مبرهنة يابانية في مضلع دائري

مجموع أنصاف أقطار الدوائر الخضراء = مجموع أنصاف أقطار الدوائر الحمراء

في الهندسة الرياضية، تنص المبرهنة اليابانية على أنه مهما كان شكل تثليث مضلع دائري، فإن مجموع أنصاف أقطار الدوائر الداخلية للمثلثات يكون ثابتا.[1][2][3]

وعكس المبرهنة أيضاً صحيح، بحيث إذا كان مجموع أنصاف أقطار الدوائر الداخلية لتثليث معين مستقلاً عن شكل التثليث، فإن المضلع يكون دائرياً.

مراجع

  1. ^ Fukagawa، Hidetoshi؛ Pedoe، D. (1989). Japanese Temple Geometry. Manitoba, Canada: Charles Babbage Research Center. ص. 125–128. ISBN:0919611214.
  2. ^ In search of "Japanese theorem نسخة محفوظة 29 يوليو 2010 على موقع واي باك مشين.
  3. ^ Reyes، Wilfred (2002). "An Application of Thébault's Theorem" (PDF). Forum Geometricorum. ج. 2: 183–185. مؤرشف من الأصل (PDF) في 2018-10-24. اطلع عليه بتاريخ 2015-09-02.
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