Zobrazeno 1 - 10
of 103
pro vyhledávání: '"01A20"'
Autor:
Cruz, Luis, Koshkin, Sergiy
The quadratrix received its name from the circle quadrature, squaring the circle, but it only solves it if completed by taking a limit, as pointed out already in antiquity. We ask if it can square the circle without limits and restrict its use accord
Externí odkaz:
http://arxiv.org/abs/2406.14032
Autor:
Shen, Alexander
The exposition in Euclid's Elements contains an obvious gap (seemingly unnoticed by most commentators): he often compares not just angles, but *groups* of angles, and at the same time he avoids summing angles (and considering angles greater than $\pi
Externí odkaz:
http://arxiv.org/abs/2404.02272
Autor:
Venner, Nicole
While geometry with transcendental curves, like the Quadratrix of Hippias and the Spiral of Archimedes, played a significant role in our modern developments of geometry and algebra. The investigation has fallen off in the modern era despite advanceme
Externí odkaz:
http://arxiv.org/abs/2303.12514
Autor:
Koshkin, Sergiy
Publikováno v:
College Mathematics Journal 51 (2020) no. 2, 124-131
A horn angle between a circle and its tangent is considered in Euclid's Elements, and Euclid remarks that it is smaller than any acute rectilinear angle. Already in antiquity, Proclus wondered whether it is possible to bisect horn angles. We will giv
Externí odkaz:
http://arxiv.org/abs/2206.09499
In this paper, we analyze the two geometrical passages in Plato's Meno, (81c -- 85c) and (86e4 -- 87b2), from the points of view of a geometer in Plato's time and today. We give, in our opinion, a complete explanation of the difficult second geometri
Externí odkaz:
http://arxiv.org/abs/2111.03946
Autor:
Baloglou, George, Thomaidis, Yannis
We debate, departing from 2-3 readings of a single sentence in Proclus' Commentary to Plato's Republic, the plausibility of a rigorous (inductive) arithmetical derivation of an infinite sequence of pairs of side and diameter numbers by Proclus.
Externí odkaz:
http://arxiv.org/abs/2011.07335
We address the issue of angular measure, which is a contested issue for the International System of Units (SI). We provide a mathematically rigorous and axiomatic presentation of angular measure that leads to the traditional way of measuring a plane
Externí odkaz:
http://arxiv.org/abs/2011.05779
Autor:
Katz, Mikhail G.
Publikováno v:
Journal of Humanistic Mathematics 10 (2020), no. 1, 475-515
We compare several approaches to the history of mathematics recently proposed by Blasjo, Fraser--Schroter, Fried, and others. We argue that tools from both mathematics and history are essential for a meaningful history of the discipline. In an extens
Externí odkaz:
http://arxiv.org/abs/2002.00249
Autor:
Hernández, Jonathan Taborda
A brief review of the history of the conic sections would not be complete without an exhaustively tolerable account of all the things related to the subject that can be found in the extensive work of the wise Archimedes. There is no strong evidence t
Externí odkaz:
http://arxiv.org/abs/1906.03756
Autor:
Amer, Mohamed A.
Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced later on. The
Externí odkaz:
http://arxiv.org/abs/1904.01422