Self-study
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
Analysis by KevinLin
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 ███ ████ ████████ ██ ███ ████ █████ ██ ███ █████ ██ ███ ████████████ ███████ ██ ███ ██████ ██ ███ ███████ ████ ██████ ███ ███ █████████████