October 31st: A day to celebrate the Witch of Agnesi.
Around the world, October 31st is marked by the celebration of Halloween. On this date, it is common for children to wear costumes, go door-to-door asking for candy, and have fun telling scary stories.
Before becoming a festival for witches, Halloween marked the eve of All Saints' Day, lasted three days, and was dedicated to remembering the dead, saints, and martyrs. Many of the traditions of the current celebration originated from the Celtic harvest festival of Samhain.
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The connection between the date and witches only happened much later. Legend has it that witches gathered at pagan festivals twice a year: April 30th and, obviously, October 31st. To reach these gatherings, they traveled on their flying broomsticks, transformed into other beings, and cast spells and curses on people. Over time, it was proven that this wasn't entirely true. Thus, Halloween acquired new characteristics until it became a global celebration.
And what about mathematics in all this? Well, it's impossible to say that it has a direct connection to October 31st, but one thing is certain: there is one of those magical beings among mathematicians: The Witch of Agnesi.
Agnesi's Witch is the nickname for Agnesi's Curve, which traces the height of a point on the edge of a circle as it rolls along a line.
Quite common in the modeling of certain physical phenomena, the curve is also related to probability functions and can be described as follows: given a circle, take a point O on it. From any other point A on the circle, draw the secant OA. Let M be the point diametrically opposite to O. The intersection between the line OA and the tangent line to the circle at point M is point N. Through A, draw a line parallel to MN, and through N a line parallel to OM. Let P be the intersection between these two lines. The path that P takes as we vary A is called the Curve of Agnesi .
The curve was described by the Italian mathematician Maria Gaetana Agnesi (1718-1799) in the book “ I stituzioni analitiche ad uso della gioventù italiana ”. It ended up gaining the curious name of “Agnesi's Witch” due to a translation error.
It is said that the mathematician John Colson (1680-1760), a professor at Cambridge, learned Italian solely to translate Agnesi's work into English. Upon reading *la versiera di Agnesi* , which means curve of Agnesi, he interpreted it as *l'avversiera *, meaning witch in Italian. Since then, the curve has received this name in many languages.
The Witch of Agnesi was studied by Pierre de Fermat in 1630, but it wasn't until 1703 that a statue was built, designed by Guido Grandi.
So famous were Agnesi and her curve that they became a Google Doodle (above) in 2014, on the 29Fridays anniversary of the Italian mathematician's birth.
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