Public learning track
Cartographic Map Projections and Metric Distortions
9th Grade · Math · Open Global Math
7 lessons
Goal
Analyze how mapping a 3D spherical surface onto 2D planes induces metric distortions in angles, scale, and surface area across cylindrical, conic, and azimuthal projections.
Featured Diagrams
Geometry of the Sphere, Great Circles, and Gaussian Curvature
7 lessons
0 of 7 done
- 1Geometry of the Sphere, Great Circles, and Gaussian CurvatureUp nextStart
- 2Cylindrical Projections and Areal Distortion: The Mercator MapPremiumNot started yet
- 3Equal-Area Cylindrical Projections and Angular DistortionNot started yet
- 4Conic Projections and Mid-Latitude Metric AccuracyNot started yet
- 5Azimuthal Projections, Polar Navigation, and Great-Circle RoutesNot started yet
- 6Tissot's Indicatrix: Quantifying Local Metric DistortionNot started yet
- 7Evaluating and Selecting Map Projections for Geospatial ProblemsNot started yet
Curriculum Framework
9th Grade · Math · Open Global Math
1
7 lessons
The Pythagorean Theorem: Geometric Proofs, Converse, and Applications
Master geometric and similarity-based proofs of the Pythagorean theorem, use its converse to classify triangles, and solve complex multi-step geometric problems.
2
9 lessons
Foundations of Right Triangle Trigonometry
Establish sine, cosine, and tangent ratios through triangle similarity, derive exact trigonometric values for special angles, and utilize fundamental trigonometric identities.
3
7 lessons
Right Triangle Trigonometry: Solving Triangles and Real-World Applications
Solve unknown sides and angles in right triangles and apply trigonometric techniques to solve complex multi-step real-world problems.
4
5 lessons
Circle Metrics: Arc Length, Sectors, and Circular Segments
Derive and calculate arc length, sector area, and circular segment area in degrees and radians, and solve composite geometric problems.
5
10 lessons
Cavalieri's Principle and Spatial Measurement of 3D Solids
Use Cavalieri's principle and solid decomposition methods to derive and calculate surface areas and volumes of prisms, cylinders, pyramids, cones, spheres, and composite solids.
6
7 lessons
Cartographic Map Projections and Metric Distortions
Analyze how mapping a 3D spherical surface onto 2D planes induces metric distortions in angles, scale, and surface area across cylindrical, conic, and azimuthal projections.