Hans Zantema

Playing with Infinity (eBook, ePUB)

Turtles, Patterns, and Pictures

• Format: ePub

Produktbeschreibung

This book will provide a fascinating read for anyone interested in number theory, infinity, math art, and/or generative art, and could be used a valuable supplement to any course on these topics. Along the way the author will demonstrate how infinity can be made to create beautiful 'art', guided by the development of underlying mathematics.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 250
• Erscheinungstermin: 22. April 2024
• Englisch
• ISBN-13: 9781040010143
• Artikelnr.: 70127303

Autorenporträt

Hans Zantema was born in 1956 in The Netherlands. He studied mathematics and received his PhD in pure mathematics in 1983. After a few years in industry he returned to university, in computer science. Apart from his position as an associate professor in computer science at Eindhoven University of Technology, from 2007 until his retirement in 2022 he was part time full professor at Radboud University in Nijmegen. His professional interest is mainly in mathematical reasoning, in particular applied to computation and automated reasoning. His hobbies include solving and designing logical puzzles.

Inhaltsangabe

1. What is this book about? 1.1. Infinitely many. 1.2. Infinite sequences
and turtle figures. 1.3. Morphic sequences and symmetry. 1.4. Fractal
turtle figures. 1.5. Mathematical challenges. 1.6. Who is this book for,
how is it organized and how to read it? Challenge: the paint pot problem.
2. Numbers of the simplest kind. 2.1. Natural numbers. 2.2. Induction
Strong induction. 2.3. Addition. 2.4. Multiplication. 2.5. Divisors and
prime numbers. Challenge: number of divisors. 3. More complicated numbers.
3.1. Integer numbers. 3.2. Rational numbers. 3.3. Real numbers. 3.4.
Complex numbers. Challenge: ten questions. 4. Flavors of infinity. 4.1. The
Hilbert Hotel. 4.2. Smaller than? 4.3. Equal size? 4.4. Countable sets.
4.5. Uncountable sets. 4.6. Computable numbers. 4.7. Cardinal numbers.
Challenge: monotone functions. 5 Infinite sequences. 5.1. Operations on
sequences Morphisms. 5.2. Periodic and ultimately periodic sequences. 5.3.
Decimal notation of numbers. 5.4. Frequency of symbols. 5.5. Challenge: the
marble box. 6. Turtle figures. 6.1. Turtle figures of words and sequences.
6.2. Turtle figures of periodic sequences Some theory. 6.3. Finite turtle
figures of periodic sequences. 6.4. Infinite turtle figures of periodic
sequences. 6.5. Ultimately periodic sequences. Challenge: subword with zero
angle. 7. Programming. 7.1. Turtle programming in Python. 7.2. Turtle
programming in Lazarus. 7.3. Some theory. Challenge: knight moves. 8. More
complicated sequences. 8.1. Random sequences. 8.2. The spiral sequence.
8.3. Pure morphic sequences. 8.4. Morphic sequences. 8.5. Programming
morphic sequences. Challenge: a variation on the spiral sequence. 9. The
Thue-Morse sequence. 9.1 A fair distribution. 9.2. The Thue-Morse sequence
as a morphic sequence 9.3. Alternative characterizations. 9.4. Finite
turtle figures of more general sequences. 9.5. Finite turtle figures of the
Thue-Morse sequence. 9.6. Thue-Morse is cube free. 9.7. Stuttering variants
of Thue-Morse. Challenge: finiteness in the spiral sequence. 10. More
finite turtle figures. 10.1 A new theorem. 10.2. Two equal consecutive
symbols. 10.3. Rosettes. 10.4. More Symbols. 10.5. Adding a tail.
Challenge: one more finite turtle figure. 11. Fractal turtle figures.
11.1. Mandelbrot sets. 11.2. Fractal turtle figures. 11.3. The main
theorem. 11.4. Examples with rotation. 11.5. Examples with u = ü. 11.6.
Other examples. Challenge: googol. 12. Variations on Koch. 12.1. Koch
curve. 12.2. Koch curve as a turtle figure. 12.3. Other scaling factors.
12.4. The period-doubling sequence. 12.5. Fractal turtle figures of
variants of p. Challenge: googolplex. 13. Simple morphic sequences. 13.1.
Koch-like turtle figures of Thue-Morse. 13.2. Relating t and p. 13.3.
Finite turtle figures. 13.4. Other simple morphic sequences. 13.5. The
binary Fibonacci sequence. 13.6. Turtle figures of the binary Fibonacci
sequence. 13.7. Frequency of symbols in morphic sequences. Challenge:
frequency of 1 percent. 14. Looking back. 14.1. Turtle figures of morphic
sequences. 14.2. Other types of turtle figures. 14.3. More exciting
pictures: cellular automata. 14.4. Mathematical challenges. 14.5. Almost
infinite. Challenge: the greatest value.