σ-Bezier Eğrilerinin Gauss-Bonnet Teoreminin Hesaplanması

Öz

Enerji, insanlar ve diğer canlı nesneler için en önemli kaynaklardan biridir. Güneş enerjisinin kainattaki en önemli enerji kaynağı olduğunu biliyoruz. Güneş yaşamın kaynağıdır. Fen ve teknoloji gelişmeye başladığında, insanlar pek çok çeşit enerji buldular, ancak bunların pek çoğu doğadan olanlardı. Örneğin Güneş enerjisi doğaldır fakat elektrik enerjisi güneşten veya başka doğal kaynaklardan (rüzgar, su,…vb.) üretilmektedir. Elektrik enerjisi, su, rüzgar,…vb. kapasite miktarları hesaplanabilmektedir. Enerjiyi hesaplamak için matematik ve fizik kullanmak gereklidir. Son dönemlerde geometriciler eğrilerin Willmore ve Horn metoduyla fonksiyon ve enerjilerini hesaplamışlardır. Bu makalede σ-Bezier eğrilerinin H3’ te Willmore fonksiyonu ve Willmore metodu kullanılarak Gauss-Bonnet teoremi hesaplanmıştır.

Anahtar Kelimeler

• Bezier eğrileri
• eğrilik
• torsiyon
• Gauss eğriliği
• Ortalama eğrilik
• Willmore enerji

Computing Gauss-Bonnet Theorem of σ-Bezier Curves

Abstract

The energy is one of the most important source for people and the other living things. We know that the energy of sun is the most energy source in universe. The sun is the source of the life. When the science and technology began to progressed, people found a lot of types of energy, but most of them are from the nature. For example energy of sun is naturel but energy of electric is produced by sun and using a lot of other nature sources (wind, water,…etc). The amount and capasity of the energy of the electric, water, wind,…etc. are calculated. For calculating energy we have to use mathematics and physics. Geometricians calculated the functions and energies of the curves by using Willmore and Horn’ method lately. In this paper the Wilmore function of the σ-Bezier curves in H3 and Gauss-Bonnet theorem of the σ-Bezier curves are calculated by using Willmore method.

Keywords

• Bezier curves
• curvature
• torsion
• Gauss curvature
• Mean Curvature
• Willmore energy

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