Self-study
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
26.
The
a
The Koch curve ██ ███ ████ ██████ ██████████ ███ █████████ ███ ████ ██████████ ██ ███ █████ ███████ ██ ███████ ██████████
The author doesn’t indicate that the enthusiastic practitioners think the Koch curve is the “most important” form studied by fractal geometry.
b
Fractal geometry will ██████████ ██ ████ ██ ██ ████ ██ ███ ████ ████████████ ███ █████ ███████████ ████████ ██ ███ █████
The author doesn’t indicate that the enthusiastic practitioners think fractal geometry will be used in the “same applications” as traditional geometry is now used. Although they think fractal geometry will describe natural forms “as easily and precisely as an architect can describe a house using the language of traditional geometry,” this doesn’t imply they think fractal geometry will be used in the SAME applications. The comparison is just about the ease of describing a form — fractal geometry can describe a cloud as easily as traditional geometry can describe a house.
c
The greatest importance ██ ████████ ██████ ██ ████████ ██ █████ ███████ ██ █████ ███████ ████████ ██ ███ █████████ ██ █ █████ ███████
The author doesn’t indicate that the enthusiastic practitioners think the “greatest” importance of images of fractals is the wider attention it can bring. There’s no hint of a ranking of reasons for importance.
d
Studying self-similarity was ██████████ ██████ ███ ███████████ ██ █████████████ ████████ █████████████
The author doesn’t indicate that the enthusiastic practitioners think studying self-similarity was “impossible” before computers. We don’t have any hint of their opinion regarding the possibility of studying self-similarity before sophisticated computer technologies.
e
Certain complex natural █████ ███████ █ ████ ██ ███████████████ ████ ████ █████████ ██ █████████