تطبيق هندسي لمبدأ القيمة القصوى

Authors

  • حسن بدور
  • رودى بيـدو

Abstract

في هذا البحث نستخدم مبدأ القيمة القصـوى ( يوفي- تيخوميروف Ioffe -Tichomirov) لإيجاد الشروط التي يجب أن تحققها النقاط التي تمثل رؤوس مضلع ( عدد أضلاعه n) مرسوم داخل دائرة حتى يكون مجموع مربعات أضلاعه أكبر ما يمكن . وقد تم إيجاد حل المسألة بشكل خاص في حالة الشكل الرباعي، حيث تبين أن الشكل المواتي هو أي شكل رباعي دائري ينطبق أحد قطريه على قطر الدائرة.

In this paper we apply the Extremum Principle of Ioffe – Tichomirov  to  find the conditions that are satisfied by points of polygon ( with n sides ) inscribed in a given circle in order that the sum of the squares of these sides has the maximal value.

It has been shown –as a special case - that the sum of the squares of quadrilateral (n=4) has the maximal value when one of its diameters coincides with diameter of the circle .

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Published

2018-12-06

How to Cite

1.
بدور ح, بيـدو ر. تطبيق هندسي لمبدأ القيمة القصوى. TUJ-BA [Internet]. 2018Dec.6 [cited 2024May10];31(2). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/5121

Issue

Vol. 31 No. 2 (2009): العلوم الأساسية

Section

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