300 CE
Pappus's Theorem
Greek mathematician Pappus of Alexandria publishes his Collection, which includes Pappus's theorem, an early result in projective geometry concerning collinearity of points on lines. #math #geometry
Chronological Storyline (41 Milestones)
1415 CE
Brunelleschi and Linear Perspective
Filippo Brunelleschi demonstrates linear perspective, establishing mathematical principles for projecting three-dimensional space onto a plane, a precursor to projective geometry. #art #math
By Cmglee - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=83384053
1636 CE
Desargues' Theorem
Girard Desargues publishes his theorem on perspective triangles, a foundational result in projective geometry that relates triangle vertices and lines. #geometry #history
By Jujutacular - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=9659371
1640 CE
Pascal's Theorem
Blaise Pascal, at age 16, publishes his theorem on hexagons inscribed in conic sections, a key result in projective geometry. #math #youth
By Wcherowi - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=22820278
1673 CE
La Hire's Projective Works
French mathematician Philippe de La Hire publishes works on conics and projective geometry, advancing the field. #geometry
By Unknown author - Unknown. This is a contemporary engraving., Public domain, https://commons.wikimedia.org/w/index.php?curid=1139639
1795 CE
Monge's Descriptive Geometry
Gaspard Monge develops descriptive geometry, a system for representing three-dimensional objects in two dimensions using projections, influencing projective geometry. #geometry #engineering
By Hasanisawi intersection of solids https://isawi.blogspot.com/2023/01/final-digital-exam-intersection-of.html - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=2859643
1822 CE
Poncelet's Traité des Propriétés Projectives
Jean-Victor Poncelet publishes the first systematic treatise on projective geometry, introducing continuity principle and cross-ratio. #math #history
By Smithsonian Libraries, https://library.si.edu/image-gallery/74037 (You must cite and link to, when possible, the SI Website as the source of the Content) see [3] - [1] and [2], Public domain, https://commons.wikimedia.org/w/index.php?curid=179179
1827 CE
Möbius and Barycentric Coordinates
August Ferdinand Möbius introduces barycentric coordinates, a coordinate system for projective geometry. #geometry #algebra
By Rubybrian - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=4842309
1832 CE
Steiner's Systematische Entwickelung
Jakob Steiner publishes a synthetic approach to projective geometry, developing the concept of harmonic bundles. #geometry
By Unknown author - Hanns Peter Holl: Jeremias Gotthelf. Zürich/München 1988, S. 33 – originally uploaded to german wikipedia: 9. Sep. 2005, 19:18 Paenultima (Diskussion / Beiträge) hat „Bild:JakobSteiner.jpg“ hochgeladen (Jakob Steiner Quelle: Hanns Peter Holl, Jeremias Gotthelf, Zürich / München 1988, S. 33 {{PD-old}} ), Public domain, https://commons.wikimedia.org/w/index.php?curid=658272
1847 CE
von Staudt's Geometrie der Lage
Karl Georg Christian von Staudt publishes a purely projective geometry without metric concepts, establishing foundations. #math
By Unknown author - http://www.rsg.rothenburg.de/, Public domain, https://commons.wikimedia.org/w/index.php?curid=5533638
1849 CE
Cayley's Algebraic Projective Geometry
Arthur Cayley unifies projective geometry with algebra via homogeneous coordinates. #algebra #geometry
By Herbert Beraud (1845–1896) - http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Cayley.html, Public domain, https://commons.wikimedia.org/w/index.php?curid=904674
1852 CE
Plücker Coordinates
Julius Plücker introduces line coordinates and studies line geometry, contributing to projective geometry. #geometry
1872 CE
Klein's Erlangen Program
Felix Klein proposes the Erlangen Program, classifying geometries by transformation groups, with projective geometry as a central case. #math #group
By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=38617
1883 CE
Cantor Set
Georg Cantor describes the Cantor set, a fractal-like set of points with self-similarity, laying groundwork for fractal geometry. #fractals #settheory
By Thefrettinghand at English Wikibooks - Transferred from en.wikibooks to Commons., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=61785435
1890 CE
Peano Space-Filling Curve
Giuseppe Peano constructs a continuous curve that fills a square, challenging notions of dimension and inspiring fractal concepts. #fractals #dimension
1904 CE
Koch Snowflake
Helge von Koch describes the Koch snowflake, a continuous curve with infinite length but finite area, a classic fractal. #fractals #geometry
By Wrtlprnft - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=1225322
1915 CE
Sierpinski Triangle
Wacław Sierpiński introduces the Sierpinski triangle, a self-similar fractal constructed by recursively removing triangles. #fractals
By Unknown author, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=8862246
1918 CE
Hausdorff Dimension
Felix Hausdorff defines fractional dimensions, crucial for quantifying fractal structures. #fractals #math
By Original: Chas_zzz_brown,Shibboleth Vector: The original uploader was Wxs at Wikimedia Commons. - Own work based on: KochFlake.png, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1898291
1918 CE
Julia Sets
Gaston Julia and Pierre Fatou study iterated rational functions, leading to Julia sets, foundational in complex dynamics and fractals. #fractals #complex
By Morn - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=75993344
1925 CE
Bézier Curves Emerge
Pierre Bézier develops parametric curves for car design, using projective geometry concepts; later used in computer graphics. #geometry #design
By MarianSigler - Self-drawn using gedit, based on Bezier.png, Public domain, https://commons.wikimedia.org/w/index.php?curid=780454
1935 CE
Lévy C Curve
Paul Lévy describes the Lévy C curve, a continuous fractal curve with self-similarity. #fractals
1945 CE
Coxeter's Projective Geometry Text
H.S.M. Coxeter publishes introductory text on projective geometry, influencing modern teaching. #geometry #textbook
By Konrad Jacobs, Erlangen - https://opc.mfo.de/detail?photo_id=738, CC BY-SA 2.0 de, https://commons.wikimedia.org/w/index.php?curid=6608250
1960 CE
Projective Geometry in Algebra
Algebraic geometry adopts projective spaces extensively via Grothendieck's schemes, linking projective geometry to algebra. #algebra #geometry
By User:MikKBDFJKGeMalak - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=805589
1975 CE
Mandelbrot Coins 'Fractal'
Benoit Mandelbrot introduces the term 'fractal' to describe irregular, self-similar shapes, revolutionizing geometry and nature study. #fractals #math
By Steve Jurvetson - https://www.flickr.com/photos/jurvetson/4770047266/, CC BY 2.0, https://commons.wikimedia.org/w/index.php?curid=155438846
1978 CE
L-Systems Model Plant Fractals
Aristid Lindenmayer develops L-systems for simulating plant growth and fractal patterns, used in biology and computer graphics. #fractals #biology
By User:Solkoll - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=61990
1980 CE
Mandelbrot Set Visualized
Benoit Mandelbrot produces first computer visualizations of the Mandelbrot set, an iconic fractal from complex dynamics. #fractals #computergraphics
By Created by Wolfgang Beyer with the program Ultra Fractal 3. - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=321973
1982 CE
Mandelbrot's 'The Fractal Geometry of Nature'
Mandelbrot publishes his seminal book, popularizing fractals and their applications in nature, art, and science. #fractals #book
1985 CE
Fractal Compression
Michael Barnsley develops fractal image compression, using self-similarity to compress images efficiently. #fractals #compression
By Original: Marekd Vector: Theki - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=162766420
1986 CE
Iterated Function Systems
Michael Barnsley and Stephen Demko introduce iterated function systems (IFS) for generating fractals. #fractals #math
By António Miguel de Campos - self made using own JAVA animation, Public domain, https://commons.wikimedia.org/w/index.php?curid=2091769
1988 CE
Fractal Antenna Beginnings
Nathan Cohen patents first fractal antenna, demonstrating fractal geometry improves antenna performance. #fractals #engineering
By Nathan Cohen - http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&co1=AND&d=PTXT&s1=6452553.PN.&OS=PN/6452553&RS=PN/6452553, Public domain, https://commons.wikimedia.org/w/index.php?curid=41700498
1990 CE
Projective Geometry in Computer Vision
Computer vision adopts projective geometry for camera calibration and 3D reconstruction from images. #computervision #geometry
1991 CE
Fractal Cosmology Models
Astrophysicists propose fractal models for the large-scale structure of the universe, sparking debate. #fractals #cosmology
By Jonathan Huot - https://www.facebook.com/photo.php?fbid=10153188043864019&set=a.10151374960234019.501003.730509018&type=1&theater, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=43087770
1993 CE
Ifs and Fractal Flame
Scott Draves creates fractal flame algorithm, generating intricate, colorful fractal art. #fractals #art
By Unknown author, CC BY 2.5, https://commons.wikimedia.org/w/index.php?curid=569616
1995 CE
Projective Geometry in Graphics
3D graphics pipelines use projective transformations for perspective rendering, standardizing projective geometry in computer graphics. #graphics #geometry
1999 CE
Fractal Geometry in Finance
Mandelbrot applies fractal geometry to financial markets, modeling price fluctuations with self-similarity. #fractals #finance
2004 CE
Fractal Art Mainstream
Fractal software like Fractint enables wide creation and appreciation of fractal art, entering mainstream culture. #fractals #art
By Hessemer, Friedrich Maximilian Friedrich Maximilian Hessemer (Q1461066) - https://sammlung.staedelmuseum.de/de/werk/aegyptisches-kapitell-3, PDM-owner, https://commons.wikimedia.org/w/index.php?curid=97475313
2005 CE
Projective Geometry in Robotics
Robotics uses projective geometry for visual servoing and object recognition, enhancing autonomy. #robotics #geometry
2009 CE
Fractal Antennas in Mobile Phones
Fractal antennas become common in mobile devices, offering compact, efficient designs. #fractals #tech
2014 CE
Projective Geometry and Deep Learning
Researchers explore integrating projective geometry into neural networks for improved spatial understanding. #deeplearning #geometry
2018 CE
Fractal Patterns in Cellular Automata
Discovery of fractal patterns in cellular automata rules, linking complexity to self-similarity. #fractals #complexity
2020 CE
Fractal Geometry in COVID-19 Research
Fractal geometry analyzes lung damage caused by COVID-19, aiding medical imaging diagnostics. #fractals #medical