Instruments for impossible problems: Around the work of Ljubomir Klerić (1844‑1910)
Résumé
Klerić uses a new instrument, called tractoriograph, for the construction of "impossible" mathematical problems. The major part of these constructions is based on the “circular tractrix”, that is the tractrix of a circle traced with the condition that the length or the tractoriograph is equal to the radius of the circle. A spectacular property of this curve is that, if it is joined to a ruler and a compass, it allows the rectification of any arc of the circle. From that, it is easy to construct the number π, to rectify and to square the circle, and to inscribe in it a regular polygon with any number of sides. Incidentally, by using the tractrix of a straight line, Klerić proves that the number e is also constructible with his tractoriograph.
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