The Cosine Rule II for a Spherical Triangle on the Dual Unit Sphere

M Kazaz,H Uğurlu,A Özdemir

doi:10.3390/mca10030313

Abstract

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In this work, we proved the Cosine Rule II for a spherical triangle on the dual unit sphere

Highlights

Dual numbers had been introduced by W
Study used dual numbers and dual vectors in his research on line geometry and kinematics. He devoted special attention to the representation of directed line by dual vectors and defined the mapping that is said with his name
We prove the Cosine Rule II for a spherical triangle on the dual unit sphere %S 2

Summary

INTRODUCTION

Dual numbers had been introduced by W. Study used dual numbers and dual vectors in his research on line geometry and kinematics (see [3]). He devoted special attention to the representation of directed line by dual vectors and defined the mapping that is said with his name. There exists one to one correspondence between the vectors of dual unit sphere %S 2 and the directed lines of the space R3 of lines (E.Study’s mapping). In plane geometry it is studied points, lines, triangles, etc. We prove the Cosine Rule II for a spherical triangle on the dual unit sphere %S 2.

Thus we have

Sin γ γ