기하학

3. 역사

기하학의 가장 초기 기록은 기원전 2000년경 메소포타미아와 고대 이집트에서 찾아볼 수 있다.^[5][6] 초기 기하학은 길이, 각도, 면적, 부피에 대한 경험적으로 발견된 원리들의 집합이었으며, 이는 측량, 건축, 천문학, 다양한 공예 분야의 실용적인 요구를 충족시키기 위해 개발되었다. 기하학에 관한 가장 오래된 텍스트는 이집트의 린드 수학 파피루스 (기원전 2000–1800년)와 모스크바 수학 파피루스 (기원전 1890년경), 그리고 바빌로니아의 점토판, 예를 들어 플림톤 322 (기원전 1900년)이다.^[7] 예를 들어, 모스크바 파피루스는 잘린뿔의 부피를 계산하는 공식을 제공한다.^[7]

고대 그리스의 역사가 헤로도토스의 기록^[159][160]에 따르면, 이집트에서는 매년 봄 나일강이 범람하여 밭 경계선이 유실되었기 때문에, 측량 전문 집단인 "밧줄 기술자"가 토지를 구획하는 기술이 발달했다. 피타고라스의 정리는 고대 이집트에서 5000년 전에 이미 경험칙으로 알려져 있었고, 밧줄 기술자들은 3:4:5 비율로 표시된 밧줄을 이용해 밭의 직각을 잡았다고 한다.^[152]

3. 1. 고대 기하학

3. 2. 인도와 이슬람의 기하학

3. 3. 중세 및 르네상스 시대의 기하학

3. 4. 근대 기하학의 발전

3. 5. 현대 기하학

4. 주요 개념 및 분야

• 유클리드 기하학
• 심플렉틱 기하학
• 비유클리드 기하학: 리만 기하학
• 대수기하학
• 해석기하학
• 미분기하학
• 복소기하학
• 사영기하학
• 위상수학
• 프랙탈
• 종합 기하학
• * 유클리드 기하학
• ** 초등 기하학

• ** 기하학 기초론
• * 비유클리드 기하학
• ** 타원 기하학

• ** 쌍곡 기하학
• 비 아르키메데스 기하학
• 사영 기하학
• 아핀 기하학
• 해석 기하학
• 대수 기하학
• * 수론 기하학
• * 디오판토스 기하학
• 미분 기하학
• * 리만 기하학
• * 심플렉틱 기하학
• 복소 기하학
• 유한 기하학
• 이산 기하학
• * 디지털 기하학
• 볼록 기하학
• 계산 기하학
• 프랙탈
• 인시던스 기하학
• 비가환 기하학
• * 비가환 대수 기하학

4. 1. 유클리드 기하학

4. 2. 비유클리드 기하학

4. 3. 해석기하학

4. 4. 미분기하학

4. 5. 대수기하학

4. 6. 위상수학

4. 7. 이산 기하학

4. 8. 계산 기하학

4. 9. 기하학적 군론

5. 응용

기하학은 수학의 다른 분야뿐만 아니라 물리학, 공학, 컴퓨터 과학, 건축, 예술 등 다양한 분야에 응용된다.

6. 한국의 기하학

참조

_[1] 웹사이트 Geometry - Formulas, Examples {{!}} Plane and Solid Geometry https://cuemath.com/[...] 2023-08-31
_[2] 서적 Mathematizing Space: The Objects of Geometry from Antiquity to the Early Modern Age https://books.google[...] Birkhäuser 2019-09-14
_[3] 서적 Geometry: the language of space and form https://archive.org/[...] Infobase Publishing 2014
_[4] 서적 Geometry and Its Applications https://books.google[...] Elsevier 2019-09-14
_[5] 저널 Methods and traditions of Babylonian mathematics 1981
_[6] 서적 The Exact Sciences in Antiquity Dover Publications 2021-02-27
_[7] 문서 Egypt
_[8] 저널 Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph 2016-01-29
_[9] 저널 Gnomons at Meroë and Early Trigonometry 1998-01-01
_[10] 웹사이트 Neolithic Skywatchers http://www.archaeolo[...] 1998-05-27
_[11] 문서 Ionia and the Pythagoreans
_[12] 서적 An Introduction to the History of Mathematics Saunders
_[13] 저널 The Discovery of Incommensurability by Hippasus of Metapontum Annals of Mathematics, Trustees of Princeton University on Behalf of the Annals of Mathematics, Mathematics Department, Princeton University
_[14] 저널 The Pentagram and the Discovery of an Irrational Number https://www.tandfonl[...] 2022-09-09
_[15] 문서 The Age of Plato and Aristotle
_[16] 문서 Euclid of Alexandria
_[17] 문서 Euclid of Alexandria
_[18] 서적 An Introduction to the History of Mathematics Saunders
_[19] 웹사이트 A history of calculus http://www-groups.dc[...] University of St Andrews 1996-02
_[20] 저널 Greek and Vedic Geometry
_[21] 문서 The arithmetic content of the ''Śulva Sūtras''
_[22] 문서
_[23] 문서
_[24] 서적 The development of Arabic mathematics : between arithmetic and algebra https://archive.org/[...] 1994
_[25] 문서 The Arabic Hegemony
_[26] 웹사이트 Al-Mahani
_[27] 웹사이트 Al-Sabi Thabit ibn Qurra al-Harrani
_[28] 웹사이트 Omar Khayyam
_[29] 서적 Geometry Routledge
_[30] 서적 History of Analytic Geometry https://books.google[...] Courier Corporation 2019-09-18
_[31] 서적 The Historical Development of the Calculus https://books.google[...] Springer Science & Business Media 2019-09-18
_[32] 서적 The Geometrical Work of Girard Desargues https://books.google[...] Springer Science & Business Media 2019-09-18
_[33] 서적 Introduction to Projective Geometry https://books.google[...] Courier Corporation 2019-09-18
_[34] 서적 Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century https://books.google[...] Springer Science & Business Media 2019-09-18
_[35] 서적 Geometric Algebra Applications Vol. I: Computer Vision, Graphics and Neurocomputing https://books.google[...] Springer 2019-09-18
_[36] 서적 Mathematical Thought From Ancient to Modern Times: Volume 3 https://books.google[...] Oxford University Press 2019-09-14
_[37] 서적 Using History to Teach Mathematics: An International Perspective https://books.google[...] Cambridge University Press 2019-09-14
_[38] 서적 The King of Infinite Space: Euclid and His Elements https://archive.org/[...] Basic Books
_[39] 서적 Geometry: Euclid and Beyond https://books.google[...] Springer Science & Business Media 2019-09-14
_[40] 서적 The Learning and Teaching of Geometry in Secondary Schools: A Modeling Perspective https://books.google[...] Taylor & Francis 2019-09-14
_[41] 서적 A Simple Non-Euclidean Geometry and Its Physical Basis: An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity https://books.google[...] Springer Science & Business Media 2019-09-14
_[42] 서적 Geometry: Our Cultural Heritage https://books.google[...] Springer Science & Business Media 2019-09-14
_[43] 서적 Euclid's Elements – All thirteen books in one volume Green Lion Press
_[44] 서적 Handbook of incidence geometry: buildings and foundations North-Holland
_[45] 학술지 Individuals and Points 1985-01
_[46] 서적 Analytic Geometry of the Point, Line, Circle, and Conic Sections https://archive.org/[...]
_[47] 서적 Handbook of incidence geometry : buildings and foundations https://www.worldcat[...] Elsevier 2022-09-09
_[48] 웹사이트 geodesic – definition of geodesic in English from the Oxford dictionary https://www.oxforddi[...] OxfordDictionaries.com 2016-01-20
_[49] 서적 Topology https://www.worldcat[...] Prentice Hall, Inc 2000
_[50] 서적 From Affine to Euclidean Geometry https://books.google[...] Springer 2022-09-09
_[51] 서적 Complex analysis : an introduction to the theory of analytic functions of one complex variable https://books.google[...] McGraw-Hill 2022-09-09
_[52] 서적 Principles of geometry. Vol. 2 CUP Archive
_[53] 서적 Calculus. "Early Transcendentals."
_[54] 서적 Differential geometry of curves and surfaces https://books.google[...] Prentice-Hall 2022-09-09
_[55] 서적 The Red Book of Varieties and Schemes Includes the Michigan Lectures on Curves and Their Jacobians Springer-Verlag
_[56] 서적 The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions Basic Books
_[57] 백과사전 Angle
_[58] 서적 Trigonometry https://books.google[...] Birkhäuser 2022-09-10
_[59] 서적 Calculus: Early Transcendentals Brooks Cole Cengage Learning
_[60] 서적 Riemannian Geometry and Geometric Analysis Springer-Verlag
_[61] 서적 History and Measurement of the Base and Derived Units https://books.google[...] Springer International Publishing 2019-09-25
_[62] 서적 Geometry of Lengths, Areas, and Volumes https://books.google[...] American Mathematical Soc. 2019-09-25
_[63] 서적 Calculus https://books.google[...] SIAM 2019-09-25
_[64] 서적 A Primer of Lebesgue Integration https://books.google[...] Academic Press 2019-09-25
_[65] 서적 A Course in Metric Geometry American Mathematical Society
_[66] 서적 General Relativity University of Chicago Press 1984
_[67] 서적 An Introduction to Measure Theory https://books.google[...] American Mathematical Soc. 2019-09-25
_[68] 서적 Euclidean and Transformational Geometry: A Deductive Inquiry https://books.google[...] Jones & Bartlett Learning 2019-09-25
_[69] 서적 Mathematics for Elementary School Teachers: A Process Approach https://books.google[...] Cengage Learning 2019-09-25
_[70] 서적 Transformation Geometry: An Introduction to Symmetry https://books.google[...] Springer Science & Business Media 2019-09-25
_[71] 서적 The Emergence of the Fourth Dimension: Higher Spatial Thinking in the Fin de Siècle https://books.google[...] Oxford University Press 2019-09-18
_[72] 서적 Papers https://books.google[...] The Academy 2019-09-18
_[73] 서적 Infinite-Dimensional Dynamical Systems in Mechanics and Physics https://books.google[...] Springer Science & Business Media 2019-09-18
_[74] 서적 Recent Advances in Real Algebraic Geometry and Quadratic Forms: Proceedings of the RAGSQUAD Year, Berkeley, 1990–1991 https://books.google[...] American Mathematical Soc. 2019-09-18
_[75] 서적 Why Beauty Is Truth: A History of Symmetry https://books.google[...] Basic Books 2019-09-23
_[76] 서적 Mathematics Of Harmony: From Euclid To Contemporary Mathematics And Computer Science https://books.google[...] World Scientific 2019-09-23
_[77] 서적 Symmetry as a Developmental Principle in Nature and Art https://books.google[...] World Scientific 2019-09-23
_[78] 서적 Introduction to Symmetry Analysis https://books.google[...] Cambridge University Press 2019-09-23
_[79] 서적 Geometry of Lie Groups https://books.google[...] Springer Science & Business Media 2019-09-23
_[80] 서적 Beyond Geometry: Classic Papers from Riemann to Einstein https://books.google[...] Courier Corporation 2019-09-23
_[81] 서적 Strings, Conformal Fields, and Topology: An Introduction https://books.google[...] Springer Science & Business Media 2019-09-23
_[82] 서적 Geometric Group Theory https://books.google[...] American Mathematical Soc. 2019-09-23
_[83] 서적 Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra https://books.google[...] World Scientific Publishing Company 2019-09-23
_[84] 서적 Directions in General Relativity: Volume 1: Proceedings of the 1993 International Symposium, Maryland: Papers in Honor of Charles Misner https://books.google[...] Cambridge University Press 2019-09-23
_[85] 서적 Projective Geometry https://archive.org/[...] McGraw-Hill book Company, Incorporated
_[86] 서적 Bundles of Topological Vector Spaces and Their Duality https://books.google[...] Springer 2019-09-23
_[87] 서적 Constructivism and Science: Essays in Recent German Philosophy https://books.google[...] Springer Science & Business Media 2019-09-20
_[88] 서적 Science https://books.google[...] Moses King 2019-09-20
_[89] 서적 Practical Geometry and Engineering Graphics: A Textbook for Engineering and Other Students https://books.google[...] Springer Science & Business Media 2019-09-20
_[90] 서적 Architecture and Geometry in the Age of the Baroque https://books.google[...] University of Chicago Press 2019-09-20
_[91] 서적 Geodesy: The Concepts https://books.google[...] Elsevier 2019-09-20
_[92] 서적 Applied Computational Aerodynamics https://books.google[...] Cambridge University Press 2019-09-20
_[93] 서적 Geometry of Navigation https://books.google[...] Horwood Pub. 2019-09-20
_[94] 학술지 A Coherent Curriculum: The Case of Mathematics. https://www.nifdi.or[...] 2002
_[95] 서적 Multivariable Calculus and Differential Geometry https://books.google[...] De Gruyter 2019-09-23
_[96] 서적 Differential Forms with Applications to the Physical Sciences https://books.google[...] Courier Corporation 2019-09-23
_[97] 서적 Applications of Differential Geometry to Econometrics https://books.google[...] Cambridge University Press 2019-09-23
_[98] 서적 Mathematics of Bioinformatics: Theory, Methods and Applications https://books.google[...] John Wiley & Sons 2019-09-23
_[99] 서적 General Theory of Relativity https://books.google[...] Princeton University Press 2019-09-23
_[100] 서적 Information Geometry https://books.google[...] Springer 2019-09-23
_[101] 서적 Essential Topology https://books.google[...] Springer Science & Business Media 2019-09-24
_[102] 서적 Topology and Geometry for Physicists https://books.google[...] Elsevier 2019-09-24
_[103] 서적 Transformation Geometry: An Introduction to Symmetry https://books.google[...] Springer Science & Business Media 2019-09-24
_[104] 서적 A Concise Course in Algebraic Topology https://books.google[...] University of Chicago Press 2019-09-24
_[105] 서적 Algebraic Geometry https://books.google[...] Springer Science & Business Media 2019-09-24
_[106] 서적 History of Algebraic Geometry https://books.google[...] CRC Press 2019-09-24
_[107] 서적 The Millennium Prize Problems https://books.google[...] American Mathematical Soc. 2019-09-24
_[108] 서적 Algebraic Geometry for Coding Theory and Cryptography: IPAM, Los Angeles, CA, February 2016 https://books.google[...] Springer 2019-09-24
_[109] 서적 Enumerative Invariants in Algebraic Geometry and String Theory: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 6–11, 2005 https://books.google[...] Springer 2019-09-24
_[110] 서적 Complex geometry : an introduction https://books.google[...] Springer 2005-01-01
_[111] 서적 Principles of algebraic geometry John Wiley & Sons
_[112] 서적 Differential analysis on complex manifolds https://books.google[...] Springer-Verlag 2022-09-09
_[113] 서적 Mirror symmetry American Mathematical Soc.
_[114] 서적 Lectures on Riemann surfaces Springer Science & Business Media
_[115] 서적 Algebraic curves and Riemann surfaces American Mathematical Soc.
_[116] 서적 Riemann surfaces https://www.worldcat[...] Oxford University Press 2022-09-09
_[117] 간행물 Faisceaux algébriques cohérents Annals of Mathematics
_[118] 간행물 Géométrie algébrique et géométrie analytique Annales de l'Institut Fourier
_[119] 서적 Lectures on Discrete Geometry https://books.google[...] Springer Science & Business Media 2019-09-25
_[120] 서적 The Cube – A Window to Convex and Discrete Geometry https://books.google[...] Cambridge University Press 2019-09-25
_[121] 서적 Convex and Discrete Geometry https://books.google[...] Springer Science & Business Media 2019-09-25
_[122] 서적 Discrete and Computational Geometry https://books.google[...] Princeton University Press 2019-09-25
_[123] 서적 Classical Topics in Discrete Geometry https://books.google[...] Springer Science & Business Media 2019-09-25
_[124] 서적 Computational Geometry: An Introduction https://books.google[...] Springer Science & Business Media 2019-09-25
_[125] 서적 Computational Conformal Geometry https://books.google[...] International Press 2019-09-25
_[126] 서적 Geometric Group Theory: An Introduction https://books.google[...] Springer 2019-09-25
_[127] 서적 The Geometrization Conjecture https://books.google[...] American Mathematical Soc. 2019-09-25
_[128] 서적 From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry: 3-manifolds, Right-angled Artin Groups, and Cubical Geometry https://books.google[...] American Mathematical Soc. 2019-09-25
_[129] 서적 Office Hours with a Geometric Group Theorist https://academic.oup[...] Princeton University Press 2017-07-11
_[130] 서적 Geometric Group Theory https://www.ams.org/[...] 2024-12-08
_[131] 서적 Handbook of Convex Geometry https://books.google[...] Elsevier Science 2019-09-24
_[132] 서적 Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry https://books.google[...] Springer Science & Business Media 2019-09-25
_[133] 서적 Geometry of Design: Studies in Proportion and Composition https://books.google[...] Princeton Architectural Press 2019-09-25
_[134] 서적 The Everything Cartooning Book: Create Unique And Inspired Cartoons For Fun And Profit https://books.google[...] Adams Media 2019-09-25
_[135] 서적 The Golden Ratio: The Story of PHI, the World's Most Astonishing Number https://books.google[...] Crown/Archetype 2019-09-25
_[136] 서적 M. C. Escher's Legacy: A Centennial Celebration https://books.google[...] Springer 2019-09-25
_[137] 서적 Drawing Course 101 https://archive.org/[...] Sterling Publishing Company, Inc.
_[138] 서적 Integrating the Arts Across the Elementary School Curriculum https://books.google[...] Cengage Learning 2019-09-25
_[139] 서적 Advances in Architectural Geometry 2010 https://books.google[...] Birkhäuser 2019-09-25
_[140] 서적 Architectural geometry https://books.google[...] Bentley Institute Press 2019-09-25
_[141] 서적 A World History of Architecture https://books.google[...] Laurence King Publishing 2019-09-25
_[142] 서적 Spherical Astronomy https://books.google[...] Cambridge University Press 2019-09-25
_[143] 서적 Recent Developments in Pseudo-Riemannian Geometry https://books.google[...] European Mathematical Society 2019-09-25
_[144] 서적 The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions https://books.google[...] Basic Books 2019-09-25
_[145] 서적 Geometry of Quantum States: An Introduction to Quantum Entanglement Cambridge University Press
_[146] 서적 Calculus with Analytic Geometry https://books.google[...] Elsevier Science 2019-09-25
_[147] 서적 Calculus https://books.google[...] W. H. Freeman 2019-09-25
_[148] 서적 Number Theory and Geometry: An Introduction to Arithmetic Geometry https://books.google[...] American Mathematical Soc. 2019-09-25
_[149] 서적 Pythagoras' Revenge: A Mathematical Mystery https://archive.org/[...] Princeton University Press
_[150] 서적 Modular Forms and Fermat's Last Theorem https://books.google[...] Springer Science & Business Media 2019-09-25
_[151] 서적 広辞苑第六版「幾何学」
_[152] 서적 ブリタニカ国際大百科事典2013小項目版「幾何学」
_[153] 웹사이트 幾何原本. 第1-6巻 / 利瑪竇 口訳 ; 徐光啓 筆受 https://www.wul.wase[...] 2020-12-07
_[154] 간행물 イエスズ会士と西洋数学の伝入 https://archives.buk[...] 佛教大学中国言語文化研究会 2001-07
_[155] 웹사이트 The Elements of Geometry https://www.wdl.org/[...] 2020-12-07
_[156] 간행물 The first Chinese translation of the last nine books of Euclid's Elements and its source https://doi.org/10.1[...]
_[157] 간행물 満洲語資料からみた「幾何」の語源について (数学史の研究) https://hdl.handle.n[...] 京都大学数理解析研究所 2024-02-26
_[158] 웹사이트 西学凡 / 艾儒畧 答述 https://www.wul.wase[...] 2020-12-07
_[159] 서적 岩波数学辞典 第4版 岩波書店
_[160] 서적 現代に活かす初等幾何入門 http://www.iwanami.c[...] 岩波書店
_[161] 서적 ユークリッド原論 追補版 http://www.kyoritsu-[...] 共立出版
_[162] 서적 円の数学 http://www.shokabo.c[...] 裳華房
_[163] 서적 円錐曲線論 http://www.kyoiku.co[...] 大学教育出版
_[164] 서적 大辞林「幾何学的精神」
_[165] 서적 大辞林「学問に王道なし」
_[166] 서적 Géométrie
_[167] 서적 関数を考える http://www.iwanami.c[...] 岩波書店
_[168] 서적 物理学への道程 https://www.msz.co.j[...] みすず書房
_[169] 서적 オイラーの解析幾何 http://www.kaimeisha[...] 海鳴社
_[170] 서적 多面体と宇宙の謎に迫った幾何学者 http://ec.nikkeibp.c[...] 日経BP社
_[171] 서적 幾何学入門上・下 筑摩書房
_[172] 서적 岩波数学辞典 第4版 岩波書店
_[173] 서적 ブリタニカ国際大百科事典2013小項目版「幾何学基礎論」
_[174] 서적 Grundlagen der Geometrie Teubner
_[175] 서적 ヒルベルト幾何学の基礎、クライン・エルランゲン・プログラム http://www.kyoritsu-[...] 共立出版
_[176] 서적 幾何学基礎論 http://www.chikumash[...] 筑摩書房 2005
_[177] 서적 幾何への誘い http://www.iwanami.c[...] 岩波書店 2000
_[178] 웹사이트 AlphaGeometry, a System That Nears Expert Proficiency in Proving Complex Geometry Theorems https://www.deeplear[...] 2024-01-26
_[179] 서적 수학의 기초와 기본 개념 경문사
_[180] 웹사이트 geometry http://www.etymonlin[...]
_[181] 서적 Euclid in China Brill 1998
_[182] 간행물 “几何”曾经不是几何学 — 明末“几何”及相关学科命名新探 http://blog.sciencen[...] 中国科学院科学传播局 2020-07-24
_[183] 저널 満洲語資料からみた「幾何」の語源について https://repository.k[...] 2020-07-26
_[184] 웹사이트 Pythagorean Theorem http://www.cut-the-k[...]
_[185] 웹사이트 Conic Sections http://xahlee.info/S[...]
_[186] 서적 수학으로 우주재패 살림MATH 2008
_[187] 문서 카를 프리드리히 가우스
_[188] 문서 십칠각형