BSHM meeting news

Abstract

s from past meetings History of mathematics and flight Saturday 2 July 2022 Concorde Centre, Manchester Airport A day of talks about the history of mathematics and flight. Flight was broadly conceived to cover the flight of man-made objects and animals; flight formation, navigation and control. The day included a tour of Concorde. Kate Hindle (St Andrews): D’Arcy Thompson and flight D’Arcy Thompson (1860–1948) is most remembered for his influential book On Growth and Form (1917), which looked to maths to explain why biological creatures take the shapes that they take. In January 1917, a few months before this book was released, Thompson had a letter to the editor published in Nature titled ‘Stability in Flight’. A month later Herbert Maxwell (1845–1937) – a baronet, politician, and fellow of several learned societies – published a letter in Nature as a criticism of Thompson’s work. Thompson reacted to this criticism with a defensive response letter, showing that he was affected by it. This exchange also highlights how Thompson conceptualized advancements in maths as a guiding light for biology, showing how his views on flight coincide with his other biomathematical work. Jane Wess (Independent): Benjamin Robins: Elegant Mathematics Versus Experimental Inconvenience? While academically a constituent of fluid mechanics, practically ballistics was an important area of knowledge for nation states in the eighteenth century. William Mountaine, a mathematics teacher, wrote in 1781 ‘it is not possible in the nature of things for any one kingdom to continue long in a state of peace, the art of gunnery has from time to time engaged the attention of the most eminent mathematicians’. However, the essential nature of the knowledge of the flight of cannon balls did not result in an efficacious mathematical description for a remarkable length of time. Whereas both Huygens and Newton had acknowledged the role of air resistance, textbooks continued to discuss parabolas following Galileo, Torricelli, Halley, and Cotes until the end of the eighteenth century. The obvious question is ‘why?’ There may be several factors at play, including the status of Robins, who challenged the status quo, but it will be argued that beautiful and simple mathematics can be beguiling. As for the case of epicycloidal teeth in gearing, it seems many of those who advocated a mathematical approach were not completely au fait with the most advanced thinking on the topic, in this case by Huygens, Newton, and of course later and most effectively, by Euler. Deborah Kent (St Andrews): A champion’s counterexample? PG Tait and the flight of a golf ball Nineteenth-century mathematician and physicist Peter Guthrie Tait (1831–1901) is well known for the Treatise on Natural Philosophy, which he co-wrote with William Thomson (later Lord Kelvin), and collaborations with James Clerk Maxwell. Less familiar are his aerodynamical studies from the 1890s, which resulted in over a dozen papers on the path of a rotating spherical projectile. Tait’s culminating work Volume 37 (2022) 259