التحدب الإحداثي واجتماع أربع مجموعات نجمية في R2
Abstract
يقال عن مجموعة في المستوي الإقليدي إنها محدبة إحداثياً إذا كان تقاطع أي مستقيم موازيا لأي من المحورين الإحداثيين مع مجموعة محدبة 0 و يقال عن مجموعة في المستوي الإقليدي أيضاً أنها مجموعة نجمية إذا وجدت نقطة مثل في هذه المجموعة بحيث تكون جميع القطع المستقيمة من أجل كل واقعة في وعندئذ يقال إن جميع نقاط المجموعة مرئية ضمن من النقطة .
وفي هذا البحث سوف نبرهن النظرية التالية : "إذا كانت مجموعة محدبة إحداثياً و متراصة في المستوي الإقليدي عندئذ تكون المجموعة اجتماعاً لأربع مجموعات نجمية فقط إذا وجد في أربع نقاط مثل بحيث تكون كل نقطة جبهية لـ مرئية ضمن من إحدى النقاط أو على الأقل "In the Euclidean plane, we say that the set is coordinate convex set, if and only if, any parallel line to any coordinate axes was intersected with is convex set . And we say that the set is star shaped set, if and only if, a point existed in A as (a), so that, every line segment [a, x] for all lie in A , in this case we say that every point was visible via A from a .
In this study will prove the following theory:
“If the set A is coordinate convex and compact set in the Euclidean plane then: The set A is union of four star shaped sets, if and only if, it existed in the set A four points as a,b,c,d , so that, every boundary point of A in this set will be visible from a,b,c or d at least.”
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