CONSTRUCTIVE GEOMETRY AND THE PARALLEL POSTULATE
نویسندگان
چکیده
منابع مشابه
Constructive Geometry and the Parallel Postulate
Euclidean geometry, as presented by Euclid, consists of straightedge-andcompass constructions and rigorous reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. This involves finding “uniform” constructions where normally a case distinction is used. For example, in finding a perpendicular to line L through point p, ...
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Euclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. A consideration of the relation of the Euclidean “constructions” to “constructive mathematics” leads to the development of a first-order theory ECG of the “Euclidean Constructive Geometry”, which can serve as an axiomatization of Euclid ...
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Euclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. A consideration of the relation of the Euclidean “constructions” to “constructive mathematics” leads to the development of a first-order theory ECG of the “Euclidean Constructive Geometry”, which can serve as an axiomatization of Euclid ...
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1. INTRODUCTION. We begin with an often-told story from the Budget of Paradoxes by Augustus de Morgan: " Lagrange, in one of the later years of his life, imagined " that he had solved the problem of proving Euclid's parallel postulate. " He went so far as to write a paper, which he took with him to the [Institut de France], and began to read it. " But, De Morgan continues, " something struck hi...
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In the current problem set we are investigating two problems in computational geometry using concepts from our study of the computable real numbers and calculus. The main problem we are examining is the notion of a set of points in the plane and how to compute their convex hull. In the last lecture we briefly discussed how it is possible to investigate computational geometry in a more abstract ...
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ژورنال
عنوان ژورنال: The Bulletin of Symbolic Logic
سال: 2016
ISSN: 1079-8986,1943-5894
DOI: 10.1017/bsl.2015.41