Kazaz M.2024-07-222024-07-2220051300686Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/19698The sine and cosine rules for a spherical pure triangle on the dual Lorentzian sphere were proved. On the Lorentzian sphere, there are points, but there are no straight lines, at least not in the usual sense. However, straight timelike, spacelike and lightlike lines in the Lorentzian plane are characterized by the fact that they are the shortest paths between points. The curves on the Lorentzian sphere with the same property are timelike, spacelike and lightlike circles. Thus it is natural to use these circles as replacements for lines.EnglishDifferentiation (calculus)FunctionsMathematical operatorsSet theoryTheorem provingVectorsCosine rulesDual Lorentzian spaceDual unit sphereSpacelike and timelike vectorsNumerical methodsArticle