/Type /XObject Non-Euclidean Geometry Figure 33.1. /BBox [0 0 100 100] stream The lecture notes are part of a book in progress by Professor Etingof. Class Worksheets and Lecture Notes. /Resources 21 0 R >> xÚÓÎP(Îà ýð /FormType 1 xÚÓÎP(Îà ýð Group actions on Similar Triangles - pdf. Basic Concepts 13 2.1. 0000001074 00000 n /S 1878 Sphere 5 1.2. endobj /Type /XObject /Length 15 /Resources 18 0 R << /Length 15 This is the amended file that contains the graphics. /Length 1149 endstream >> xÚÓÎP(Îà ýð 0000014938 00000 n 1.1 Transitional geometry Continuous passage between spherical and hyperbolic geometry, containing in the middle Euclidean geometry. stream xÚÓÎP(Îà ýð /Subtype /Form Euclidean Geometry (T2) Term 2 Revision; Analytical Geometry; Finance and Growth; Statistics; Trigonometry; Euclidean Geometry (T3) Measurement; Term 3 Revision; Probability; Exam Revision; Grade 11. 1. Let ABC be a right triangle with sides a, b and hypotenuse c.Ifd is the height of on the hypotenuse, show that 1 a2 + 1 b2 = 1 d2. /FormType 1 /Length 15 Revising Lines and Angles This lesson is a revision of definitions covered in previous grades. /Subtype /Form /Subtype /Form Lecture 33. Euclid [300 BC] understood euclidean plane via points, lines and circles. (line from centre ⊥ to chord) If OM AB⊥ then AM MB= Proof Join OA and OB. Motivating examples 5 1.1. >> << endstream >> endstream 7 0 obj Chapter 4 – To Boldly Go Where No Man Has Gone Before. Similar Triangles - pdf. >> << << >> /T 1114885 endstream 29 0 obj Suc h sur face s look the same at ev ery p oin t and in ev ery directio n and so oug ht to ha ve lots of symmet ries . /Length 15 xÚÓÎP(Îà ýð Ë endobj xÚíX]o›0}ϯð#HÃõ÷ÇÛº®ë6uÓÒòÖí’"èHªiÿ~ۄ¤4i“‡IRÀÆ6÷ܜsíkƒÀ p5A®ÄæŽ@s—˜B(H—“ŸÀô_vÐAª¿@Ó. Chapter 5 – Euclidean Geometry: Revisited. << %âãÏÓ euclidean geometry: grade 12 2. euclidean geometry: grade 12 3. euclidean geometry: grade 12 4. euclidean geometry: grade 12 5 february - march 2009 . endobj /Type /XObject endobj /BBox [0 0 100 100] /Matrix [1 0 0 1 0 0] Contents Chapter 1. /Resources 36 0 R /Subtype /Form /ID [] << (Construction of integer right triangles) It is known that every right triangle of integer sides (without common divisor) can be obtained by xÚÓÎP(Îà ýð /Matrix [1 0 0 1 0 0] /Type /XObject stream This PDF file should be readable by any PDF reader. 7 Pythagorean Theorem - pdf. /Resources 8 0 R This lesson introduces the concept of Euclidean geometry and how it is used in the real world today. stream endobj /N 40 /BBox [0 0 100 100] << Cylinder 7 1.3. CIRCLES 4.1 TERMINOLOGY Arc An arc is a part of the circumference of a circle Chord A chord is a straight line joining the ends of an arc. endobj Non-Euclidean geometry is nowadays an essential tool in physical theories that attempt to unite gravitation with other fun-damental forces. Aims and outcomes of tutorial: Improve marks and help you achieve 70% or more! 9 0 obj /Subtype /Form Chapter 1: Generalities on Quantum Field Theory ( PDF ) /FormType 1 /Length 15 /E 67719 Projective geometry provides a better framework for understanding how shapes change as perspective varies. xÚÓÎP(Îà ýð >> 0000015131 00000 n Class Worksheets and Lecture Notes. /Length 15 << 0000003610 00000 n /Resources 32 0 R Geometries 13 2.2. /Matrix [1 0 0 1 0 0] /O 569 >> These include line Groups 16 2.3. /H [ 1074 1242 ] Differential structures and the hyperbolic space, with relevant advertising. Euclidean Geometry 7 & 8 10 Aug – 23 Aug Worksheet Memo Watch the following videos Euclidean Geometry - Theory grades 8 - 11 Euclidean Geometry - Exam type question 1 Euclidean Geometry - Exam type question 2 Euclidean Geometry - Theory grade 12 Euclidean Geometry - Exam type question 3 Euclidean Geometry - Exam type question 4 Probability Thurston talked about the transition between 8geometries in dimen-sion 3. /Filter /FlateDecode /BBox [0 0 100 100] ¶ÿ§^×Ù卒 J¦+P¿€”L£ ‰’¡„ú äÎ5a\N…ääáÜ)¶¾u36­?8›ž[wì\¦«œÈɽ oq „ÊŸêÝì¨ KV”J,Ž¨‘U¨*Ãta¢çzȑsÂ"cõ|ÛÖ&Ϊ¥«/×ù“€œn~âϱD B±Ê$֒Àu6ø&_»w;„ÎõaA,4 J.G. The Contents page has links to all the sections and significant results. endstream >> >> /FormType 1 0000000972 00000 n /Matrix [1 0 0 1 0 0] stream lecture notes pdf way to generate one system can be evaluated by copyright, preview is a few days. stream €ì';¶ÛŸOœå[)o¡bÙ厣9¿ýïÖLOfAHzÉÊÂ5zoýŽE¿mƒñ= '¤}gF¤–ë4Í-®ôÛ°¹%7®-pWagRwaïõž½‘þ‹> O`ÙÝt¬Ë¯²§<. More examples 10 Chapter 2. Euclidean geometry in this classification is parabolic geometry, though the name is less-often used. stream /Subtype /Form /BBox [0 0 100 100] /Resources 30 0 R 0000019910 00000 n Quizzes Status. >> /Length 19 /FormType 1 /Filter /FlateDecode Course notes:— MAU23302 Course Notes, Hilary Term 2020, Part II, Section 1 (Stereographic Projection) Please refer to the calendar section for reading assignments for this course. stream 35 0 obj /BBox [0 0 100 100] 0000019194 00000 n 0000019639 00000 n endobj Chapter 1 – The Origins and Weapons of Geometry Read this short story about π. Chapter 3: Euclidean Constructions from January 30, … Euclidean geometry length and angle are well-de ned, measurable quantities independent of the observer. Because of Theorem 3.1.6, the geometry P 2 cannot be a model for Euclidean plane geometry, but it comes very ‘close’. /Linearized 1 /BBox [0 0 100 100] /Resources 12 0 R endstream Chapter 1 – The Origins of Geometry (available as a PDF file) Chapter 2 – Euclidean Geometry. >> 0000020521 00000 n /Matrix [1 0 0 1 0 0] /Subtype /Form /Filter /FlateDecode Euclid's Elements of Geometry, Books I—IV (PDF Version) Euclid's Elements, Book I—IV, translated and edited by Thomas, L. Heath (1908), PDF Version; Lecture Material covering Part II (Non-Euclidean Geometry) for Hilary Term 2020. 0000020321 00000 n /FormType 1 ŒaM›i&>”}i¦Î»¼‚_úè™Ùçÿû?ÏyÎsžÙ   `ô@ << << Chapter 6 – Euclidean Constructions. /FormType 1 /Filter /FlateDecode 5 Midpoint Theorem - pdf. 0000014631 00000 n YIU: Euclidean Geometry 4 7. 6 Pythagorean Theorem - video. /Type /XObject %PDF-1.5 4 0 obj Kneebone, Algebraic projective geometry, Clarendon Press, Oxford (1952) Chapter 1: History from January 9, 2002, available as a PDF file. 0000024570 00000 n 1 The euclidean plane 1.1 Approaches to euclidean geometry Our ancestors invented the geometry over euclidean plane. /Matrix [1 0 0 1 0 0] /Resources 5 0 R The algebra of the real numbers can be employed to yield /ViewerPreferences 566 0 R /Resources 34 0 R xÚÓÎP(Îà ýð 0000015426 00000 n Radius A radius is any straight line from the centre of the circle to a point on the circumference /Subtype /Form 567 25 0000002768 00000 n /Length 15 who founded what is now called Riemannian geometry that was studied by Clifford (1845–1879, he was at King’s as a teenager), and Einstein (1879–1955) to formulate the theory of General Relativity. stream 4 Midpoint Theorem - video. 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