Post on 19-Jan-2016
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 (1377-1466)
• Alberti (1404-1472) ↑
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 (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
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.
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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