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International Workshop on Automated Deduction in Geometry

ADG 2006: Automated Deduction in Geometry pp 203–211Cite as

Constructing a Tetrahedron with Prescribed Heights and Widths

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4869))

Abstract

Employing a method of distance geometry, we present a symbolic solution to the following problem: express the edge-lengths of a tetrahedron in terms of its heights and widths.

This work is supported in part by NKBRPC-2004CB318003 and NNSFC-10471044.

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References

  1. Blumenthal, L.M.: Theory and Applications of Distance Geometry, Chelsea, New York (1970)

    Google Scholar 

  2. Cairns, G., McIntyre, M., Strantzen, J.: Geometric proofs of recent results of Yang Lu. Math. Mag. 66, 263–265 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Gröbner, W.: Matrizenrechnung, Bibliographisches Institut AG, Mannheim, F. R. G, pp. 119–126 (1966)

    Google Scholar 

  4. Hodge, W.V., Pedoe, D.: Methods of Algebraic Geometry, Cambridge, vol. I (1953)

    Google Scholar 

  5. Lee, J.R.: The Law of Cosines in a Tetrahedron. J. Korea Soc. Math. Ed. Ser. B: Pure Appl. Math. 4, 1–6 (1997)

    Google Scholar 

  6. Michelucci, D., Foufou, S.: Using Cayley-Menger Determinants for Geometric Constraint Solving. In: ACM Symposium on Solid Modelling and Applications (2004)

    Google Scholar 

  7. Muir, T.: A Treatise on the Theory of Determinants. In: Longmans, W.H. (ed.) revised by. Green, New York, pp. 166–170 (1933)

    Google Scholar 

  8. Sippl, M.J., Scheraga, H.A.: Cayley-Menger coordinates. In: Proc. Natl. Acad., USA, vol.  83, pp. 2283–2287 (1986)

    Google Scholar 

  9. Yang, L.: Distance coordinates used in geometric constraint solving. In: Winkler, F. (ed.) ADG 2002. LNCS (LNAI), vol. 2930, pp. 216–229. Springer, Heidelberg (2004)

    Google Scholar 

  10. Yang, L.: A new method of automated theorem proving. In: Johnson, J.H., Loomes, M.J. (eds.) The Mathematical Revolution Inspired by Computing, pp. 115–126. Oxford University Press, New York (1991)

    Google Scholar 

  11. Yang, L.: Solving spatial constraints with global distance coordinate system. International Journal of Computational Geometry & Applications 16(5-6), 533–548 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Yang, L., Zhang, J.Z.: A class of geometric inequalities on finite points. Acta Math. Sinica 23(5), 740–749 (1980)

    MATH  MathSciNet  Google Scholar 

  13. Yang, L., Zhang, J.Z.: The concept of the rank of an abstract distance space. Journal of China University of Science and Technology 10(4), 52–65 (1980) (in Chinese)

    MathSciNet  Google Scholar 

  14. Yang, L., Zhang, J.Z.: Metric equations in geometry and their applications. I.C.T.P. Research Report, IC/89/281, International Centre for Theoretical Physics, Trieste, Italy (1989)

    Google Scholar 

  15. Zhang, J.Z., Yang, L., Yang, X.C.: The realization of elementary configurations in Euclidean space. Science in China A 37(1), 15–26 (1994)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Theoretical Computing, East China Normal University, Beijing 100083, China

    Lu Yang & Zhenbing Zeng

  2. Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu 610041, China

    Lu Yang

Authors
  1. Lu Yang
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  2. Zhenbing Zeng
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Editor information

Francisco Botana Tomas Recio

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© 2007 Springer-Verlag Berlin Heidelberg

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Yang, L., Zeng, Z. (2007). Constructing a Tetrahedron with Prescribed Heights and Widths. In: Botana, F., Recio, T. (eds) Automated Deduction in Geometry. ADG 2006. Lecture Notes in Computer Science(), vol 4869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77356-6_13

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  • DOI: https://doi.org/10.1007/978-3-540-77356-6_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77355-9

  • Online ISBN: 978-3-540-77356-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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