Andre's Art and Infinity worksheet
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Art and Infinity Worksheet
Objective: Identify techniques used to represent infinity, explore logarithmic relationships, explore infinitely small versus infinitely large
The concept of infinity is used by many artists, including Escher. Tools used to represent infinity include repeating patterns in tessellations, changes in scale, or figures receding into hyperbolic space.
1) The concept of infinity is also often associated with representations of God. Escher’s Tower of Babel can be considered biblical representations of man’s striving for the infinite power and wisdom of God. Looking at the figure:
a) Will the tower reach to infinity? Explain how you can tell.
b) Can you estimate how many stories the tower of Babel will reach before it consists to a single brick? Justify your estimate with a calculation
Tower of Babel
2) Escher's Whirlpool is another representation of infinity. How does it differ from the Tower of Babel ? What technique is used?.
a) Measure the diameter of the first 7 loops. Create a scatterplot of diameter of loop versus loop number.
b) What type relationship do you see? Using your graphing calculator, find an equation to predict the diameter of the loop given the loop number. How well does your equation fit the measurements?
c) What is the diameter of the 15th loop? The 25th loop?
d) Will the loop diameter ever equal zero?
Whirlpool
