Constructive harmonic conjugates

被引：0
作者：
Mandelkern, Mark [1 ]
机构：
[1] New Mexico State Univ, Dept Math, Las Cruces, NM 88003 USA
来源：
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2019年 / 60卷 / 02期
关键词：
Projective geometry; Harmonic conjugates; Constructive mathematics;
D O I：
10.1007/s13366-018-0411-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the synthetic study of the real projective plane, harmonic conjugates have an essential role, with applications to projectivities, involutions, and polarity. The construction of a harmonic conjugate requires the selection of auxiliary elements; it must be verified, with an invariance theorem, that the result is independent of the choice of these auxiliary elements. A constructive proof of the invariance theorem is given here; the methods used follow principles put forth by Errett Bishop.
引用
收藏
页码：391 / 398
页数：8
相关论文
共 50 条
[31]   The swap of integral and limit in constructive mathematics [J].
Taschner, Rudolf .
MATHEMATICAL LOGIC QUARTERLY, 2010, 56 (05) :533-540
[32]   Can constructive mathematics be applied in physics? [J].
Bridges, DS .
JOURNAL OF PHILOSOPHICAL LOGIC, 1999, 28 (05) :439-453
[33]   A constructive version of the Sylvester–Gallai theorem [J].
M. Mandelkern .
Acta Mathematica Hungarica, 2016, 150 :121-130
[34]   Formalizing Constructive Projective Geometry in Agda [J].
Calderon, Guillermo .
ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE, 2018, 338 :61-77
[35]   Constructive equivalents of the uniform continuity theorem [J].
Berger, J .
JOURNAL OF UNIVERSAL COMPUTER SCIENCE, 2005, 11 (12) :1878-1883
[36]   Making the use of maximal ideals constructive [J].
Yengui, Ihsen .
THEORETICAL COMPUTER SCIENCE, 2008, 392 (1-3) :174-178
[37]   The constructive completion of the space D(R) [J].
Yoshida, S .
MATHEMATICAL LOGIC QUARTERLY, 2005, 51 (01) :77-82
[38]   First steps in constructive game theory [J].
Bridges, DS .
MATHEMATICAL LOGIC QUARTERLY, 2004, 50 (4-5) :501-506
[39]   A constructive semantics for non-deducibility [J].
Ciraulo, Francesco .
MATHEMATICAL LOGIC QUARTERLY, 2008, 54 (01) :35-48
[40]   The Vitali covering theorem in constructive mathematics [J].
Diener, Hannes ;
Hedin, Anton .
JOURNAL OF LOGIC AND ANALYSIS, 2012, 4
12345