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
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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 $x^2 - x - 1.$

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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.

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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}

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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.

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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.

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7. Robert Milewski. Properties of the Internal Approximation of Jordan's Curve, Formalized Mathematics 10(2), pages 111-115, 2002. MML Identifier: JORDAN14
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