Williams College

Egg Drop Problems: They Are All They Are Cracked Up to Be!

We illustrate how to invite and excite students about research by exploring higher-dimensional generalizations of the classical egg drop problem, in which the goal is to locate a breaking point using the fewest number of trials. Beginning with the one-dimensional case, we prove t...

Properties of Multidimensional Vector Zeckendorf Representations

A generalization of Zeckendorf’s theorem states for integer k≥3, every nonnegative integer has a unique k-Zeckendorf representation as a sum of distinct k-bonacci numbers, where no k consecutive k-bonacci numbers are present in the representation. Anderson and Bicknell Johnson ex...

Above Room Temperature Ferroelectricity in Epitaxially Strained KTaO 3

ABSTRACT Epitaxial strain is a powerful means to engineer emergent phenomena in thin films and heterostructures. Here, we demonstrate that , a cubic perovskite in bulk form, can be epitaxially strained into a highly tunable ferroelectric. films grown commensurate to (001) substra...