Formalized Mathematics    (ISSN 1426-2630)
Volume 10, Number 2 (2002): pdf, ps, dvi.
1. Robert Milewski. Upper and Lower Sequence on the Cage, Upper and Lower Arcs, Formalized Mathematics 10(2), pages 73-80, 2002. MML Identifier: JORDAN1J
Summary:
2. Robert M. Solovay. Fibonacci Numbers, Formalized Mathematics 10(2), pages 81-83, 2002. MML Identifier: FIB_NUM
Summary: We show that Fibonacci commutes with g.c.d.; we then derive the formula connecting the Fibonacci sequence with the roots of the polynomial $x^2 - x - 1.$
3. Andrzej Trybulec. Preparing the Internal Approximations of Simple Closed Curves, Formalized Mathematics 10(2), pages 85-87, 2002. MML Identifier: JORDAN11
Summary: We mean by an internal approximation of a simple closed curve a special polygon disjoint with it but sufficiently close to it, i.e. such that it is clock-wise oriented and its right cells meet the curve. We prove lemmas used in the next article to construct a sequence of internal approximations.
4. Mariusz Giero. On the General Position of Special Polygons, Formalized Mathematics 10(2), pages 89-95, 2002. MML Identifier: JORDAN12
Summary: In this paper we introduce the notion of general position. We also show some auxiliary theorems for proving Jordan curve theorem. The following main theorems are proved: \begin{enumerate} \item End points of a polygon are in the same component of a complement of another polygon if number of common points of these polygons is even; \item Two points of polygon $L$ are in the same component of a complement of polygon $M$ if two points of polygon $M$ are in the same component of polygon $L.$ \end{enumerate}
5. Andrzej Trybulec. Introducing Spans, Formalized Mathematics 10(2), pages 97-98, 2002. MML Identifier: JORDAN13
Summary: A sequence of internal approximations of simple closed curves is introduced. They are called spans.
6. Yatsuka Nakamura. General Fashoda Meet Theorem for Unit Circle, Formalized Mathematics 10(2), pages 99-109, 2002. MML Identifier: JGRAPH_5
Summary: Outside and inside Fashoda theorems are proven for points in general position on unit circle. Four points must be ordered in a sense of ordering for simple closed curve. For preparation of proof, the relation between the order and condition of coordinates of points on unit circle is discussed.
7. Robert Milewski. Properties of the Internal Approximation of Jordan's Curve, Formalized Mathematics 10(2), pages 111-115, 2002. MML Identifier: JORDAN14
Summary: