Projective & Fractal Geometry: Major Case Studies & Paradigm Shifts
Encyclopedia/1. The Cosmos & The Natural World/1. Mathematics & Formal Systems/01. Geometry & Spatial Systems • Curated by Admin Timeline.sg
A deep timeline of projective and fractal geometry, from ancient foundations to modern breakthroughs, highlighting key figures and paradigm shifts in the study of spatial relationships and self-similarity.
Chronological Storyline (37 Milestones)
300 BCE
Euclid's Elements
Euclid publishes 'Elements', laying the groundwork for geometry, including conic sections later used in projective geometry. #geometry #history
Euclid's Elements By University of Pennsylvania Museum of Archaeology and Anthropology - https://openn.library.upenn.edu/Data/0016/html/e2748.html, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=169166171
200 BCE
Apollonius Studies Conics
Apollonius of Perga writes 'Conics', systematically studying conic sections, foundational for projective geometry. #geometry #history
Apollonius Studies Conics By Giovanni Battista Memo - File:ApolloniiPergeiOpera1537.jpg, Public domain, https://commons.wikimedia.org/w/index.php?curid=70830662
300 CE
Pappus of Alexandria's Mathematical Collection
Pappus states the Pappus hexagon theorem, a foundational result in projective geometry. #geometry #projective
Pappus of Alexandria's Mathematical Collection By Pappus Alexandrinus - https://www.christies.com/en/lot/lot-6069499, Public domain, https://commons.wikimedia.org/w/index.php?curid=132586197
1415 CE
Brunelleschi's Perspective
Filippo Brunelleschi demonstrates linear perspective, using projective principles for realistic art. #art #geometry
Brunelleschi's Perspective By scan uploaded by Sailko, cropped by MenkinAlRire - Wikimedia Commons; Sailko; book: Elena Capretti, Brunelleschi, Giunti Editore, Firenze 2003, Public domain, https://commons.wikimedia.org/w/index.php?curid=171034830
1435 CE
Alberti's De Pictura
Leon Battista Alberti formalizes linear perspective in 'De Pictura', influencing projective geometry. #art #geometry
Alberti's De Pictura By Leon Battista Alberti - https://archive.org/stream/dellapitturaedel00albe#page/n177/mode/2up, Public domain, https://commons.wikimedia.org/w/index.php?curid=42911315
1525 CE
Dürer's Underweysung der Messung
Albrecht Dürer publishes a treatise on measurement and perspective, advancing projective ideas. #art #geometry
1636 CE
Desargues' Perspective Treatise
Girard Desargues publishes 'Brouillon project d'une atteinte aux événements des rencontres du cône avec un plan', introducing foundational projective concepts like points at infinity. #geometry #projective
Desargues' Perspective Treatise By Théobald Chartran - https://medium.com/language-lab/i-think-therefore-i-am-cartesian-3ebfa6afd44e, Public domain, https://commons.wikimedia.org/w/index.php?curid=187058981
1640 CE
Pascal's Hexagrammum Mysticum
Blaise Pascal publishes 'Essay pour les coniques', stating Pascal's theorem on conics, a major projective result. #geometry #projective
Pascal's Hexagrammum Mysticum By Wcherowi - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=22820278
Monge's Descriptive Geometry By François-Séraphin Delpech - http://www.sil.si.edu/digitalcollections/hst/scientific-identity/CF/by_name_display_results.cfm?scientist=Monge,%20Gaspard, Public domain, https://commons.wikimedia.org/w/index.php?curid=646122
1822 CE
Poncelet's Traité des Propriétés Projectives
Jean-Victor Poncelet publishes the first systematic treatise on projective geometry, establishing it as a discipline. #geometry #projective
Poncelet's Traité des Propriétés Projectives 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 Plücker's Homogeneous Coordinates
August Möbius and Julius Plücker independently introduce homogeneous coordinates, a key tool in projective geometry. #geometry #projective
Möbius and Plücker's Homogeneous Coordinates By Wojciech Muła - Own work (Python script, final touches Inkscape), CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1196334
1854 CE
Riemann's Inaugural Lecture on Geometry
Bernhard Riemann presents his ideas on curved spaces, influencing later geometric thought including projective geometry. #geometry #projective
1859 CE
Cayley's Sixth Memoir on Quantics
Arthur Cayley connects projective geometry to invariants, introducing the concept of absolute. #geometry #projective
Cayley's Sixth Memoir on Quantics 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
1872 CE
Klein's Erlangen Program
Felix Klein publishes the Erlangen Program, classifying geometries via group theory, with projective geometry as a unifying framework. #geometry #projective
Klein's Erlangen Program By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=38617
1882 CE
Pasch's Axioms for Projective Geometry
Moritz Pasch proposes the first complete axiom set for projective geometry, influencing Hilbert. #geometry #projective
Pasch's Axioms for Projective Geometry By Open Logic - https://www.flickr.com/photos/131844291@N06/17183010995/, Public domain, https://commons.wikimedia.org/w/index.php?curid=118361234
1883 CE
Cantor's Set Theory and Fractals Precursor
Georg Cantor publishes on set theory, introducing the Cantor set, an early fractal concept. #fractal #mathematics
Cantor's Set Theory and Fractals Precursor 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's Space-Filling Curve
Giuseppe Peano constructs a continuous curve that fills a square, challenging notions of dimension and foreshadowing fractals. #fractal #mathematics
Peano's Space-Filling Curve By No machine-readable author provided. Arbol01 assumed (based on copyright claims). - No machine-readable source provided. Own work assumed (based on copyright claims)., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1776029
1899 CE
Hilbert's Foundations of Geometry
David Hilbert publishes 'Grundlagen der Geometrie', providing a rigorous axiomatic treatment including projective geometry. #geometry #projective
1904 CE
Koch Snowflake
Helge von Koch describes the Koch snowflake, a continuous, nowhere differentiable curve and early fractal. #fractal #mathematics
Koch Snowflake By Wrtlprnft - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=1225322
1915 CE
Sierpiński Triangle
Wacław Sierpiński constructs the Sierpiński triangle, a self-similar fractal set. #fractal #mathematics
Sierpiński Triangle By Unknown author, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=8862246
1918 CE
Hausdorff Dimension
Felix Hausdorff introduces the Hausdorff dimension, a key concept for fractal geometry. #fractal #mathematics
Hausdorff Dimension 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 and Fatou Sets Discovered
Gaston Julia and Pierre Fatou independently study complex iteration, discovering Julia sets, foundational for fractal geometry. #fractal #complex
Julia and Fatou Sets Discovered By Morn - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=75993344
1922 CE
Besicovitch's Work on Hausdorff Dimension
Abram Besicovitch advances measure theory and fractal dimensions, influencing fractal geometry. #fractal #mathematics
1938 CE
Lévy C Curve
Paul Lévy describes the Lévy C curve, an early fractal curve. #fractal #mathematics
1948 CE
Wiener's Generalized Harmonic Analysis
Norbert Wiener applies fractal-like methods to signal processing and Brownian motion. #fractal #mathematics
Wiener's Generalized Harmonic Analysis By Garry Olsh - Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=148383228
1960 CE
Mandelbrot's Early Work on Fractals
Benoit Mandelbrot begins studying statistical self-similarity in phenomena like the Nile River and cotton prices, coining 'fractal' later. #fractal #mathematics
Mandelbrot's Early Work on Fractals By Steve Jurvetson - https://www.flickr.com/photos/jurvetson/4770047266/, CC BY 2.0, https://commons.wikimedia.org/w/index.php?curid=155438846
1975 CE
Mandelbrot Coins 'Fractal'
Benoit Mandelbrot introduces the term 'fractal' in his book 'Les Objets Fractals: Forme, Hasard et Dimension', launching modern fractal geometry. #fractal #mathematics
Mandelbrot Coins 'Fractal' By Unknown author, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=149840902
1980 CE
Discovery of the Mandelbrot Set
Benoit Mandelbrot and others visualize the Mandelbrot set, an iconic fractal from complex dynamics. #fractal #mathematics
Discovery of the Mandelbrot Set 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 landmark book, popularizing fractals and linking them to natural phenomena. #fractal #mathematics
1983 CE
Mandelbrot Set Computed and Visualized
High-resolution computer graphics of the Mandelbrot set reveal its infinite complexity, sparking public fascination. #fractal #visualization
1990 CE
Fractal Compression
Michael Barnsley develops fractal image compression, applying self-similarity to data compression. #fractal #technology
Fractal Compression By Original: Marekd Vector: Theki - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=162766420
2000 CE
Fractal Antennas and Applications
Fractal geometry is applied to antenna design, improving multi-band performance. #fractal #engineering
Fractal Antennas and Applications 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
2004 CE
Fractal Geometry in Computer Graphics
Fractals become standard in CGI for terrain generation and natural textures, widely used in movies and games. #fractal #computergraphics
Fractal Geometry in Computer Graphics By António Miguel de Campos - en:User:Tó campos - self made based in own JAVA animation, Public domain, https://commons.wikimedia.org/w/index.php?curid=618030
2010 CE
Fractal Cosmology
Research explores fractal patterns in large-scale structure of the universe, sparking debate. #fractal #cosmology
Fractal 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
2016 CE
Fractal Geometry in Biology and Medicine
Fractal analysis becomes a tool for characterizing physiological structures and diagnosing diseases. #fractal #biology
Fractal Geometry in Biology and Medicine By SALOMON LUDOVIC - Own work, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=2892754
2020 CE
Projective Geometry in Quantum Computing
Projective geometry and Grassmannians are used in quantum error correction and entanglement theory. #projective #quantum
2022 CE
Fractal AI Art and Diffusion Models
Fractal algorithms inspire generative art and machine learning models for texture synthesis. #fractal #AI
Fractal AI Art and Diffusion Models 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
