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In the 1770s, Euler wrote a series of papers (E563, E691 and E692) about finding the ellipse with minimal area or perimeter in the family of all ellipses passing through a fixed set of points. This is a translation of all three papers from…
In his \textit{Brouillon Project} on conic sections, Girard Desargues studies the notion of \textit{traversale}, which generalizes that of diameter introduced by Apollonius. One often reads that it is equivalent to the notion of…
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…
The Euclid mission is a visionary project undertaken by the European Space Agency (ESA) to probe the universe's evolution and geometry by surveying the position and gravitational shape distortion of billions of galaxies. These observations…
During the summer of 1837 Christian Ludwig Gerling, a former student of Carl Friedrich Gauss, organized the world wide first determination of a vertical deflection in longitude. From a mobile observatory at the Frauenberg close to Marburg…
The validity of Kepler Laws for the {\it spherical Kepler problem} -- namely, the problem of the motion of a particle on the unit sphere {in $\mathbb R^3$} undergoing an attraction by another particle in the sphere, tangent to the geodesic…
In this paper we make some considerations about using a dynamic geometry software for teaching history of mathematica at university level. After a short introduction to the software GeoGebra, we discuss four activities. The first is an…
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…
Nicolas-Auguste Tissot (1824--1897) was a French mathematician and cartographer. He introduced a tool which became known among geographers under the name ``Tissot indicatrix'', and which was widely used during the first half of the…
J{\'e}r{\^o}me Lalande, a famous French astronomer in the 18th century, collaborated throughout his career with several female calculators in astronomy: Nicole Reine Lepaute, Marie Louise Dupi{\'e}ry and Marie Jeanne Lefran{\c c}ois. Taking…
In two papers titled "On the so-called non-Euclidean geometry", I and II, Felix Klein proposed a construction of the spaces of constant curvature -1, 0 and and 1 (that is, hyperbolic, Euclidean and spherical geometry) within the realm of…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
We re-derive Thales, Pythagoras, Apollonius, Stewart, Heron, al Kashi, de Gua, Terquem, Ptolemy, Brahmagupta and Euler's theorems as well as the inscribed angle theorem, the law of sines, the circumradius, inradius and some angle bisector…
Initially applied in astronomy and geodesy, the linear regression model aimed to find the best estimates for parameters with predefined meanings. E.g., orbital elements, geodetic constants. As its use expanded to other disciplines, often to…
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…
This is an introduction (in German) to projective geometry by the late Heinz Lueneburg. Projective spaces are treated as lattices with particular properties, and finite geometries receive special attention. The final chapters deal with…
Supportive attitudes can bring to a blossoming science, while neglect can quickly make science absent from everyday life and provide a very primitive view of the world. We compare one important Greek achievement, the computation of the…
The Sun has been observed through a telescope for four centuries. However, its study made a prodigious leap at the end of the nineteenth century with the appearance of photography and spectroscopy, then at the beginning of the following…
This paper was written as part of a book entitled: "Questions of Modern Cosmology - Galileo's Legacy" which is a celebrative book dedicated to Galileo Galilei. The book is published in 2009, the International Year of Astronomy, since it is…
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…