Halloween is almost here and I am sure everyone is into scary things and decorated (or is decorating) their homes with frightening ornaments. I am not here to discuss those ornaments, but I feel that something mathematical would work perfect for that day. If you want to find out more about this chapter check my old post Scary Mathematics. But today and in the next couple of days I want to talk about some specific interesting mathematical concepts. For the start it is “The Which of Agnesi”.
The curve has interesting history. In 1630 was studied by the famous Pierre de Fermat. It took a lot of years until Guido Grandi gave a construction for it. In 1718, Grandi named the curve “versoria”, in a paper if his. The word means “nautical sheet” in Latin. From here another 30 years passed until Maria Gaetana Agnesi published Analytical Institutions for the Use of Italian Youth, which was regarded as the best introduction extant to the works of Euler. In this book she talked about the curve “versoria”. Good to know is that Agnesi was the first woman to write a mathematics handbook and the first woman appointed as a Mathematics Professor at a University.
Time passed and a couple of translations were made of Maria Agnesi work and “versoria” became something else. The first to use the term ‘witch’ in this sense may have been B. Williamson, Integral calculus, 7 (1875). It is believed that the mistake was made due to the fact that “versiora” (latin) was misunderstood for the Italian “versiera” or “avversiera” . The Italian word is derived from Latin ‘Adversarius’, a nickname for Devil, “Adversary of God”, which was synonymous with “witch”. Maybe someone that knows more Italian than me could help us here.
It took even more time to find the practicability of this curve besides its mathematical curve. In early twenty-first century it has been found that the equation of the curve approximates the spectral line distribution of optical lines and x-rays, as well as the amount of power dissipated in resonant circuits. Also, the curve is equivalent to the probability density function of the Cauchy distribution. Moreover, the cross-section of a smooth hill and that of a a single water wave also have a similar shape. This has been used as the generic topographic obstacle in a flow in mathematical modeling.
I hope you found this article interesting. Thank you for your help and support. You can find me on Facebook, Tumblr, Google+, Twitter, Instagram and Lettrs, I will try to post there as often as possible. Don’t forget that maths is everywhere! Enjoy!