Related papers: Benedetti's constructions of ovals
The early Renaissance artist Albrecht Durer published a book on geometry a few years before he died. This was intended to be a guide for young craftsmen and artists giving them both practical and mathematical tools for their trade. In the…
We consider several appearances of the notion of convexity in Greek antiquity, more specifically in mathematics and optics, in the writings of Aristotle, and in art. The final version of this article will appear in the book `Geometry in…
In this paper, we examine the evolution of a specific mathematical problem, i.e. the nine-point conic, a generalisation of the nine-point circle due to Steiner. We will follow this evolution from Steiner to the Neapolitan school (Trudi and…
Confocal quadrics capture (encode) and geometrize spectral properties of symmetric operators. Certain metric-projective properties of confocal quadrics (most of them established in the first half of the XIX$^{\mathrm{th}}$ century) {\it…
On Boxing Day, 1838, Jacobi found a solution to the problem of geodesics on a triaxial ellipsoid, with the course of the geodesic and the distance along it given in terms of one-dimensional integrals. Here, a numerical implementation of…
Geodesic domes, convex polyhedrons with almost spherical shape or parts of them, were the subject of great attention in the twenty years between the mid-1950s and the 1970s, especially thanks to Richard Buckminster Fuller. After a building…
We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide…
More than two centuries ago Malfatti (see \cite{malfatti}) raised and solved the following problem (the so-called Malfatti's construction problem):Construct three circles into a triangle so that each of them touches the two others from…
Inspired by a didactic experience in an academic environment, and following the idea given by M. Villa in \cite{Villa}, we illustrate two different proofs of an important result in Euclidean geometry studied in the first two years of…
Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to…
We show how the birth of perspective painting in the Italian Renaissance led to a new way of interpreting space that resulted in the creation of projective geometry. Unlike other works on this subject, we explicitly show how the craft of…
Geometrical optical illusions have been object of many studies due to the possibility they offer to understand the behaviour of low-level visual processing. They consist in situations in which the perceived geometrical properties of an…
The bisection of trapezoids by transversal lines has many examples in Babylonian mathematics. In this article, we study a similar problem in Elamite mathematics, inscribed on a clay tablet held in the collection of the Louvre Museum and…
In this note we discuss a class of hyperelliptic curves introduced by Abel in a 1826 paper. After some indications of the context in which he introduced them and a description of his main result we give some results on the moduli space of…
We describe a balance weight dated to the Early Islamic Period from the Hecht Museum at the University of Haifa (Israel) Its polyhedral shape was attributed to a truncated elongated octagonal bipyramid. To our knowledge, the earliest…
In 1955 B. Segre showed that any oval in a projective plane over a finite field of odd order is a conic. His proof constructs a conic which matches the oval in some points and tangents, and then shows that it actually coincides with the…
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is an English translation of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825).…
This paper discusses a central theorem in birational geometry first proved by Eugenio Bertini in 1891. J.L. Coolidge described the main ideas behind Bertini's proof, but he attributed the theorem to Clebsch. He did so owing to a short note…
Three versions of Luca Pacioli's 'De Dvina Proportione' remain: a manuscript held in Milan, another in Geneva and a printed version edited in Venice. A recent book, 'Antologia della Divina Proporzione', has all three in one volume, allowing…
This is an English translation of the Italian version of an encyclopedia chapter that appeared in the Italian Encyclopedia of the Physical Sciences, edited by Bruno Bertotti (1994). Following requests from colleagues we have decided to make…