Advances in Applied Clifford Algebras

, Volume 24, Issue 1, pp 193–203 | Cite as

The Mother Minkowski Algebra of Order m

  • Spencer T. Parkin


It is found that all polynomials of up to degree m have an encoding as m-vectors in a geometric algebra referred to as the Mother Minkowski algebra of order m. It is then shown that all conformal transformations may be applied to these m-vectors, the results of which, when converted back into polynomial form, give us the transformed surfaces in terms of the zero sets of the original and final polynomials.


Algebraic Surface Conformal Model Conformal Transformation Geometric Algebra 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Doran C., Hestenes D., Sommen F., Van Acker N.: Lie groups as spin groups. J. Math. Phys. 34, 8 (1993)CrossRefMathSciNetGoogle Scholar
  2. 2.
    L. Dorst, D. Fontijne and S. Mann, Geometric algebra for computer science. Morgan Kaufmann, 2007.Google Scholar
  3. 3.
    D. Hestenes, Old wine in new bottles: A new algebraic framework for computational geometry. Advances in Geometric Algebra with Applications in Science and Engineering (2001), 1-14.Google Scholar
  4. 4.
    L. Hongbo, D. Hestenes and A. Rockwood, Generalized homogeneous coordinates for computational geometry. Geometric Computing with Clifford Algebra Volume 24., Berlin Heidelberg, Springer-Verlag (2001), 27-60.Google Scholar
  5. 5.
    A. Lasenby, Recent applications of conformal geometric algebra. IWMM 2004, LNCS 3519 Springer-Verlag (2005).Google Scholar
  6. 6.
    J. Miller, Geometric approaches to nonplanar quadric surface intersection curves. ACM Transactions on Graphics Vol. 6, No. 4, pp. 274-307.Google Scholar
  7. 7.
    J. Milne, Algebraic geometry. (v5.22), 2012, Available at, p. 260.
  8. 8.
    G. Sobczyk, Conformal mappings in geometric algebra. AMS Notices Volume 59 (2012), 264-5.Google Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Salt Lake CityUSA

Personalised recommendations