A Curious Property of Tangents

Summary

We give two proofs of a surprising elementary result concerning tangents drawn to the graphs of convex functions.

Notes

1 A supporting line for a set $G\subset {\mathbb{R}}^2$ is a line that touches G at at least one point, and with G lying entirely on one side of the line. For example, the graph of $y=\left|x\right|$ has supporting lines y = mx for $-1⩽m⩽1$.

Additional information

Notes on contributors

David Treeby

Marty Ross ([email protected]) is a mathematical nomad, currently residing in Melbourne, Australia. He can occasionally be spotted helping out The Mathologer.

Marty Ross

David Treeby ([email protected]) completed his PhD at Monash University, in Australia. He now teaches mathematics at Scotch College in Melbourne.