Ponceletove krivulje - Dobovišek, Mirko (Obzornik za matematiko in fiziko, 2013)
In the 18th century mathematicians established the following: given two circles ?$C_1$?, inscribed to a given triangle, and ?$_2$?, circumscribed to the same triangle, then ?$C_1$? and ?$C_2$? are inscribed and circumscribed circle to an infinite number of triangles. Such a pair of curves are called Poncelet's curves. In this article the early history of Poncelet's porism is discussed. The same property occurs also in the case of an ?$n$?-sided polygon. In 1998 it was proved that the boundary of the numerical range on any ?$n times n$? matrices that admits unitary bordering is an ?$n+1$?-Poncelet's curve with respect to the unitary circle, and that such curves need not be quadrics. The example of a Poncelet's curve that is not a quadric is given in this article. It is already known that not all Poncelet's curves are boundaries of a numerical range. All Poncelet's curves with respect to a circle have not yet been classified.
Keywords: great Poncelet theorem; veliki Ponceletov izrek; n-Poncelet property; n-Ponceletova lastnost; Poncelet curve; Ponceletova krivulja; numerical range; numerični zaklad; dilacija; dilation; unitarna dilacija; unitary dilation