Related papers: On the Marinus--Ptolemy and Delisle--Euler conical…
The history of astrometry, the branch of astronomy dealing with the positions of celestial objects, is a lengthy and complex chronicle, having its origins in the earliest records of astronomical observations more than two thousand years…
Lambert's theorem (1761) on the elapsed time along a Keplerian arc drew the attention of several prestigious mathematicians. In particular, they tried to give simple and transparent proofs of it (see our timeline \S 9). We give two new…
This is a translation from Latin of E348 'Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi', in which Euler develops a method to alleviate the astronomical computations in a typical…
We consider a multi-parameter family of canonical coordinates and mirror maps o\ riginally introduced by Zudilin [Math. Notes 71 (2002), 604-616]. This family includes many of the known one-variable mirror maps as special cases, in…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
This is a point of view of the work of Herbert Busemann (1905-1994), seen as a return to the geometry of Ancient Greece. The importance of this work, its recognition and its relation with other works are discussed. The final version of this…
Bibliographic and co-citation coupling are two analytical methods widely used to measure the degree of similarity between scientific papers. These approaches are intuitive, easy to put into practice, and computationally cheap. Moreover,…
The multi-layered nature of societal developments poses a challenge in the teaching and learning of history of mathematics. As an attempt to tackle this challenge we experimented with the use of Knowledge-Maps. The focus of our interest…
The proper Euclidean geometry is considered to be metric space and described in terms of only metric and finite metric subspaces (sigma-immanent description). Constructing the geometry, one does not use topology and topological properties.…
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…
We give an expansion in $1/N$ and $\beta$ of the cumulants of power sums of the particles of the $\beta$-ensemble. This new expansion is obtained using the tridiagonal model of Dumitriu and Edelman. The coefficients of the expansion are…
By the Riemann-mapping theorem, one can bijectively map the interior of an $n$-gon $P$ to that of another $n$-gon $Q$ conformally. However, (the boundary extension of) this mapping need not necessarily map the vertices of $P$ to those $Q$.…
Special curves and surfaces have an important place in mathematics, engineering and other fields of science. Loxodromes are special curves which cut all meridians on the Earth's surface at a constant angle and they are very popular in…
E727 in the Enestrom index. This is a translation from the Latin original "Accuratior evolutio problematis de linea brevissima in superficie quacunque ducenda" (1779). Given a surface $pdx+qdy+rdz=0$, Euler wants to develop equations that…
Participation of mathematicians in the implementation of economic projects in Poland, in which mathematics-based methods played an important role, happened sporadically in the past. Usually methods known from publications and verified were…
We define a class a metric spaces we call Brownian surfaces, arising as the scaling limits of random maps on general orientable surfaces with a boundary and we study the geodesics from a uniformly chosen random point. These metric spaces…
We study geodesics in the Brownian map $(\mathcal{S},d,\nu)$, the random metric measure space which arises as the Gromov-Hausdorff scaling limit of uniformly random planar maps. Our results apply to all geodesics including those between…
Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the G\"odel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described…
This is a historian's view of how modern astronomy data can be used to discuss the shifting historical worldview of Late Antiquity. In this article an attemp is made to construct an approximate model of how the cycles of astronomical…
This is a paper about triangle cubics and conics in classical geometry with elements of projective geometry. In recent years, N.J. Wildberger has actively dealt with this topic using an algebraic perspective. Triangle conics were also…