المربع السحري: حاصل جمع كل الصفوف والأعمدة والأقطار

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26 مارس 2013

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في الرياضيات المسلية، المربع السحري هي مصفوفة مربعة ذات حيز $(n)$ ، مكونة من

$n^2$ أعداد صحيحة، بحيث أن حاصل جمع $(n)$ رقم في كلّ من الصفوف والأعمدة

والأقطار الرئيسية يؤدي لنفس الحاصل. توجد مربعات سحرية مهما كان الحيز $n\ge1$

بإقصاء $n=2$ (أربع أعداد)، مع كون الحالة $n=1$ تعتبر أمرا بديهيا.

يبين الشكل التالي مثالا لمربع سحري من $n=3$

لاحظ أن مجموع كل سطر وعمود وقطر رئيسي يساوي دائما 15. يسمى هذا المجموع

ثابتا سحريا $(M)$ وقيمته بصفة عامة:

$M(n) = \frac{n(n^2+1)}{2}$

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المربع السحري: حاصل جمع كل الصفوف والأعمدة والأقطار

أخر المواضيع من قسم : الرياضيات المسلية

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