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11B: Perspective and Symmetry

Discover the fascinating relationship between art and mathematics through the principles of perspective and symmetry. Delve into the history of perspective, from its origins with Brunelleschi and Alberti to its evolution with Leonardo da Vinci and Albrecht Durer. Learn how symmetry brings balance and patterns to art, whether through reflection, rotation, or translation. Explore tilings and geometrical shapes that create captivating patterns. Uncover how these mathematical concepts influence artistic creation and perception. Dive into your homework and explore the intriguing questions that arise from the interplay of perspective and symmetry in art. Get inspired to see the world through a mathematical lens.

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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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