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passage 4
P1
Fractal geometry is a mathematical theory devoted to the study of complex shapes called fractals. ████████ ██ █████ ██████████ ██ ████████ ███ ███ ████ ████████████ ████████ ████████ ███████ ███ ████████ ██ ████████████████ ███ ███████████ ██ █████████ ███████ ██ ████████ ██ █████████████ ███████ ██████ ██ ████ ████ █████ ████ ██████████ █████ █████████ ████ ███ ██████ ██ █ ██████ ███
Spotlight ·
Fractal geometry
No exact definition of fractals, but they show self-similarity: small details in shape look like the shape as a whole.
Example ·
Koch curve
The Koch curve is an example of a fractal. (Details of what the Koch curve looks like. No need to memorize this. Will come back if asked about it.)
P2
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More on the Koch curve ·
Can be created by computer
Interesting point about fractal geometry ·
Simple processes can create complex patterns
This is one of the major reasons people are into fractal geometry.
P3
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Enthusiasts ·
Believe fractal geometry will rival importance of calculus
Also believe it will allow mathematicians to effectively describe natural forms (such as a cloud).
Skeptics ·
Fractal geometry will have lasting ro in math only if it can support theorems and proofs
Passage Style
Critique or debate
Spotlight
25.
Each of the following statements █████ ███ ████ █████ ███ ██ ████████ ███████ ████ ███ ███████████ █████ ██ ███ ███████ ███████
a
The total number ██ ███████████ ██ ███ ████ █████ ██ ███ █████ ██ ███ ████████████ ███████ ██ ███ ██████ ██ ███ ███████ ████ ██████ ███ ███ █████████████
b
The line segments ██ ████ ██████████ █████ ██ ███ ████████████ ██ ███ ████ █████ ███ ███████ ████ ███ ████████ ██ ███ ████████ ██████
c
Theoretically, as the ████ █████ ██ ███████████ ███ ████ ████████ ██████ ██████████ ██████
d
At every stage ██ ████████████ ███ ████ ██████ ███ ███ ████ ████████ █████████ ██ ███ ██ █████ ███████
e
The length of ███ ████ ████████ ██ ███ ████ █████ ██ ███ █████ ██ ███ ████████████ ███████ ██ ███ ██████ ██ ███ ███████ ████ ██████ ███ ███ █████████████