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Cutting a Simplex with a Hyperplane Question of Volume


  • Leroux, A.


Simplex is a geometric figure which is extensively used in economic theory. Depending on the needs of the theory, a simplex S is sometimes cut with a hyperplane H, which separates it into two parts T and T'. It may be useful to appreciate the manner in which the simplex in cut. One mode of comparison is to evaluate the "size" of the different subsets by calculating their "volumes". The aim of this paper is to give a simple expression of the ratio : "volume" of T/"volume" of S. Furthermore, when S is the unit simplex and H goes through O, this expression becomes a nice analytical formula. By the way, we establish directly a remarkable identity of real numbers.

Suggested Citation

  • Leroux, A., 2000. "Cutting a Simplex with a Hyperplane Question of Volume," G.R.E.Q.A.M. 00a13, Universite Aix-Marseille III.
  • Handle: RePEc:fth:aixmeq:00a13

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    References listed on IDEAS

    1. Eric Jondeau, 1992. "La soutenabilité de la politique budgétaire," Économie et Prévision, Programme National Persée, vol. 104(3), pages 1-17.
    2. MARCHAND, M. & MICHEL, Ph. & PESTIEAU, P., 1990. "Optimal intergenerational transfers in a growth model with fertility and productivity changes," CORE Discussion Papers 1990059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Bertrand Crettez & Philippe Michel & Bertrand Wigniolle, 2002. "Debt Neutrality and the Infinite-Lived Representative Consumer," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 4(4), pages 499-521, October.
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    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General


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