Close to the infinity
Antonis Margaritis, Andreas Varverakis, Ioanna Mountriza, Alexandros Sygkelakis and Irini Perissinaki On Wednesday 13th of March 2019, the Medical Museum of the University of Crete organized a day conference with title "Adolesence and brain developement" which was attended by numerous students from many schools (program). Our school, as co-organizer, participated to the activities. The Maths -as the year before- was present with an exhibition about infinity, prepared both by students and teachers. For sure, the infinity is hardly conceived by our brain and gets it to its limits creating paradoxes. Our exhibits have been categorized in 8 themes -the numbers shown below (which you'll have to click them). Each image can be enlarged by a click on it and by a second click it gets back to the original size. 1. The lemniscate ∞: the symbol of infinity
The symbol of an "eight on its side" is known as the lemniscate and is the symbol of infinity. The English mathematician John Wallis (1616-1703) introduced the symbol to represent mathematical infinity in his Arithmetica Infinitorum of 1655, while the Swiss mathematician Jacob Bernoulli (1654-1705) first called the shape a lemniscus (Latin word for ribbon) in an article in Acta Eruditorum in 1694. These are our exhibits for the symbol of infinity
The poster created by Natalia (B3).
The poster was created by Georgia and Elias (B1). See also this article of Math Laboratory.
If we get one photo of the Sun each week the same day and hour (for instance when it gets to its highest point) then in a year we shall have 52 photos which combined will show a solar path in a shape of a non-symmetric lemniscate. The non-symmetry is due to the fact that the Sun moves faster during winter. The photos below where taken by Anthony Ayiomamiti, here is a link to his collection.
It takes only three steps to construct a lemniscate with GeoGebra (download the complete file from here) - In the imput line type x^2-y^2=1 to create the hyperbola x
^{2}-y^{2}=1. - Then type x^2+y^2=1 to create the circle x
^{2}+y^{2}=1. - Finaly, choose the tool of "inversion on a circle" and first click the hyperbola and then the circle. The lemniscate will be instantly created.
You may experiment on the Jacob Bernoullis' lemniscate with this application created by the mathematician Soula Soufari.
When we chose the "infinity" as our subject for the math exhibition in the brain event we had no idea that the brain itself has its own lemnisci... |

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