: I don’t know. I worked 9 hours today, so my pay would be 8.5 times 9…
Lao Chen: 9 squared is 81. 9 times 5 is 4.5. 81 minus 4.5 is 76.5.
(Muffled gasps of wonder from back of the car.)
Ruth: So my tips would be [omitted]. I think the Manager paid me an hour less.



Finding existing solutions to compare with an existing arithmetic problem (and them solving it rapidly) gives me a strange pleasure. Of course, it can be used to impressed boys and girls, but that is obviously an utter misuse of mathematics.

You can probably tell that I'm showing off.