تطبيق هندسي لمبدأ القيمة القصوى
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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