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
20.
Which one of the following ████ ██████████ █████████ ███ ████ █████ ██ ███ ████████
a
Because of its ██████ ██████ ███████ ████████ ██ ██████████ █████████ ██ ████████ ██████████ ███ ██ █████████ ██████ ██ ████ ██ ██████████ ███ ██████ ███████████ ███████████ █████████
The author doesn’t take sides in the debate about fractal geometry. So we don’t know the author believes fractal geometry will grow in importance or make pre-fractal math obsolete.
b
Though its use ██ ███ ██████████ ██ █████████ ███████ █████ █████ ███████ ████████ ██ ██████████ ███ ████████████ ███████ ██ ██ ███ ███ ███████████ ████████ ██ ██████ ████████ ███ ███████████ █████ ██ ███████████ ████████████
This is the best answer. Fractal geometry is intriguing due to its ability to generate complex forms. But there are also some skeptics who don’t think it’s proven itself enough.
c
Fractal geometry is ███████████ ███████ ██ ███ ███ ██ ████████████████ █ ███████ ████ ███ ███████ █████████ ██ ████████ █████████ ████████ ████████ ██████ ██ ███████ ██████
Although
d
Using the Koch █████ ██ █ ██████ ███████ █████████ ████ █████████ █ ███ ████████████ ████████ ████ ██ ██████████ ██████ ██ █████████████ ████████ ███████ ██ ████ ███ ████ ██ █████████
The author doesn’t suggest fractal geometry is useful due to lack of reliance on theorems.
e
Though fractal geometry ███ ████ ███ ████ ██ █████ █████ ███ ███ ████████ ██ ██████ ████████ ████████████ ███████ ██ ██ ███ ████████ ██ ██ ██████ ███ ███ ███████████ ██ ████████ ███████ ███████
Actually, the author says