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Date	Section	Topic	Exercises
Mon 29 Aug	1.1	Geometry of triangles	HW 1: Due Wed Sep 7
			p7 1.1: 1df, 3c, 2a, p34 2.1: 1, 2 choose one for each, write half a page on each.
	2.1	Euclid Proposition 2
	2.2
Wed 31 Aug	2.3	Geometry of triangles
Mon 5 Sep		No class
Wed 7 Sep	2.3	Geometry of triangles
Mon 12 Sep	3.1	Non-neutral Euclidean Geometry
Wed 14 Sep	3.2	Non-neutral Euclidean Geometry	HW 2: Read Sections 2.3, 3.1 - 3.3 from the text book.
			p64: Q1, 2, p83: Q17abcde, p93: 1,2
			This website gives around 100 different proofs of
			the Pythagorean Theorem! Describe one proof
			which you like, give some history if available and say why you like it. Due Wed Sep 21.
Mon 19 Sep	3.3	Non-neutral Euclidean Geometry
	3.4
Wed 21 Sep	3.5	Non-neutral Euclidean Geometry
Mon 26 Sep		No class
Wed 28 Sep	4.1	Circles	HW 3: Due Oct 12
			1. Read Sections 3.4 - 3.5 from the text book.
			2. Solve and submit the following problems.
			p97: Q11, p109: Q5, 10, p117: 12, p131: 15abfnp
			3. In Book 2, Proposition 6 (Prop 3.4.1 in the text book) Euclid constructed
			the golden ratio. Write half a page about the Golden Ratio and why you
			think its interesting.
			You can use wikipedia or cut-the-knot or other
			sources (please cite the source you use).
			https://en.wikipedia.org/wiki/Irrational_number
			https://www.cut-the-knot.org/do_you_know/GoldenRatio.shtml
Thu 29 Sep	4.2	Circles
Mon 3 Oct	4.3	Circles
Wed 5 Oct		No class
Mon 10 Oct		No class
Wed 12 Oct	4.4	Circles	HW 4: Due Oct 26
			1. Read Chapter 4 from the text book.
			2. p146 Q14, p149 Q5, p154 Q1, 4, 5, p163 Q1, 2, p165 Q21
			3. Please write a summary of Section 4.5 Impossible Constructions.
			Please mention all the 4 construction problems. Your summary should
			be between 1-2 pages (and no more).
Mon 17 Oct	5.1	Towards projective geometry
	5.2
Wed 19 Oct	5.3	Projective geometry	HW 5: Due Wed Nov 9
			1. Read Chapter 5 from the text book.
			2. p182 Q 7d, 11c, 16, p188 Q4, 11, p195 Q5, p196 Q8fghk
			3. Please write one page about “Finite Geometries”. Please cite your references.
Mon 24 Oct	6.1	Planar symmetries
Wed 26 Oct	6.2	Planar symmetries
Mon 31 Oct		Review
Wed 2 Nov		Midterm exam
Mon 7 Nov	6.3	Planar symmetries
Wed 9 Nov	6.4	Planar symmetries	HW 6: Due Wed Nov 23
			1. Read Chapter 6 from the text book.
			2. p202 Q2, 8, p208, Q20, p215 Q20, p218, Q6, 8, p227 Q6, 8, 12, 14
			3. Write a one page summary of Section 6.6 “Frieze Patterns”.
	6.5
Mon 14 Nov	1.1	Spherical geometry: points, lines
Wed 16 Nov		Spherical geometry
Mon 21 Nov		Girard’s Theorem, Euler’s Formula
Wed 23 Nov		Spherical trigonometry	HW 7: Due Wed Dec 7
			1. Using the spherical distance formula prove that the antipodal map
			is a spherical isometry.
			2. Find the great circle containing the following pairs of points:
			(a) P = (0, 0, -1) and Q = (0, 1, 0),
			(b) P = (1/2, -1/2, 1/ 2) and Q = (2/3, 1/3, -2/3).
			3. Are the points P = (0, 0, −1), Q = (0, 1, 0) and R = (0, 0, 1) collinear ?
			4. Find the spherical distance between the following pairs of points:
			(a) P = (0, 0, -1), Q = (0, 1, 0),
			(b) P = (1/2, -1/2, 1/ 2), Q = (2/3, 1/3, -2/3),
			(c) P = (0, 1/2, \(\sqrt{3}/2\)) and −P = (0, -1/2, -\(\sqrt{3}/2\)).
			5. Find angle between the following great circles:
			(a) \(L_{\bf j}\) and \(L_{\bf k}\),
			(b) \(L_{\langle 1/3,2/3,2/3 \rangle}\) and \(L_{\langle -3/5,4/5,0 \rangle}\).
			6. Find the area of the triangle with the following vertices:
			(a) P = (1, 0, 0), Q = (0, −1, 0) and R = (0, 0, −1),
			(b) P = (1/2, −1/2, 1/ 2), Q = (2/3, 1/3, -2/3), and R = (1, 0, 0).
			7. Can we have a polyhedron consisting of 12 hexagonal faces
			and every vertex of degree 4?
Mon 28 Nov		Taxicab geometry
Wed 30 Nov		Hyperbolic geometry
Mon 5 Dec		Hyperbolic geometry
Wed 7 Dec		Report presentations
Mon 12 Dec		Review

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