Dancing Elves and a Flower's View of Euclid's Algorithm

Goldstine, Susan
September 2006
Mathematical Intelligencer;Fall2006, Vol. 28 Issue 4, p23
Academic Journal
The article discusses the use of Euclid's algorithm to solve the dancing elf puzzle and to determine the arrangement of sunflower seeds. The author explains the connection between dancing elves and sunflowers. He states that the angular positions of the sunflower seed are the same as those of the elf's steps. An overview on how Euclid's algorithm has solved both the puzzle and the phyllotactic patterns of the sunflower seed is offered.


Related Articles

  • A Relaxation of a Min-Cut Problem in an Anisotropic Continuous Network. Nozawa, R.; Temam, R. // Applied Mathematics & Optimization;Jul/Aug99, Vol. 40 Issue 1, p1 

    Strang [18] introduced optimization problems on a Euclidean domain which are closely related with problems in mechanics and noted that the problems are regarded as continuous versions of famous max-flow and min-cut problems. In [15] we generalized the problems and called the generalized...

  • Erratum to: A mixed breadth-depth first strategy for the branch and bound tree of Euclidean k-center problems. Fayed, Hatem; Atiya, Amir // Computational Optimization & Applications;Apr2013, Vol. 54 Issue 3, p705 

    A correction to the article "A Mixed Breadth-Depth First Strategy for the Branch and Bound Tree of Euclidean k-Center Problems" that was published in a previous issue, is presented.

  • Some classes of general solutions of the U(N) chiral σ models in two dimensions. Piette, Bernard; Zakrzewski, Wojciech J. // Journal of Mathematical Physics;Oct89, Vol. 30 Issue 10, p2233 

    The factorization theorems of Uhlenbeck and Wood are used to derive various finite action solutions to the classical equations of motion of the Euclidean U(N) chiral model in two dimensions. They are obtained by adding a general basic uniton to solutions of the Grassmannian models. A brief...

  • The Schücking problem. Ozsváth, István; Sapiro, Leland // Journal of Mathematical Physics;Sep87, Vol. 28 Issue 9, p2066 

    The embedding problem for a three-parametric family of homogeneous three-spaces into a higher-dimensional Euclidean space is considered. These three-spaces occur as space sections in cosmological models. After general consideration a certain two-parametric family is embedded into a...

  • Models of q-algebra representations: q-integral transforms and ‘‘addition theorems’’. Kalnins, E. G.; Miller, Willard // Journal of Mathematical Physics;Apr94, Vol. 35 Issue 4, p1951 

    In his classic book on group representations and special functions Vilenkin studied the matrix elements of irreducible representations of the Euclidean and oscillator Lie algebras with respect to countable bases of eigenfunctions of the Cartan subalgebras, and he computed the summation...

  • The Hurwitz transformation: Nonbilinear version. Davtyan, Levon S.; Sissakian, Aleksey N.; Ter-Antonyan, Valery M. // Journal of Mathematical Physics;Feb95, Vol. 36 Issue 2, p664 

    Discusses the development of an alternative approach to the Hurwitz (H) transformation reducing Euclidean space E[sup 8] to Euclidean space E[sup 5]. Problem conditions; Left and right a-matrix; Geometric structure of the H-transformation.

  • Wavelet frames and admissibility in higher dimensions. Fuhr, Hartmut // Journal of Mathematical Physics;Dec96, Vol. 37 Issue 12, p6353 

    Studies the relations between discrete and continuous wavelet transforms on k-dimensional Euclidean space. Construction of continuous wavelet transforms with the help of square-integrable representations of certain simidirect products; Admissibility criterion or the continuous wavelet transform.

  • Random walk representations for spinor and vector propagators. Jacobson, Ted // Journal of Mathematical Physics;Jul85, Vol. 26 Issue 7, p1600 

    A Euclid-invariant random walk representation for spin-½ and vector propagators is developed in analogy to random walks with internal states.

  • Harmonic analysis on the Euclidean group in three-space. Rno, Jung Sik // Journal of Mathematical Physics;Apr85, Vol. 26 Issue 4, p675 

    We develop the extensive harmonic analysis on the universal covering group of the Euclidean group in three-space.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics