Negation-Free and Contradiction-Free Proof of the Steiner-Lehmus Theorem

被引：6

作者：

Pambuccian, Victor ^{[1
]}

机构：

[1] Arizona State Univ West Campus, Sch Math & Nat Sci, Phoenix, AZ 85069 USA

来源：

NOTRE DAME JOURNAL OF FORMAL LOGIC | 2018年 / 59卷 / 01期

关键词：

Steiner-Lehmus theorem; direct proof; indirect proof; sequent calculus; absolute geometry;

D O I：

10.1215/00294527-2017-0019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By rephrasing quantifier-free axioms as rules of derivation in sequent calculus, we show that the generalized Steiner-Lehmus theorem admits a direct proof in classical logic. This provides a partial answer to a question raised by Sylvester in 1852. We also present some comments on possible intuitionistic approaches.

引用

页码：75 / 90

页数：16

共 4 条

[1] More on the Steiner-Lehmus Theorem
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Hajja, Mowaffaq
JOURNAL FOR GEOMETRY AND GRAPHICS, 2010, 14 (02): : 127 - 133
[2] A Stronger Form of the Steiner-Lehmus Theorem
Nicula, Virgil
Pohoata, Cosmin
JOURNAL FOR GEOMETRY AND GRAPHICS, 2009, 13 (01): : 25 - 27
[3] On the Equality of Cevians: Beyond the Steiner-Lehmus Theorem
Myrianthis, Kostantinos
JOURNAL FOR GEOMETRY AND GRAPHICS, 2016, 20 (02): : 185 - 207
[4] Echos of the Steiner-Lehmus equal bisectors theorem
Borgers, Christoph
Grinberg, Eric L.
Orhon, Mehmet
Shen, Junhao
ACTA MATHEMATICA SCIENTIA, 2025, 45 (01) : 257 - 263

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