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Optimal block stacking and combinatorial identities via Archimedes' method

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thesis
posted on 16.01.2018 by DAVID TREEBY
What is the maximum overhang that can be obtained when a set of blocks of variable width are stacked so that there is one block at each level? We determine the configuration of blocks that maximises the overhang when these blocks are stacked in a prescribed order. We also describe infinite sets of blocks of variable width that can be stacked to yield towers with arbitrarily large overhang. Additionally, we consider various symmetric configurations of blocks and point masses in the plane. By considering the centres of mass of such configurations we establish various well-known summation formulas, and discover others that are new and appealing.

History

Campus location

Australia

Principal supervisor

Burkard Polster

Additional supervisor 1

Heiko Dietrich

Year of Award

2018

Department, School or Centre

Mathematical Sciences

Course

Doctor of Philosophy

Degree Type

DOCTORATE

Faculty

Faculty of Science

Exports