Acknowledgements
This week was written by Katie Chicot. The course is adapted from the book What We Cannot Know by Marcus du Sautoy.
Except for third party materials and otherwise stated (see terms and conditions [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] ), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence.
The material acknowledged below (and within the course) is Proprietary and used under licence (not subject to Creative Commons Licence). Grateful acknowledgement is made to the following sources for permission to reproduce material in this free course:
Images
Figure 1: The Milky Way: AstroAnthony https://creativecommons.org/licenses/by/4.0/deed.en https://commons.wikimedia.org/wiki/File:Milky_way_nebula.jpg
Figure 2:
(a) Reinhard Genzel: https://commons.wikimedia.org/wiki/File:Reinhard_Genzel.jpg https://creativecommons.org/licenses/by-sa/3.0/deed.en;
(b) Andrea Ghez: Sipa US/Alamy Stock Photo;
(c) Sir Roger Penrose: Biswarup Ganguly https://commons.wikimedia.org/wiki/File:Roger_Penrose_9552.JPG https://creativecommons.org/licenses/by/3.0/deed.en
Figure 3: David Hilbert (1862–1943) Image: University of Göttingen
Figure 6: Fractions between fractions: adapted from https://www.basic-mathematics.com/density-property.html Basic-mathematics.com
Figure 7: Fraction grid: Cronholm144 https://commons.wikimedia.org/wiki/File:Diagonal_argument.svg https://creativecommons.org/licenses/by-sa/3.0/deed.en
Figure 9: Dividing a chocolate bar: Hyacinth https://commons.wikimedia.org/wiki/File:Eye_of_Horus_square.png https://creativecommons.org/licenses/by-sa/3.0/deed.en
Figure 10: Fractals:
(a) Romanesco broccoli: Ivar Leidus https://en.wikipedia.org/wiki/File:Romanesco_broccoli_(Brassica_oleracea).jpg https://creativecommons.org/licenses/by-sa/4.0/deed.en;
(b) lightning strike: José Eugenio Gómez Rodríguez https://www.flickr.com/photos/jegomezr/2926143475 https://creativecommons.org/licenses/by-nc-sa/2.0/;
(c) partial view of the Mandelbrot set: Wolfgang Beye https://en.wikipedia.org/wiki/File:Mandel_zoom_08_satellite_antenna.jpg https://creativecommons.org/licenses/by-sa/2.5/deed.en;
(d) an abstract computer generated fractal: Diep Hoang Hai/Shutterstock.com
Figure 11: Russian dolls: demidoffaleks/Getty Images
Figure 12: Koch snowflake: António Miguel de Campos https://commons.wikimedia.org/wiki/File:Von_Koch_curve.gif
Figure 13: Sierpinski triangle: Beojan Stanislaus https://commons.wikimedia.org/wiki/File:Sierpinski_triangle.svg
Audio/Video
Video 4: Fractals in animation. Clip from BBC Two series from 2011. Marcus du Sautoy interviews Loren Carpenter. Collaboration with The Open University © BBC (2011)
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