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Geometric Construction of Some Lehmer Means

Author

Listed:
  • Ralph Høibakk

    (Department of Computer Science and Computational Engineering, Faculty of Engineering Science and Technology, UiT the Arctic University of Norway, Lodve Langesgate 2, N8505 Narvik, Norway)

  • Dag Lukkassen

    (Department of Computer Science and Computational Engineering, Faculty of Engineering Science and Technology, UiT the Arctic University of Norway, Lodve Langesgate 2, N8505 Narvik, Norway
    NORUT Narvik, Rombaksveien 47, N8517 Narvik, Norway)

  • Annette Meidell

    (Department of Computer Science and Computational Engineering, Faculty of Engineering Science and Technology, UiT the Arctic University of Norway, Lodve Langesgate 2, N8505 Narvik, Norway
    NORUT Narvik, Rombaksveien 47, N8517 Narvik, Norway)

  • Lars-Erik Persson

    (Department of Computer Science and Computational Engineering, Faculty of Engineering Science and Technology, UiT the Arctic University of Norway, Lodve Langesgate 2, N8505 Narvik, Norway)

Abstract

The main aim of this paper is to contribute to the recently initiated research concerning geometric constructions of means, where the variables are appearing as line segments. The present study shows that all Lehmer means of two variables for integer power k and for k = m 2 , where m is an integer, can be geometrically constructed, that Lehmer means for power k = 0 , 1 and 2 can be geometrically constructed for any number of variables and that Lehmer means for power k = 1 / 2 and − 1 can be geometrically constructed, where the number of variables is n = 2 m and m is a positive integer.

Suggested Citation

  • Ralph Høibakk & Dag Lukkassen & Annette Meidell & Lars-Erik Persson, 2018. "Geometric Construction of Some Lehmer Means," Mathematics, MDPI, vol. 6(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:251-:d:182903
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