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11B: Perspective and Symmetry

11B: Perspective and Symmetry. Two of the three aspects of Art that relate directly to Mathematics!. Perspective. Use of geometrical ideas  developed by the Greeks. Knowledge lost, then regained during Renaissance! What do you see? How do you paint it?. Perspective.

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11B: Perspective and Symmetry

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  1. 11B: Perspective and Symmetry Two of the three aspects of Art that relate directly to Mathematics!

  2. Perspective • Use of geometrical ideas  developed by the Greeks. • Knowledge lost, then regained during Renaissance! What do you see? How do you paint it?

  3. Perspective • Brunelleschi (1377-1466) • Alberti (1404-1472) ↑ Two painters credited with first developing a method of painting perspective that involved geometrical thinking.

  4. Perspective • Geometrical Method of Drawing Perspective Involves… • Vanishing Point: All lines that are parallel in the real scene and perpendicular to the canvas must intersect at the principal vanishing point of the painting.

  5. Perspective • Horizon Line: A horizontal line passing through the Principal Vanishing Point. The Line at which parallel lines meet.

  6. History! • Leonardo da Vinci (1452-1519): Contributed to the science of perspective through his paintings. • Albrecht Durer (1471-1528): Developed woodcutting techniques for showing perspective • Jan Vredman de Vries (1527-1604): Made extensive sketches to study perspective

  7. Symmetry • Refers to: Balance in a picture or shape, or repetition of patterns. • IN MATHEMATICS: Symmetry is a property of objects that remain unchanged after certain operations. (Rotation, Reflection, and Translation.)

  8. Symmetry • Reflection Symmetry: An object that remains unchanged when reflected across a straight line. • Rotation Symmetry: An object that remains unchanged when rotated through some angle about a point.

  9. Symmetry • Translation Symmetry: An object that remains that same when repeated, creating a pattern. XXXXXXXXXXX 

  10. Symmetry • Symmetry in Art:

  11. Symmetry • Tilings: covering a flat area with geometrical shapes; An arrangement of polygons into a pattern.

  12. Perspective And Symmetry • Homework! • Questions: 1, 24, 30, 32, 37

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