Foundations of Geometry
A proof-based course in geometry, beginning from axioms for plane geometry. We will also look at properties involving distance, angles, triangles, quadrilaterals, and circles, as well as Euclidean and non-Euclidean geometry.
Course curriculum
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2
Incidence Geometry
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Day 3 - Axiomatic Systems and Incidence Geometry
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Day 4 - Incidence Geometry Theorems and Proofs
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3
Neutral Geometry
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Day 5 - Plane Geometry
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Day 6 - Metrics
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Day 7 - Half-Planes and Angles
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Day 8 - Crossbar Theorem, Linear Pair Theorem, and Perpendiculars
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Day 9 - Side-Angle-Side Congruence
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Day 10 - Parallel Postulates and Neutral Geometry
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Test 1
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Test 1 Upload
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4
Triangles
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Day 11 - Triangle Congruence
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Day 12 - Inequalities for Triangles
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Day 13 - Parallel Lines and Angles Sums for Triangles
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5
Quadrilaterals
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Day 14 - Quadrilaterals
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Day 15 - Equivalence to Euclidean Parallel Postulate
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Day 16 - Rectangles
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Day 17 - Existence of Rectangles
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6
Euclidean Geometry
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Day 18 - Euclidean Geometry
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Day 19 - Pythagorean Theorem and Trigonometry
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Test 2
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Test 2 Upload
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7
Hyperbolic Geometry
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Day 20 - Hyperbolic Geometry: A Descent Into Madness
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Day 21 - Additional Parallels
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Day 22 - Asymptotes and Classifying Parallels
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Day 23 - The Critical Function and Defect Revisited
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8
Area
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Day 24 - Area
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Day 25 - Dissection
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Day 26 - Circles
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Day 27 - Circumference and Area of Euclidean Circles
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Day 28 - Area in Hyperbolic Geometry
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9
Conclusion
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Day 29 - Concluding Thoughts
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Test 3
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Test 3 Upload
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