Lecture Notes in Modern Geometry RUI WANG The content of this note mainly follows John Stillwell’s book geometry of surfaces. Aims and outcomes of tutorial: Improve marks and help you achieve 70% or more! 3.1.7 Example. Chapter 3 – Transformation Geometry: First View. %âãÏÓ /Root 568 0 R /BBox [0 0 100 100] << /FormType 1 >> %ÐÔÅØ >> Chapter 2: Euclidean Geometry from January 9, 16, and 23, available as one PDF file. There are analogies between hyperbolic and spherical geometries. 0000014631 00000 n 0000046097 00000 n 20 0 obj J.G. /Length 15 /BBox [0 0 100 100] /Matrix [1 0 0 1 0 0] endobj 4 Midpoint Theorem - video. General Relativity Without Calculus: A Concise Introduction to the Geometry of Relativity (Undergraduate Lecture Notes in Physics) Kindle Edition. Lecture Notes in Euclidean Geometry: Math 226 Dr. Abdullah Al-Azemi Mathematics Department Kuwait University January 28, 2018 /Length 276 /BBox [0 0 100 100] /Filter /FlateDecode De nition 1. 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. Class Worksheets and Lecture Notes. 1.1 Transitional geometry Continuous passage between spherical and hyperbolic geometry, containing in the middle Euclidean geometry. 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. 0000002768 00000 n EUCLIDEAN GEOMETRY Technical Mathematics GRADES 10-12 INSTRUCTIONS FOR USE: This booklet consists of brief notes, Theorems, Proofs and Activities and should not be taken as a replacement of the textbooks already in use as it only acts as a supplement. 0000020142 00000 n > Grade 12 – Euclidean Geometry. startxref The line drawn from the centre of a circle perpendicular to a chord bisects the chord. << Euclid’s fth postulate Euclid’s fth postulate In the Elements, Euclid began with a limited number of assumptions (23 de nitions, ve common notions, and ve postulates) and sought to prove all the other results (propositions) in … What is Euclidean Geometry? Radius A radius is any straight line from the centre of the circle to a point on the circumference << 31 0 obj 5 Midpoint Theorem - pdf. >> 60 0 obj > Grade 10 – Euclidean Geometry. << I also discuss connections between Minkowskian geometry and non-Euclidean (= hyperbolic) plane geometry. Euclidean geometry in this classification is parabolic geometry, though the name is less-often used. /Subtype /Form /Matrix [1 0 0 1 0 0] This is the amended file that contains the graphics. << Kneebone, Algebraic projective geometry, Clarendon Press, Oxford (1952) /Resources 10 0 R Links are outlined in red: clicking on them moves you to the point indicated. /BBox [0 0 100 100] /Subtype /Form 8 Euclidean Geometry … Differential structures and the hyperbolic space, with relevant advertising. Lecture Notes – Math 119 Some Fundamental Topics in Analytic & Euclidean Geometry 1. /Subtype /Form endstream endobj /FormType 1 /Length 15 /E 67719 endobj 0000002316 00000 n >> /Type /XObject /BBox [0 0 100 100] >> 0000015131 00000 n stream endstream /Filter /FlateDecode /Pages 562 0 R >> This lesson introduces the concept of Euclidean geometry and how it is used in the real world today. Grade 11 Euclidean Geometry 2014 1 GRADE 11 EUCLIDEAN GEOMETRY 4. ˒›Á,7A]) 6 5–XDȔJ 23 0 obj /Type /Catalog /N 40 567 0 obj /Subtype /Form /Resources 12 0 R Sphere 5 1.2. xÚÓÎP(Îà ýð The geometr y of the sphere and the plane are familia r; hyp erb olic ge-ometr y is the geometry of the third case. endstream 0000000972 00000 n /Resources 36 0 R 0000003208 00000 n 0000000017 00000 n xÚÓÎP(Îà ýð /Length 15 /BBox [0 0 100 100] The projective geometry most relevant to painting is called the real projective plane, and is denoted RP2 or P(R3). /Matrix [1 0 0 1 0 0] 51 0 obj /Lang (en-ZA) Ë stream Further we discuss non-Euclidean geometry: (11) Neutral geometry geometrywithout the parallelpostulate; (12) Conformaldisc model this is a construction of the hyperbolic plane, an example of a neutral plane which is not Euclidean. endstream 7 Pythagorean Theorem - pdf. /Length 15 >> /Resources 18 0 R >> stream stream /Subtype /Form /Subtype /Form 17 0 obj Contents Chapter 1. 0000003610 00000 n Gauss (1777{1855) was the son CHAPTER 8 EUCLIDEAN GEOMETRY BASIC CIRCLE TERMINOLOGY THEOREMS INVOLVING THE CENTRE OF A CIRCLE THEOREM 1 A The line drawn from the centre of a circle perpendicular to a chord bisects the chord. 29 0 obj trailer 33 0 obj Non-Euclidean geometry is nowadays an essential tool in physical theories that attempt to unite gravitation with other fun-damental forces. The Contents page has links to all the sections and significant results. Quiz - Euclidean Geometry. /BBox [0 0 100 100] /FormType 1 << /Resources 5 0 R /Type /XObject /Subtype /Form Thurston talked about the transition between 8geometries in dimen-sion 3. /Filter /FlateDecode 1 The euclidean plane 1.1 Approaches to euclidean geometry Our ancestors invented the geometry over euclidean plane. /Subtype /Form 2 Basics of spherical geometry /Matrix [1 0 0 1 0 0] ¶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 /Filter /FlateDecode /ViewerPreferences 566 0 R /Length 15 >> stream /Linearized 1 26 0 obj /Info 565 0 R stream 1. ŒaM›i&>”}i¦Î»¼‚_úè™Ùçÿû?ÏyÎsžÙ   `ô@ Chapter 4 – To Boldly Go Where No Man Has Gone Before. >> These include line 1.3 Bibliography The books below served as references for these notes. Basic Concepts 13 2.1. >> 0000020321 00000 n /FormType 1 /BBox [0 0 100 100] stream Fix a plane passing through the origin in 3-space and call it the Equatorial Plane by analogy with the plane through the equator on the earth. xœí•mPTUÇϹ÷î î؀ò endstream endstream In (13) we discuss geometry of the constructed hyperbolic plane this is the highest point in the book. Groups 16 2.3. Geometries 13 2.2. Projective Geometry AfÞne Geometry Euclidean Geometry Figure 1.3: The geometry hierarchy. /Type /XObject The following examinable proofs of theorems: The line drawn from the centre of a circle perpendicular to a chord bisects the chord; The angle subtended by an arc at the centre of a circle is double the size of the angle subtended Spherical geometry is still rather dormant. /FormType 1 0000065909 00000 n xÚÓÎP(Îà ýð xÚÓÎP(Îà ýð endobj 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. /FormType 1 /Type /XObject /Resources 21 0 R More examples 10 Chapter 2. << With this idea, two lines really >> Chapter 6 – Euclidean Constructions. stream Functionality and topology geometric geodesy notes pdf Class Worksheets and Lecture Notes. You need to have a copy of Adobe Reader to open these. << 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. /Filter /FlateDecode endstream xÚÓÎP(Îà ýð xÚíX]o›0}ϯð#HÃõ÷ÇÛº®ë6uÓÒòÖí’"èHªiÿ~ۄ¤4i“‡IRÀÆ6÷ܜsíkƒÀ p5A®ÄæŽ@s—˜B(H—“ŸÀô_vÐAª¿@Ó. Cylinder 7 1.3. 0000019639 00000 n /FormType 1 0000020521 00000 n /Size 592 0000014938 00000 n /T 1114885 5 Quadrilaterals - video. 57 0 obj Denote by E 2 the geometry in which the E-points consist of all lines << Progress. /Length 15 /Subtype /Form 6 Quadrilaterals - pdf. << endstream /Matrix [1 0 0 1 0 0] stream endstream Chapter 1 – The Origins and Weapons of Geometry Read this short story about π. 0000003910 00000 n the Euclidean plane; and if K < 0 it is the hyp erb olic plane, also called 2-dimensiona l hyp erb olic space. Course 224: Geometry - Continuity and Differentiability Lecture Notes by Prof. David Simms LATEXed by Chris 0000003412 00000 n Group actions on /Type /XObject They include computer vision books that present comprehensive chapters on projective geometry. endobj If you don't see any interesting for you, use our search form on bottom ↓ . << /Subtype /Form Quizzes Status. /Filter /FlateDecode xÚÓÎP(Îà ýð 9 0 obj /Length 15 0000065989 00000 n stream The lecture notes are part of a book in progress by Professor Etingof. The page number at the foot of each page is a link back to the Contents page. /Length 19 Non-Euclidean Geometry Figure 33.1. endobj << De nition 1. (Construction of integer right triangles) It is known that every right triangle of integer sides (without common divisor) can be obtained by /Type /XObject Similar Triangles - pdf. This is a set of unpublished lecture notes for a course on "Geometry and Spacetime" that I taught several times at the University of California in Irvine. /BBox [0 0 100 100] /L 1126353 endobj %PDF-1.5 0 /Filter /FlateDecode Particles and Fundamental Interactions: An Introduction to Particle Physics (Undergraduate Lecture Notes in … 11 0 obj /Length 865 /Filter /FlateDecode 2. /Filter /FlateDecode 4 0 obj /Resources 30 0 R endobj /Type /XObject Lecture 33. 35 0 obj On this page you can read or download notes for euclidean geometry grade 12 in PDF format. /BBox [0 0 100 100] /Matrix [1 0 0 1 0 0] endstream endobj >> à,baô"…af² ˜i/˜×D#ËÚ /Matrix [1 0 0 1 0 0] 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. Spherical geometry is called elliptic geometry, but the space of elliptic geometry is really has points = antipodal pairs on the sphere. 6 Pythagorean Theorem - video. Euclid [300 BC] understood euclidean plane via points, lines and circles. /Resources 34 0 R 591 0 obj /S 1878 /Length 15 I discuss Minkowski spacetime in some detail and consider a number of issues concerning the foundations of (so called) "special relativity". Euclidean geometry length and angle are well-de ned, measurable quantities independent of the observer. endobj This lesson also traces the history of geometry. xڅ‘?OÃ0Å÷|Š ŸÛ1[QK¥ògJ'Ä`R–’¥(|zlԁéÎ:½ß{wæð stream €ì';¶ÛŸOœå[)o¡bÙ厣9¿ýïÖLOfAHzÉÊÂ5zoýŽE¿mƒñ= '¤}gF¤–ë4Í-®ôÛ°¹%7®-pWagRwaïõž½‘þ‹> O`ÙÝt¬Ë¯²§<. /Type /XObject /Matrix [1 0 0 1 0 0] xÚÓÎP(Îà ýð stream /BBox [0 0 100 100] Class notes and homework are available as PDF files. stream /Matrix [1 0 0 1 0 0] << The adjective “Euclidean” is supposed to conjure up an attitude or outlook rather than anything more specific: the course is not a course on the Elements but a wide-ranging and (we hope) interesting introduction to a selection of topics in synthetic plane geometry, with the construction of the regular pentagon taken as our culminating problem. /Length 15 /Type /XObject $52.24. Projective geometry provides a better framework for understanding how shapes change as perspective varies. The projective geometry most relevant to painting is called the real projective plane, and is denoted RP2 or P(R3). (line from centre ⊥ to chord) If OM AB⊥ then AM MB= Proof Join OA and OB. /Filter /FlateDecode (j&~w¾ÍQ’ñsA¬Q¶ï}.$ùXFn8ù0œ×¡†á|@ZLGÖÎö£¦t„ê"5«EÿçS6uö ä«mO EUCLIDEAN GEOMETRY: (±50 marks) EUCLIDEAN GEOMETRY: (±50 marks) Grade 11 theorems: 1. stream endstream Paste from the geometric lecture notes on the proof of euclidean space. /FormType 1 /Type /XObject Projective geometry provides a better framework for understanding how shapes change as perspective shifts. /Filter /FlateDecode Chapter 1: Generalities on Quantum Field Theory ( PDF ) endobj Chapter 1: History from January 9, 2002, available as a PDF file. /BBox [0 0 100 100] << >> /Filter /FlateDecode xÚÓÎP(Îà ýð TOPIC: Euclidean Geometry Outcomes: At the end of the session learners must demonstrate an understanding of: 1. /Length 15 euclidean geometry: grade 12 2. euclidean geometry: grade 12 3. euclidean geometry: grade 12 4. euclidean geometry: grade 12 5 february - march 2009 . endobj /Subtype /Form /Resources 27 0 R endstream /FormType 1 endstream The algebra of the real numbers can be employed to yield 0000019194 00000 n /Length 15 /Filter /FlateDecode xÚÓÎP(Îà ýð euclidean geometry: grade 12 6 november 2009 . /Type /XObject /Matrix [1 0 0 1 0 0] /H [ 1074 1242 ] /FormType 1 endobj Please refer to the calendar section for reading assignments for this course. /Filter /FlateDecode 567 25 /Resources 24 0 R 8. 0000024570 00000 n >> 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 /Prev 1114873 Course notes:— MAU23302 Course Notes, Hilary Term 2020, Part II, Section 1 (Stereographic Projection) /Length 1149 endstream %%EOF endobj endobj Chapter 5 – Euclidean Geometry: Revisited. 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