Skip to main content

Part of the book series: Encyclopaedia of Mathematics ((ENMA))

  • 1069 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arnol’d, V.I.: ‘The geometry of spherical curves and the algebra of quaternions’, Russian Math. Surveys 50 (1995). (Translated from the Russian.)

    Google Scholar 

  2. Chern, S.S.: Studies in global analysis and geometry, Vol. 4 of Studies in Mathematics, Math. Assoc. America, 1967.

    Google Scholar 

  3. Solomon, B.: ‘Tantrices of spherical curves’, Amer. Math. Monthly 103, no. 1 (1996), 30–39.

    Article  MathSciNet  MATH  Google Scholar 

  4. Egger, T., Fritsch, R., and Seebach, K.: ‘Zum Winkelsummensatz für Tetraeder’, Didaktik der Math. 11 (1983), 14–35.

    Google Scholar 

  5. Faulhaber, J.: Miracula Arithmetica, David Franck, 1622.

    Google Scholar 

  6. Fiedler, M.: ‘Geometrie simplexuv E n ’, Časopis Pěst. Mat.79 (1954), 297–320.

    MathSciNet  Google Scholar 

  7. Fritsch, R.: ‘Dreiecksungleichungen für Tetraeder’, Der mathem. und naturwissenschaftl. Unterr. 34 (1981), 274–278.

    Google Scholar 

  8. Fritsch, R.: ‘Energietetraeder?’, Mitteil. Math. Sem. dessen (Coxeter Festschrift II) 164 (1984), 151–177.

    MathSciNet  Google Scholar 

  9. Fritsch, R.: ‘Kantenkugeln-geometrische Anwendungen der linearen Algebra’, Math. Semesterber. 32 (1985), 84–109.

    MathSciNet  MATH  Google Scholar 

  10. Fritsch, R.: ‘An n-dimensional Bodenmiller theorem’, Crux Mathematicorum 21 (1995), 109–113.

    Google Scholar 

  11. Fritsch, R.: ‘Höhenschnittpunkte für n-Simplizes’, Elem. Math. 31 (1995), 1–8.

    MathSciNet  Google Scholar 

  12. Gerber, L.: ‘Spheres tangent to all the faces of a simplex’, J. Combin. Theory 12 (1972), 453–456.

    Article  MathSciNet  MATH  Google Scholar 

  13. Gerber, L.: ‘The orthocentric simplex as an extreme simplex’, Pacific J. Math. 56 (1975), 97–111.

    MathSciNet  MATH  Google Scholar 

  14. Gerretsen, J.C.H.: ‘An analogue of the nine-point circle in the space of n dimensions’, Indagationes Mathematicae 7(1945), 123–124.

    Google Scholar 

  15. Kupitz, Y.S., and Martini, H.: ‘The Fermat-Torricelli point and isosceles tetrahedra’, J. Geometry 49 (1994), 150–162.

    Article  MathSciNet  MATH  Google Scholar 

  16. Lagrange, J.L.: ‘Solutions analytiques de quelques problèmes sur le pyramides triangulaires’, Nouveaux Mem.Acad. R. des Sci. et Belles-Lettres (1773), 149–176.

    Google Scholar 

  17. Mitrinović, D.S., Pečaric, J.E., and Volenec, V.: Recent advances in geometric inequalities, Kluwer Acad. Publ., 1989.

    MATH  Google Scholar 

  18. Monge, G.: ‘Sur la pyramide triangulaire’, Corresp. Ecole Imp. Polytechnique 2/3 (1811), 263–266.

    Google Scholar 

  19. Steiner, J.: ‘Aufgaben und Lehrsätze’, J. Reine Angew. Math. 2 (1827), 96–98.

    Article  MATH  Google Scholar 

  20. Ando, T.: ‘Totally positive matrices’, Linear Alg. & Its Appl. 90 (1987), 165–219.

    Article  MathSciNet  MATH  Google Scholar 

  21. Gasca, M., and Micchelli, C.A. (eds.): Total positivity and its applications, Kluwer Acad. Publ., 1996.

    MATH  Google Scholar 

  22. Karlin, S.: Total positivity, Vol. I, Stanford Univ. Press, 1968.

    Google Scholar 

  23. Karlin, S., and McGregor, J.L.: ‘Classical difussion processes and total positivity’, J. Math. Anal. Appl. 1 (1960), 163–183.

    Article  MathSciNet  MATH  Google Scholar 

  24. Pinkus, A.: ‘Spectral properties of totally positive kernels and matrices’, in M. Gasca and C.A. Micchelli (eds.): Total Positivity and its Applications, Kluwer Acad. Publ., 1996, pp. 477–511.

    Google Scholar 

  25. Schumaker, L.L.: Spline functions: Basic theory, Wiley, 1981.

    MATH  Google Scholar 

  26. Dickson, L.E.: History of the theory of numbers, Vol. I: Divisibility and primality, Chelsea, reprint, 1971, pp. Ch. V; 113–155.

    Google Scholar 

  27. Lehmer, D.H.: ‘On Euler’s totient function’, Bull. Amer. Math. Soc. 38 (1932), 745–751.

    Article  MathSciNet  Google Scholar 

  28. Prasad, V. Siva Rama, and Rangamma, M.: ‘On composite n for which φ(n) ∣ n — 1’, Nieuw Archief voor Wiskunde (4) 5 (1987), 77–83.

    MATH  Google Scholar 

  29. Schlafly, A., and Wagon, S.: ‘Carmichael’s conjecture on the Euler function is valid below 1010000000’, Math. Comp. 63 (1994), 415–419.

    MathSciNet  MATH  Google Scholar 

  30. Sivamarakrishnan, R.: ‘The many facets of Euler’s totient I’, Nieuw Archief Wiskunde (4) 4 (1986), 175–190.

    Google Scholar 

  31. Sivamarakrishnan, R.: ‘The many facets of Euler’s totient II: generalizations and analogues’, Nieuw Archief Wiskunde (4) 8 (1990), 169–188.

    Google Scholar 

  32. Subbarao, M.V., and Prasad, V. Siva Rama: ‘Some analogues of a Lehmer problem on the totient function’, Rocky Mountains J. Math. 15 (1985), 609–620.

    Article  MATH  Google Scholar 

  33. Cherlin, G.: ‘Model theoretic algebra’, J. Symb. Logic 41 (1976), 537–545.

    Article  MathSciNet  MATH  Google Scholar 

  34. Eklof, P.C.: ‘Lefschetz’s principle and local functors’, Proc. Amer. Math. Soc. 37 (1973), 333–339.

    MathSciNet  MATH  Google Scholar 

  35. Ginsburg, S.: Algebraic and automata-theoretic properties of formal languages, North-Holland, 1975.

    MATH  Google Scholar 

  36. Ginsburg, S., and Greibach, S.A.: ‘Abstract families of languages’, in S. Ginsburg, S.A. Greibach, and J.E. Hopcroft (eds.): Studies in Abstract Families of Languages, Vol. 87 of Memoirs, Amer. Math. Soc, 1969.

    Google Scholar 

  37. Rozenberg, G., and Salomaa, A.: The mathematical theory of L systems, Acad. Press, 1980.

    MATH  Google Scholar 

Download references

Authors

Editor information

M. Hazewinkel

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Kluwer Academic Publishers

About this chapter

Cite this chapter

Hazewinkel, M. (1997). T. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1288-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-1288-6_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4896-7

  • Online ISBN: 978-94-015-1288-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics