Tag: maths

  • A brief history of three-dimensional manifolds

    First published November 24, 2022

    We give a broad-brush account of some milestones in the theory of 3-dimensional manifolds, particularly the Poincaré Conjecture and its proof. We also discuss Thurston’s Geometrisation Programme.

  • Measuring angles within arbitrary metric spaces

    First published October 02, 2020

    We will generalise the concept of angles in Euclidean space to any arbitrary metric space, via Alexandrov (upper) angles.

  • Hilbert's hotel, but the guests are mere mortals

    First published July 26, 2020

    We will consider a variation of Hilbert’s hotel, within which guests may not be relocated too far from their current room.

  • An upper bound on Ramsey numbers (revision season)

    First published May 02, 2019

    I will present a short argument on an upper bound for \( r(s) \), the Ramsey Number associated with the natural number \(s\).

  • Counting derangements

    First published April 21, 2019

    I present an inefficient yet novel way of recursively counting derangements of a set, and generalise this to counting permutations without short cycles.

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