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2011•Journal of Hefei Normal UniversityRequires access

The Stability of Some Inequalities for a Simplex

Yang Shi-guo

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Abstract

Using the theory and method of distance geometry to study the problems of stability of geometric inequalities for an n-dimensional simplex in the Euclidean space.From the deviation regular metric of two simplexes,we proved four important geometric inequalities for an n-dimensional simplex are all stable,and gave the stability versions of these geometric inequalities for a simplex.

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Using the theory and method of distance geometry to study the problems of stability of geometric inequalities for an n-dimensional simplex in the Euclidean space.From the deviation regular metric of two simplexes,we proved four important geometric inequalities for an n-dimensional simplex are all stable,and gave the stability versions of these geometric inequalities for a simplex.

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Available abstract

Using the theory and method of distance geometry to study the problems of stability of geometric inequalities for an n-dimensional simplex in the Euclidean space.From the deviation regular metric of two simplexes,we proved four important geometric inequalities for an n-dimensional simplex are all stable,and gave the stability versions of these geometric inequalities for a simplex.

Key concepts: Simplex, Mathematics, Euclidean space, Euclidean geometry, Stability (learning theory), Metric (unit), Inequality, Incircle and excircles of a triangle

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