# Handshakes among justices

It seems I was scooped.

In my ongoing obsession with the law and math (see post I and post II here), I learned that for many years, all the supreme court justices shake hands before each meeting.

The “Conference handshake” has been a tradition since the days of Chief Justice Melville W. Fuller in the late 19th century. When the Justices assemble to go on the Bench each day and at the beginning of the private conferences at which they discuss decisions, each Justice shakes hands with each of the other eight. Chief Justice Fuller instituted the practice as a reminder that difference of opinion on the Court did not preclude overall harmony of purpose. (here)

It still goes on today. There are 9 justices. A natural question: how many handshakes?

The “handshake problem” is a common problem in math classes. It’s equivalent to the problem of calculating the number of diagonals of a polygon. (Each vertex is a person; each line — including the edges of the polygon itself — represents a handshake.) It’s equivalent to adding the numbers $1+2+...+(n-1)$.

I was thinking it would be a good hook for a class where this problem was presented. Better than:

Assume we have n people at a dinner party who all don’t know each other. They all introduce themselves to (yawn) each other… (yawn)… and shake hands. How many (yawn) handshakes are there?

In the same sense that that’s not a true-to-life problem, neither is the supreme court handshake problem. But it’s a hook.

Of course, I looked it up to see if anyone else had thought of it (likely) and guess what? As I said: I was scooped.