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 .

Downloads

Published

2018-12-06

How to Cite

1.
بدور ح, بيـدو ر. تطبيق هندسي لمبدأ القيمة القصوى. TUJ-BA [Internet]. 2018Dec.6 [cited 2024Nov.24];31(2). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/5121

Issue

Vol. 31 No. 2 (2009): العلوم الأساسية

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

The authors retain the copyright and grant the right to publish in the magazine for the first time with the transfer of the commercial right to the Tishreen University Journal -Basic Sciences Series  

 Under a CC BY- NC-SA 04 license that allows others to share the work with of the work's authorship and initial publication in this journal. Authors can use a copy of their articles in their scientific activity, and on their scientific websites, provided that the place of publication is indicted in Tishreen University Journal -Basic Sciences Series .  The Readers have the right to send, print and subscribe to the initial version of the article, and the title of Tishreen University Journal -Basic Sciences Series   Publisher

 

journal uses a CC BY-NC-SA license which mean

You are free to:

  • Adapt — remix, transform, and build upon the material
  •  
  • The licensor cannot revoke these freedoms as long as you follow the license terms.

 

  • Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • NonCommercial — You may not use the material for commercial purposes.
  • ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.