Related papers: Benedetti's constructions of ovals
One can hardly believe that there is still something to be said about cubic equations. To dodge this doubt, we will instead try and say something about Sylvester. He doubtless found a way of solving cubic equations. As mentioned by Rota, it…
In this paper we investigate the evolution of the concept of area in Peano's works, taking into account the main role played by Grassmann's geometric-vector calculus and Peano's theory on derivative of measures. Geometric (1887) and…
As is now well known, the generalization of the square of opposition to a hexagon was discovered independently by three philosophers in the early 1950s: Paul Jacoby, Augustin Sesmat, and Robert Blanch\'{e} . Much less well known is the…
While reading ancient texts one has to be cognizant of the assumptions made about the past. One has to ask: Are these assumptions valid? Are we projecting the present views into the past? A case in point is the dating of Vedanga Jyotisa.…
The Italian astronomer Giovanni Battista Riccioli is commonly credited with performing the first precise experiments to determine the acceleration of a freely falling body, but he also went further, experimentally investigating what today…
In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…
This paper aims to provide an explanatory edition of Bolyai's 'Appendix Demonstrating the Absolute Science of Space', first published in 1832. In this treatise Bolyai began by extending neutral (or 'absolute') geometry by deriving a number…
Sequences of Genocchi numbers of the first and second kind are considered. For these numbers, an approach based on their representation using sequences of polynomials is developed. Based on this approach, for these numbers some identities…
Recent developments of affine algebraic geometry, especially the theory of open algebraic surfaces, provide means to systematically explore geometric and topological properties of polynomials in two variables. Nevertheless, there is one…
In this paper, we consider a conjecture of Erdos and Rosenfeld and a conjecture of Ruzsa when the number is an almost square. By the same method, we consider lattice points of a circle close to the x-axis with special radii.
One of the most startling mathematical discoveries of the nineteen century was the existence of plane-filling curves. As is well known, the first example of such a curve was given by the Italian mathematician Giuseppe Peano in 1890.…
In 1775, Fagnano introduced the following geometric optimization problem: inscribe a triangle of minimal perimeter in a given acute-angled triangle. A widely accessible solution is provided by the Hungarian mathematician L. Fejer in 1900.…
Compacting orthogonal drawings is a challenging task. Usually algorithms try to compute drawings with small area or edge length while preserving the underlying orthogonal shape. We present a one-dimensional compaction algorithm that alters…
The equations for geodesic flow on the ellipsoid are well known, and were first solved by Jacobi in 1838 by separating the variables of the Hamilton-Jacobi equation. In 1979 Moser investigated the case of the general ellipsoid with distinct…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen…
The angle defect, which is the standard way to measure curvature at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the…
This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were…
The notion of the magnitude of a metric space was introduced by Leinster in [8] and developed in [10], [9], [11] and [16], but the magnitudes of familiar sets in Euclidean space are only understood in relatively few cases. In this paper we…
In this article, I discuss the relationship of mathematics to the physical world, and to other spheres of human knowledge. In particular, I argue that Mathematics is created by human beings, and the number $\pi$ can not be said to have…