Matpic
mathematics, in pictures
The collection

Every essay — page 12

Page 12 of 12, continuing through the fields in the same order.

Geometry Analysis Algebra Discrete Topology Probability Number Dynamics Logic Computation Applied What's new Ladders Concepts Search

Applied

A rule for choosing, stated exactly, and what it forces on whoever adopts it.

Every order of arrival for three users of one shared capacity, and what each player adds. A table with one row per order in which the players could arrive, giving what each adds to the group already present, and the average of each column as that player's share.

Sharing a cost that is not the sum of its parts

Three users need capacities three, six and twelve of one shared thing, and serving any group costs the largest of them. Averaging what each adds over every order of arrival divides the bill — and for this family the average collapses to a rule anybody could apply by hand.

6 figures · new