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.

5. 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.

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

7. 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

9. 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.)

10. 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.

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

12. Symmetry Symmetry in Art:

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

14. Perspective And Symmetry Homework! –Questions: 1, 24, 30, 32, 37