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On a 3D Extension of the Simson-Wallace theorem

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12410%2F14%3A43888177" target="_blank" >RIV/60076658:12410/14:43888177 - isvavai.cz</a>

  • Alternative codes found

    RIV/60076658:12410/14:43888141

  • Result on the web

    <a href="http://www.heldermann.de/JGG/jggcon.htm" target="_blank" >http://www.heldermann.de/JGG/jggcon.htm</a>

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    On a 3D Extension of the Simson-Wallace theorem

  • Original language description

    The following 3D extension of the Simson-Wallace theorem is proved by a method which differs from that used in the past (Theorem 1): Let K,L,M,N be orthogonal projections of a point P to the faces BCD, ACD, ABD, and ABC of a tetrahedron ABCD. Then, all points P with the property that the tetrahedron KLMN has a constant volume belong to a cubic surface (1). Next, the main theorem (Theorem 2) is proved which states that also the converse of Theorem 1 holds. Furthermore, we verify Theorem 2 for a regular tetrahedron by descriptive geometry methods using dynamic geometry software. To do this we take advantage of the fact that this cubic surface can be represented by a parametric system of conics which lie in mutually parallel planes (Theorem 3).

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

  • Continuities

    V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Others

  • Publication year

    2014

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal for Geometry and Graphics

  • ISSN

    1433-8157

  • e-ISSN

  • Volume of the periodical

    18

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    11

  • Pages from-to

    205-215

  • UT code for WoS article

  • EID of the result in the Scopus database