Research On Heights Of Unit Equilateral Triangles And A Related Geometric Constant

In this thesis, heights of unit equilateral triangles and a related geometric constant are studied, and a characterizeation of uniform nonsquareness is obtained. This thesis is organized into three parts as following:First, the development of orthogonalities is introduced; the definitions and properties of Birkhoff orthogonality and isosceles orthogonality are presented. The last part devotes to the summary of some geometric properties and the developments of related geometric constants.Second, some basic definitions and fundamental results of normed linear spaces and some geometric properties as well as related geometric constants are introduced, including the definitions and properties of strict convexity, uniform convexity, uniform smoothness, uniformly normal structure, fixed point property for nonexpansive mappings, moduli of convexity and smoothness, and nonsquare constants.These are very necessary for the discussions in the third part.Finally, properties of bisectors and heights of unit equilateral triangles are studied.By introducing a new geometric constant h (X), a characterizeation of uniform nonsquareness and a sufficient condition for fixed point property are obtained.