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Math · Intermediate

Perspective & Projective Geometry

Renaissance painters discovered how to draw a convincing 3D world on a flat canvas. Their rules grew into projective geometry, where parallel lines meet at infinity. Learn how a pinhole projects the world, why vanishing points work, the cross-ratio that no projection can change, and the surprising unity of circles, ellipses, parabolas and hyperbolas.

7 lessons~35 min0/7 complete
1

Drawing Depth

Projection and vanishing points.

  1. The Pinhole PictureSize shrinks with distance
  2. Vanishing PointsWhere parallel lines meet
2

Projective Geometry

What survives projection.

  1. The Cross-RatioAn invariant of perspective
  2. Points at InfinityA plane where any two lines meet
3

Other Projections

Shadows and distorted art.

  1. Sunlight & ShadowsParallel versus central projection
  2. Anamorphic ArtPictures that only work from one angle
  3. Two Eyes, DepthSeeing distance through disparity