Palindromes on the $\tau$-circle: A note for Palindrome Tau Day, 6/28/26

Abstract

An integer palindrome is a self-reciprocal polynomial evaluated at its base, so its roots are symmetric about the unit circle -- where the coordinate is angle, in turns of $\tau$. Read this way, the date $\texttt{6/28/26}\to 62826$ secretly contains the primitive cube roots of unity -- at angle $\tau/3$ -- along with one further pair of roots on the circle.