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

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Presentation transcript:

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 Brunelleschi ( ) Alberti ( ) ↑ Two painters credited with first developing a method of painting perspective that involved geometrical thinking.

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.

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

History! Leonardo da Vinci ( ): Contributed to the science of perspective through his paintings. Albrecht Durer ( ): Developed woodcutting techniques for showing perspective Jan Vredman de Vries ( ): Made extensive sketches to study perspective

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.)

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.

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

Symmetry Symmetry in Art:

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

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