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Volume 5, Issue 4, Article 106 |
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The Generalized Sine Law and Some Inequalities for Simplices
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Authors: |
Shiguo Yang, |
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Keywords:
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Simplex, $k$-dimensional vertex angle, Volume, Inequality. |
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Date Received:
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31/07/03 |
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Date Accepted:
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23/04/04 |
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Subject Codes: |
52A40
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Editors: |
Anthony Sofo, |
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Abstract: |
The sines of  -dimensional vertex angles of an  -simplex is defined and the law of sines for -dimensional vertex angles of an -simplex is established. Using the generalized sine law for -simplex, we obtain some inequalities for the sines of -dimensional vertex angles of an -simplex. Besides, we obtain inequalities for volumes of -simplices. As corollaries, the generalizations to several dimensions of the Neuberg-Pedoe inequality and P. Chiakuei inequality, and an inequality for pedal simplex are given.
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