"Open four equal windows on a hemispherical dome in such a way that the remaining part of the dome turns out to be a squarable region, i.e. such that its area does not depend on \pi". Set at the end of the 17th century, that famous problem has a very elegant geometrical solution. In this article, after a brief historical and mathematical review of the subject, we describe the construction, mathematically rigorous, of two di®erent material models of the so-called Viviani's Windows. The ¯rst one is built up by cardboard parts while the second one is realized by a computer-driven milling machine from a full metal block.

### Building Viviani's windows

#### Abstract

"Open four equal windows on a hemispherical dome in such a way that the remaining part of the dome turns out to be a squarable region, i.e. such that its area does not depend on \pi". Set at the end of the 17th century, that famous problem has a very elegant geometrical solution. In this article, after a brief historical and mathematical review of the subject, we describe the construction, mathematically rigorous, of two di®erent material models of the so-called Viviani's Windows. The ¯rst one is built up by cardboard parts while the second one is realized by a computer-driven milling machine from a full metal block.
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Viviani's Windows; Models of surfaces; 3D-print of surfaces
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/19326
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