engleski

Using history in popularisation of mathematics and the sciences: Honeybees, Bošković and optimisation

One of important goals of popularisation of mathematics, particularly when addressed to general public, is to demonstrate and convince people that mathematics is an important part of our lives and not something mostly unrelated to the human society. History of mathematics is a source abundant in examples showing that mathematicians are/were integral parts of the social and political lives in the time and place they have lived in, and that mathematics is essentially linked to various aspects of the human lives. Additionally, many people think that mathematics has few real-life applications, and history of mathematics provides a sufficient number of examples that this is far from true. One such example is the description (1755.) of the form of honeybee cells achieved by the Croatian scientist Josip Ruđer Bošković (1711.–1787.). Earlier Johannes Kepler noticed that the back wall of a honeybee cell is formed by three congruent rhombi, and their angles were measured to be about 110° and 70°. René Réaumur conjectured that the reason for this is minimisation of the amount of wax used, and although some calculations to prove this were done before Bošković (by Johann Samuel König and Giacomo Filippo Maraldi), Bošković was the first to prove – by geometric and by analytical arguments – was the first to finally and flawlessly prove that the “optimal” angles, i.e. those that result in the smallest possible surface area of the cell for the given volume, are 109°28' and 70°32'. We shall present the basics of Bošković’s proof, with emphasis on this being an example of using history of mathematics in popularisation of mathematics and science in general.

Rudjer Boscovich; description of honeybee cells; popularisation of mathematics

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