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Irrational speeds of configurations growth in generalized Pascal triangles

Ivan Korec
1993 Theoretical Computer Science  
A method is presented for obtaining irrational speeds of growth of configurations in generalized Pascal triangles and one-dimensional cellular automata.  ...  This method does not use diagonalization or simulation of Turing machines but uses a number-theoretic idea.  ...  We shall use this idea to construct generalized Pascal triangles (and, hence, implicitly also one-dimensional cellular automata) with this speed of configuration growth also for some noninteger b and q  ... 
doi:10.1016/0304-3975(93)90029-s fatcat:b5krc7w47bcqbeav6j4cvyvbpa

Page 5993 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
Ivan Korec (SK-AOS; Bratislava) 94j:68218 68Q80 Korec, Ivan (SK-AOS; Bratislava) Irrational speeds of configurations growth in generalized Pascal triangles. (English summary) Theoret. Comput.  ...  Using this idea, generalized Pascal triangles and also one-dimensional cellu- lar automata with the above speed of configuration growth can be constructed for some noninteger p and q.  ... 

Generalized pascal triangles: overview of new results

Ivan Korec
1993 Banach Center Publications  
Speeds of configuration growth in GPT -Definition. Generalized Pascal triangles can be considered as computations of one-dimensional cellular automata from finite initial configurations.  ...  In the next section it is shown how to meet this condition in a nontrivial way. 5. Irrational speeds of configuration growth.  ... 
doi:10.4064/-28-1-125-134 fatcat:n6r3c6km4nhe7bjwrvedz4aioy

Phyllotaxis as a Dynamical Self Organizing Process Part I: The Spiral Modes Resulting from Time-Periodic Iterations

S. Douady, Y. Couder
1996 Journal of Theoretical Biology  
The predominance of Fibonacci order in botany is related to this continuity: during the ontogeny, because of the continuous decrease in G, only this branch is followed.  ...  The dynamic is controlled by only one parameter, G, equivalent to Richards' plastochrone ratio (1951) , which characterizes growth.  ...  The programme was written in Think Pascal (18 pages, mostly used for the presentation).  ... 
doi:10.1006/jtbi.1996.0024 fatcat:5jy5dths2vd3xlvrvfonqik5ki

Elements of Mathematics [article]

John Stillwell
2022 Zenodo  
The present chapter introduces the fields of mathematics that will be considered "elementary" in this book.  ...  They have all been considered "elementary" at some stage in the history of mathematics education, and they are all still taught at school level in some places today.  ...  For the germ of the idea that led to this book, credit should go to Vagn Lundsgaard Hansen and Jeremy Gray, who commissioned my article on Klein, and later suggested that I write a book of a similar kind  ... 
doi:10.5281/zenodo.6080488 fatcat:duf7ea2kpbemvj4yfg4ewizlw4

Chapter 6 [chapter]

Ekkehard Kopp
2020 Making up Numbers  
In the seveteenth century Blaise Pascal used induction explicitly when justifying the properties of his well-known Pascal triangle (see Figure 30 , page 122).  ...  Dedekind's elegant paper ( [8] ) is entitled Stetigkeit und Irrationale Zahlen (Continuity and irrational numbers).  ...  We might counter their concerns with Hadamard's confident assertion (quoted in Section 1) that 'essential progress in mathematics' results from including notions which, for earlier generations, 'were "  ... 
doi:10.11647/obp.0236.06 fatcat:v22whoog6bgzjfevq2dd74g35a

Billiards, Flat Surfaces, and Dynamics on Moduli Spaces

Howard Masur, Martin Möller, Anton Zorich
2011 Oberwolfach Reports  
This workshop brought together people working on the dynamics of various flows on moduli spaces, in particular the action of SL 2 (R) on flat surfaces.  ...  The new results presented covered properties of interval exchange transformations, Lyapunov spectrum of this flow and the geometry of Teichmüller space.  ...  In joint work with Pascal Hubert and Howard Masur [2] , we show that (i) H. Dim DIV(P λ ) = 1 2 if λ is irrational, and is otherwise zero; (ii) H.  ... 
doi:10.4171/owr/2011/25 fatcat:gkhpmswwgfb7pnuvzi5yy2vqku

Page 1384 of Mathematical Reviews Vol. 26, Issue Index [page]

Mathematical Reviews  
(English summary) 94j:68217 — The nilpotency problem of one-dimensional cellular automata. 94¢:68142 Korec, Ivan Irrational speeds of configurations growth in generalized Pascal triangles.  ...  M. see Ablowitz, Mark J.; et al., 94a:58101 Kiwi, Marcos A. see Goles Ch., Eric, 94f:90074 Korec, Ivan The 3x + | problem, generalized Pascal triangles and cellular automata.  ... 

Reference list of indexed articles

1995 Theoretical Computer Science  
Korec, Irrational speeds of configurations growth in generalized Pascal triangles (Note) I!2 (2) (1993) 3999412 173. J.  ...  On recursive bounds for the exceptional values in speed-. J. Berstel and M. Pocchiola, Average cost of Duval's algorithm for generating Lyndon words (Note) 132 (l-2) (1994) 415-425 519. L.  ... 
doi:10.1016/0304-3975(95)90002-0 fatcat:b7nmywx4tff6lhcd3jkoagotrm

Philosophy of Education

Michael Taylor
1977 Social Theory and Practice  
of our American heritage, its civil rights and responsibilities ▪ an understanding of the various types of work, and their function in and contribution to society The effective implementation of this  ...  Our counseling staff and teaching faculty are willing and ready to assist in the process of course selection.  ...  ; Wave Properties; Law Of Superposition • Wave Phenomena -Speed Of A Wave In A Uniform Medium; Reflection; Refrac- tion; Interference; Diffraction (Ripple Tanks) • Sound -Properties of Sound; Speed  ... 
doi:10.5840/soctheorpract1977437 fatcat:ly7e6vjrirckrdmrqgowitmesa

An episodic history of mathematics: mathematical culture through problem solving

2010 ChoiceReviews  
A B C (0,a) (b,0) (c,0) (c/2, a/2) (b/2, a/2) SOLUTION We configure the triangle on a pair of axes as in Figure 6 .16. Coordinates are assigned to each of the relevant points.  ...  The generalization of the result that is due to Thabit ibn-Qurra in fact applies to all triangles. Before we begin we must review the concept of similarity of triangles.  ...  In particular, Lagrange studied the general case of motion of a body having equal moments of inertia about two of its principal axes.  ... 
doi:10.5860/choice.48-1529 fatcat:r52umdi4vja6bfxb7kmudrn4ui

Page 687 of Mathematical Reviews Vol. 26, Issue Index [page]

Mathematical Reviews  
(Ricardo Bianconi) 94e:11138 11U05 (03C40, 11U09) — Irrational speeds of configurations growth in generalized Pascal triangles. (English summary) Theoret. Comput. Sci. 112 (1993), no. 2, 399-412.  ...  (Andrew Bremner) 94a:11196 11Y50 (11D41) — Definability of arithmetic operations in Pascal triangle modulo an integer divisible by two primes.  ... 

Compression is Comprehension, and the Unreasonable Effectiveness of Digital Computation in the Natural World [article]

Hector Zenil
2021 arXiv   pre-print
the system may be in a future state--in a shorter time than the time taken by the actual unfolding of the phenomenon in question.  ...  Chaitin's work, in its depth and breadth, encompasses many areas of scientific and philosophical interest.  ...  In algorithmic terms, rational and irrational numbers are different in nature.  ... 
arXiv:1904.10258v3 fatcat:xpdup4tcpbfszmfvv6uw4bsd2q

TME Volume 6, Numbers 1 and 2

2009 The Mathematics Enthusiast  
Manuscripts are to be submitted in electronic format to the editor in APA style. The typical time period from submission to publication is 8-11 months.  ...  Articles appearing in the journal address issues related to mathematical thinking, teaching and learning at all levels.  ...  The views expressed in this paper are those of the author, not necessarily of the University of Adelaide or the sponsoring organizations.  ... 
doi:10.54870/1551-3440.1152 fatcat:5ryv4n6d3bcc3gda7f26ruyooe

New Foundation in the Sciences: Physics without Sweeping Infinities under the Rug [article]

Victor Christianto, Florentin Smarandache, Robert Neil Boyd
2020 Figshare  
For instance, a quote from Richard Feynman goes as follows: "What the three Nobel Prize winners did, in the words of Feynman, was "to get rid of the infinities in the calculations.  ...  That is why we choose a theme here: New Foundations in the Sciences, in order to emphasize the necessity to introduce a new set of approaches in the Sciences, be it Physics, Cosmology, Consciousness etc  ...  Kiehn 326 Foundation in the Sciences insightful suggestions on the preliminary version of ideas presented herein, particularly with regard to plausible relationship between lowtemperature physics  ... 
doi:10.6084/m9.figshare.12387260 fatcat:6qqvy3zxrfgebm6ctt5jkakqz4
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