Journal of Formalized Mathematics
Volume 6, 1994
University of Bialystok
Copyright (c) 1994 Association of Mizar Users

## Extremal Properties of Vertices on Special Polygons, Part I

Yatsuka Nakamura
Shinshu University, Nagano
Czeslaw Bylinski
Warsaw University, Bialystok

### Summary.

First, extremal properties of endpoints of line segments in n-dimensional Euclidean space are discussed. Some topological properties of line segments are also discussed. Secondly, extremal properties of vertices of special polygons which consist of horizontal and vertical line segments in 2-dimensional Euclidean space, are also derived.

#### MML Identifier: SPPOL_1

The terminology and notation used in this paper have been introduced in the following articles [14] [18] [3] [15] [11] [2] [16] [6] [13] [8] [1] [4] [12] [5] [7] [17] [9] [10]

#### Contents (PDF format)

1. Preliminaries
2. Properties of line segments
3. Alternating special sequences

#### Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[5] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[7] Agata Darmochwal. Compact spaces. Journal of Formalized Mathematics, 1, 1989.
[8] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[9] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.
[10] Agata Darmochwal and Yatsuka Nakamura. The topological space \$\calE^2_\rmT\$. Arcs, line segments and special polygonal arcs. Journal of Formalized Mathematics, 3, 1991.
[11] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[12] Stanislawa Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Journal of Formalized Mathematics, 2, 1990.
[13] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[14] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[15] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[16] Andrzej Trybulec and Czeslaw Bylinski. Some properties of real numbers operations: min, max, square, and square root. Journal of Formalized Mathematics, 1, 1989.
[17] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[18] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.