1. Euclidean description of a right isosceles gasket.
(a) Write the equations for the three lines defining the outer edge of the gasket with corners (0,0), (0,1), and (1,0).
(b) Write the equations for the three new lines involved in the first stage of the construction of this gasket. (That is, in removing the middle triangle.)
(c) How many new lines are needed for the second stage of the gasket?
(d) How many new lines are needed for the third stage of the gasket?
(e) How many equations would be needed to describe the gasket in this fashion? We call this a static description of the gasket, since it focuses on the appearance as a finished object, not on the dynamical process by which it is "grown."
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