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Petrean Chemistry, Euler, and the Bridges of Koenigsberg

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The speaker describes how, some years ago, he investigated the history of one of Euler’s most famous and most easily understood contributions to Mathematics — namely, the problem concerning the Bridges of Königsberg — by making a ‘pilgrimage’ to the presentday Russian exclave/enclave of Kaliningrad, in order to attempt to execute a latterday ‘Eulerian Walk’ over the extant bridges of the modern city. Euler’s published solution to this problem (of 1736) constituted the first paper on what was called Analysis Situs (Analysis of Position). Euler in fact used Leibniz’s term, Geometria Situs (Geometry of Position), a discipline in which all that matters is how entities are connected — in contrast to the more usual geometry in which it is distances and angles that are of importance. Later still, the subject became known as Graph Theory. Euler’s seminal paper is thus generally regarded as having founded the modern subject of Graph Theory (as well as that of Topology). Some 200 years later, this idea of connectivity was fundamental to one of the first quantum-mechanical molecular-orbital theories — due to Hückel in the 1930s — which is applicable to “aromatic” hydrocarbons and other families of conjugated systems. Even though sophisticated ab initio methods of calculation are these days routinely available — and can sometimes yield remarkable accuracy — their frequently complex parametrisations and their dependence on the wave function on which they are based often mask chemical intuition and physical insight; the graph-theoretical (topological) approaches, by contrast, readily give rise to what Coulson once famously described as ‘primitive patterns of understanding.’ The speaker will briefly allude to some recent work carried out at Peterhouse in collaboration with Dr Timothy Dickens on the magnetic properties of some large conjugated systems that arise from so-called ‘topological ring-currents’.

This talk is part of the Kelvin Club - The Scientific Society of Peterhouse, Cambridge series.

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