Convex Hull - Computational Geometry
- Order:
- Duration: 0:26
- Published: 06 Dec 2009
- Uploaded: 14 May 2011
- Author: MorleyAbbott
See morleyabbott.com for full details and code.
Convex Geometry
-
Archimedes
Archimedes of Syracuse (Greek: ; c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.
http://wn.com/Archimedes -
Euclid
Euclid ( ; Eukleidēs), fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.
http://wn.com/Euclid -
Hermann Minkowski
Hermann Minkowski (June 22, 1864 – January 12, 1909) was a German mathematician of Lithuanian Jewish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.
http://wn.com/Hermann_Minkowski -
Werner Fenchel
Moritz Werner Fenchel (May 3, 1905 – January 24, 1988) was a mathematician known for his contributions to geometry and to optimization theory. Fenchel established the basic results of convex analysis and nonlinear optimization theory. Fenchel's monographs and lecture-notes were very influential also. Fenchel lived most of his life in Denmark.
http://wn.com/Werner_Fenchel
- Archimedes
- combinatorics
- convex analysis
- convex set
- discrete geometry
- Euclid
- Euclidean space
- functional analysis
- geometry
- geometry of numbers
- Hermann Minkowski
- integral geometry
- linear programming
- probability theory
- Tommy Bonnesen
- Werner Fenchel
Convex Blade Geometry Variations
- Order: Reorder
- Duration: 2:01
- Published: 21 Jun 2010
- Uploaded: 12 Aug 2011
- Author: knivesandstuff
COMMENTS By Approval only. . This is a forum video. Thanks and I dont want it filling up with jibberish PHOTOS HERE: forum.grtc.org This is a video to discuss the convex grind and the various options you can create with this grind when building a sword edge.
A Region of Scientific Excellence. Differential and convex geometry
- Order: Reorder
- Duration: 5:29
- Published: 10 Mar 2011
- Uploaded: 10 Mar 2011
- Author: fsenecaorg
convex polygon vs. concave polygon (geometry)
- Order: Reorder
- Duration: 0:51
- Published: 19 Sep 2010
- Uploaded: 22 Sep 2010
- Author: mathvideos2010
exterior angles of a convex polygon (geometry)
- Order: Reorder
- Duration: 7:30
- Published: 30 Jun 2010
- Uploaded: 21 May 2011
- Author: mathvideos2010
Introduction to Geometry - 30 - Angle Measures in Convex Polygons
- Order: Reorder
- Duration: 3:27
- Published: 07 Apr 2011
- Uploaded: 08 Aug 2011
- Author: thenewboston
- http://wn.com/Introduction_to_Geometry__30__Angle_Measures_in_Convex_Polygons
- Email this video
- Sms this video
For all of our videos, visit thenewboston.com
The Convex Knife Grind Fully Explained. The Ultimate Knife Grind
- Order: Reorder
- Duration: 25:56
- Published: 26 Jul 2011
- Uploaded: 12 Aug 2011
- Author: knivesandstuff
- http://wn.com/The_Convex_Knife_Grind_Fully_Explained_The_Ultimate_Knife_Grind
- Email this video
- Sms this video
PART 2: www.youtube.com LINK: www.youtube.com to Convex Geometry Video This is a more in-depth and detailed explanation of the merits and superiority of the convex grind (done properly). It is the best grind. This video is 25 minutes long and I dont have a teleprompter and had to prepare and think while speaking so if there are some mis-spoken words etc then LIVE WITH IT. thanks Easily proven with science or a decent knife. Makers might not "make" it the best.. but if we are talking about perfection. then it is the most perfect form in the universe and works the best.. anyone that says otherwise has only used a pathetic and poorly formed convex knife and compared it with a better built "other" grind. Many will disagree.. Many have finacial motive to disagree.. Thats fine.. I'm not saying that all the other knives out there are not Stellar, and better than you may EVER need.. I'm just saying that if it was made as an equal quality convex it will do the job better.. There are no exceptions.
CGAL: The Open Source Computational Geometry Algorithms Library
- Order: Reorder
- Duration: 54:59
- Published: 13 Mar 2008
- Uploaded: 09 Aug 2011
- Author: GoogleTechTalks
- http://wn.com/CGAL_The_Open_Source_Computational_Geometry_Algorithms_Library
- Email this video
- Sms this video
Google Tech Talks March, 3 2008 ABSTRACT Introduction Project mission statement, history, internal organization, partners, CGAL in numbers. What's in CGAL A survey on available data structures and algorithms, as well as examples how and by whom they are used. Topics include Triangulations, Voronoi diagrams, Boolean operations on polygons and polyhedra, arrangements of curves and their applications, Mesh generation, Geometry processing, Alpha shapes, Convex hull algorithms, Operations on polygons, Search structures, Interpolation, Shape analysis, fitting, and distances, Kinetic data structures... Generic Programming Paradigm CGAL data structures are C++ template classes and functions, usually taking several template parameters (with default values for ease of use). This gives developers an incredible flexibility to adapt the data structures to their needs, which is important internally for code reuse, and important for end users, as they typically integrate CGAL in already existing applications. Parts of CGAL are also interfaced with languages and software like Python, Java, Scilab, Qt and the Ipe drawing editor. Exact Geometric Computing Paradigm We present how to make geometric algorithms correct, robust, and nevertheless fast, by combining floating point arithmetic with exact arithmetic, and clever filtering mechanisms to switch between these two modes. These mechanisms can be used for geometric predicates, as well as for geometric constructions, which instead of a <b>...</b>
Lecture 3 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 74:45
- Published: 09 Jul 2008
- Uploaded: 05 Aug 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd covers subgradient methods. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Complete Playlist for the Course: www.youtube.com EE364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford University Channel on YouTube www.youtube.com
Lecture 8 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 71:04
- Published: 09 Jul 2008
- Uploaded: 16 Mar 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd introduces primal and dual decomposition methods. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Complete Playlist for the Course: www.youtube.com EE364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford University Channel on YouTube www.youtube.com
Lecture 14 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 72:45
- Published: 09 Jul 2008
- Uploaded: 12 Aug 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd continues his lecture on the Truncated Newton Method then moves into L1-Norm Methods for Convex-Cardinality Problems. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Complete Playlist for the Course: www.youtube.com EE364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford University Channel on YouTube www.youtube.com
Creating a Convex Secondary Bevel for a Tougher Edge
- Order: Reorder
- Duration: 11:58
- Published: 23 Oct 2010
- Uploaded: 02 Aug 2011
- Author: knivesfishwild
I gave my F1 a secondary convex bevel to increase edge toughness while retaining shaving-sharpness. I think this is a good improvement on the F1's original factory edge, which is relatively weak for the intended purpose of the knife - as a pilot's survival knife. The secondary convex bevel that I put on the edge essentially maximizes the overall weight & rigidity of the F1, in my opinion. Every knife lover should develop reasonable RRS (Restoration, Reprofiling & Sharpening) skills. Restoration means repairing the damaged edge and/or tip of your knife, eg. removing the chip on the edge or putting a tip back onto a knife that has its tip broken off. Reprofiling includes changing the edge geometry or angle. A wider angle (eg. 40-degree) means having more metal on the edge than one with a smaller angle (eg. 20-degree). A wider-angled or tough edge is recommended for hard use knives, because the tough edge resists curling & chipping on the edge, and could even retain its edge longer. With proper reprofiling & sharpening, you can have a tough yet shaving-sharp edge! You also have have to match edge geometry to your tasks & purposes.
Lecture 1 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 61:37
- Published: 09 Jul 2008
- Uploaded: 03 Aug 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd's first lecture is on the course requirements, homework assignments, and then goes into his first topic- Subgradients. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Complete Playlist for the Course: www.youtube.com EE 364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford University Channel on YouTube: www.youtube.com
Lecture 18 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 78:52
- Published: 09 Jul 2008
- Uploaded: 12 Aug 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd's final lecture of the quarter is on Branch-and-bound methods. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Complete Playlist for the Course: www.youtube.com EE364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford University Channel on YouTube www.youtube.com
Lecture 15 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 62:58
- Published: 09 Jul 2008
- Uploaded: 12 Aug 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd continues lecturing on L1 Methods for Convex-Cardinality Problems. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. EE 364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford on YouTube: www.youtube.com
Lecture 10 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 77:28
- Published: 09 Jul 2008
- Uploaded: 03 May 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd introduces a new topic, Decomposition Applications. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Complete Playlist for the Course: www.youtube.com EE364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford University Channel on YouTube www.youtube.com
Lecture 6 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 72:26
- Published: 09 Jul 2008
- Uploaded: 06 Aug 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd lectures on the localization and cutting-plane methods and then moves into the Analytic center cutting-plane methods. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Complete Playlist for the Course: www.youtube.com EE364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford University Channel on YouTube www.youtube.com
Lecture 16 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 79:17
- Published: 09 Jul 2008
- Uploaded: 12 Aug 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd introduces a new topic- Model Predictive Control. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Complete Playlist for the Course: www.youtube.com EE364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford University Channel on YouTube www.youtube.com
Convex Edge Conversion (Blending)
- Order: Reorder
- Duration: 9:57
- Published: 26 Aug 2009
- Uploaded: 04 Aug 2011
- Author: knivesandstuff
This is a quick video (Had to chop lots) showing the process of Blending my Bevelled Fehrman last chance into a zero edge convex. Much much nicer now.. and very very sharp. Not Just sharp, but excellent geometry
Metamorphosis of the Cube
Various foldings of polygons into convex polyhedra, and the reverse, unfoldings of convex polyhedra into polygons. Work by Erik Demaine, Martin Demaine, Anna Lubiw, Joseph O'Rourke, and Irena Pashchenko.
Lecture 5 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 75:34
- Published: 09 Jul 2008
- Uploaded: 06 Aug 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd introduces stochastic programing and the localization and cutting-plane methods. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Complete Playlist for the Course: www.youtube.com EE364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford University Channel on YouTube www.youtube.com
Lecture 17 | Convex Optimization II (Stanford)
- Order: Reorder
- Duration: 77:04
- Published: 09 Jul 2008
- Uploaded: 12 Aug 2011
- Author: StanfordUniversity
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd lectures on Stochastic Model Predictive Control, he then begins discussing Branch-and-bound methods. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications. Complete Playlist for the Course: www.youtube.com EE364B Course Website: www.stanford.edu Stanford University: www.stanford.edu Stanford University Channel on YouTube www.youtube.com
Polygons - YourTeacher.com - Geometry Help
- Order: Reorder
- Duration: 2:27
- Published: 22 Oct 2007
- Uploaded: 04 Aug 2011
- Author: yourteachermathhelp
For a complete lesson on polygons, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn the definition of a polygon, as well as the definitions of concave and convex polygons. Students also learn the following polygon classifications triangle (3 sides), quadrilateral (4 sides), pentagon (5 sides), hexagon (6 sides), heptagon (7 sides), octagon (8 sides), nonagon (9 sides), decagon (10 sides), dodecagon (12 sides).
Most Popular
-
U.S. Should Not Have Lied Then...or Now
WorldNews.com
-
Harry Potter's Daniel Radcliffe's in love with Rosanne Coker
The Examiner
-
Gaddafi claims attack in Tripoli crushed
The Independent
-
Egypt says Israel's regret is not enough
Al Jazeera
-
53 killed in first major terror attack in Pak during Ramzan
Indian Express
RELATED LINKS
Seeking Alpha
Back in 2007 and 2008 I had a shipload of posts talking about the SPX:VIX correlation, its implications for stocks and the like. I even came up with a plot that I called a “fearogram” to map how changes in the VIX relative to the SPX compared with...
Business Insider
Eric Falkenstein URL Eric Falkenstein is an expert on hedge funds, quantitative finance and the author of Falkenblog Recent Posts Treasuries: A New Kind Of Giffen Good What's The Difference Between AAA And AA+? Why That 65% Drop For Dendreon Was Overdue Risk-Loving or Stupidity? Treasuries a New...
PR Newswire
...
AL HELD PAINTINGS 1959
11 Aug 2011
The New York Times
Craig F. Starr Gallery Blog ArtsBeat The latest on the arts, coverage of live events, critical reviews, multimedia extravaganzas and much more. Join the discussion. More Arts News 5 East 73rd Street, Manhattan Through Aug. 19 In the summer of 1959 the Museum of Modern Art mounted New York’s...
Tulsa World
End of instruction exam results brought good news to school districts this year, with Tulsa Public Schools students demonstrating higher proficiency rates in four of seven subjects. Oklahoma requires exit exams for every student in Algebra I and II, English II and III, Biology I, geometry and U.S....
WRUP: Joystiq 'always-on' DRM
06 Aug 2011
Joystiq
Following the revelation that "always-on DRM" is a success and just the way things are, we've decided to implement it here on Joystiq. Going forward, new site content and use of Joystiq.com and our mobile apps will require an internet connection. In protest, the Joystiq staff is seeking other...
redOrbit
New research by scientists at the University of York gives a fresh perspective on the physics of black holes. Black holes are objects in space that are so massive and compact they were described by Einstein as "bending" space. Conventional thinking asserts that black holes swallow...
The Examiner
61. Ptolemy Soter (367-283 B.C.): Ptolemy served as a general under Alexander the Great. He played an integral part in the Indian and Afghan campaigns. After Alexander’s death, the Greek general founded the Ptolemaic Dynasty in Egypt. Around 304 B.C., he assumed the title of Pharaoh. His...
Convex geometry
Convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.
Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming, probability theory, etc. According to the American Mathematical Society Subject Classification 2010, major branches of the mathematical discipline Convex and Discrete Geometry are: General Convexity, Polytopes and Polyhedra, Discrete Geometry. Further classification of General Convexity results in the following list:
axiomatic and generalized convexity
convex sets without dimension restrictions
convex sets in topological vector spaces
convex sets in 2 dimensions (including convex curves)
convex sets in 3 dimensions (including convex surfaces)
convex sets in n dimensions (including convex hypersurfaces)
finite-dimensional Banach spaces
random convex sets and integral geometry
asymptotic theory of convex bodies
approximation by convex sets
variants of convex sets (star-shaped, (m, n)-convex, etc.)
Helly-type theorems and geometric transversal theory
other problems of combinatorial convexity
length, area, volume
mixed volumes and related topics
inequalities and extremum problems
convex functions and convex programs
spherical and hyperbolic convexity
List of convexity topics
K. Ball, An elementary introduction to modern convex geometry, in: Flavors of Geometry, pp. 1—58, Math. Sci. Res. Inst. Publ. Vol. 31, Cambridge Univ. Press, Cambridge, 1997, available online.
M. Berger, Convexity, Amer. Math. Monthly, Vol. 97 (1990), 650—678.
P. M. Gruber, Aspects of convexity and its applications, Exposition. Math., Vol. 2 (1984), 47—83.
V. Klee, What is a convex set? Amer. Math. Monthly, Vol. 78 (1971), 616—631.
T. Bonnesen, W. Fenchel, Theorie der konvexen Körper, Julius Springer, Berlin, 1934. English translation: Theory of convex bodies, BCS Associates, Moscow, ID, 1987.
R. J. Gardner, Geometric tomography, Cambridge University Press, New York, 1995. Second edition: 2006.
P. M. Gruber, Convex and discrete geometry, Springer-Verlag, New York, 2007.
P. M. Gruber, J. M. Wills (editors), Handbook of convex geometry. Vol. A. B, North-Holland, Amsterdam, 1993.
R. Schneider, Convex bodies: the Brunn-Minkowski theory, Cambridge University Press, Cambridge, 1993.
A. C. Thompson, Minkowski geometry, Cambridge University Press, Cambridge, 1996.
A. Koldobsky, V. Yaskin, The Interface between Convex Geometry and Harmonic Analysis, American Mathematical Society, Providence, Rhode Island, 2008.
W. Fenchel, Convexity through the ages, (Danish) Danish Mathematical Society (1929—1973), pp. 103-116, Dansk. Mat. Forening, Copenhagen, 1973. English translation: Convexity through the ages, in: P. M. Gruber, J. M. Wills (editors), Convexity and its Applications, pp. 120-130, Birkhauser Verlag, Basel, 1983.
P. M. Gruber, Zur Geschichte der Konvexgeometrie und der Geometrie der Zahlen, in: G. Fischer, et al. (editors), Ein Jahrhundert Mathematik 1890—1990, pp. 421—455, Dokumente Gesch. Math., Vol. 6, F. Wieweg and Sohn, Braunschweig; Deutsche Mathematiker Vereinigung, Freiburg, 1990.
P. M. Gruber, History of convexity, in: P. M. Gruber, J. M. Wills (editors), Handbook of convex geometry. Vol. A, pp. 1-15, North-Holland, Amsterdam, 1993.
The phrase convex geometry is also used in combinatorics as the name for an abstract model of convex sets based on antimatroids.
Historical note
Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity and can be traced in the works of Euclid and Archimedes, it became an independent branch of mathematics at the turn of the 19th century, mainly due to the works of Hermann Brunn and Hermann Minkowski in dimensions two and three. A big part of their results was soon generalized to spaces of higher dimensions, and in 1934 T. Bonnesen and W. Fenchel gave a comprehensive survey of convex geometry in Euclidean space Rn. Further development of convex geometry in the 20th century and its relations to numerous mathematical disciplines are summarized in the Handbook of convex geometry edited by P. M. Gruber and J. M. Wills.
See also
References
Expository articles on convex geometrySome books on convex geometry
Articles on history of convex geometry
This text is licensed under the Creative Commons CC-BY-SA License. This text was originally published on Wikipedia and was developed by the Wikipedia community.
