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
███████████████ ██ █████ ████ ███ ████████████ ███████ ██ ████████ ████████ ██ ████ █████ ███ ████ ███ ██ ███ ████████ ███████ ███ ████████ █████ ███ █████ ███ ███████ ████ ███ █████ ██ ███████ ███
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
27.
The information in the passage ████ ████████ █████ ███ ██ ███ █████████ ███████████
a
The appeal of █ ████████████ ██████ ██ ███████ ██ █████ ███████████ ███ ███ █████ ███ ████████ ███ ██████ ████████ ██ ████ ███████
Not supported, because the author indicates that a “worldwide public has become captivated by fractal geometry.” There’s no indication that the wider public understands theorems and proofs.
b
Most of the █████████ ██████ █████████████ ██ ████████████ ██████ █████ ███ ████ ████ ████████ ███████ ███ ███████ ██ █████████ ██ ███████████ █████████ ███████ ███████
The author never makes any claims about “most” (over half) of the important recent breakthroughs in math theory.
c
Fractal geometry holds ███ █████████ ██ ███████ ███████████ ████████ ██ ████ ██ ███ ███████████ █████████████
The author doesn’t indicate that fractal geometry might “replace” traditioanl geometry in “most” (over half) of engineering applications. Some practitioners think it will eventually be able to describe natural forms as easily as traditional geometry can, but this doesn’t relate to the idea of replacing traditional geometry, nor does it suggest anything about “most” engineering applications.
d
A mathematical theory ███ ██ █████████ ███ ████ ████████████ ████ ██████ ██ ███████████ █ ███████ ██████████ ██ ███ ███████ ███████
Supported, because fractal geometry has been developed and
e
Only a mathematical ██████ ████ ████████ █ ██████ ██ ████████ ███ ██████ ████ ████ ████████████ ███████ █████ █ ███████████ ██████ ██ ███████████████
Not supported, because we know that there are already enthusiastic practitioners of fractal geometry even though fractal geometry doesn’t yet support a system of theorems and proofs.