PT129.S4.P4.Q20 > Analytics

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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.

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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.)

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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.

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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).

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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 ████ ██████████ █████████ ███ ████ █████ ██ ███ ████████

Question Type

Main point

The author makes two large points in this passage. First, fractal geometry has become attractive, because it shows that simple processes can be responsible for complex patterns. Second, there are conflicting views about the likely promise of fractal geometry. Some think fractal geometry will become important; others think it will achieve a lasting role only if it can support a system of theorems and proofs.

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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.

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.

88%

Fractal geometry is ███████████ ███████ ██ ███ ███ ██ ████████████████ █ ███████ ████ ███ ███████ █████████ ██ ████████ █████████ ████████ ████████ ██████ ██ ███████ ██████

Although some mathematicians believe fractal geometry will be able to describe complex natural forms, it’s not yet clear that fractal geometry currently allows this. In addition, (C) is too narrowly focused on self-similarity. Fractal geometry is significant because it shows how simple processes can be responsible for complex patterns. Self-similarity is part of fractal geometry, but the author doesn’t suggest that fractal geometry is significant because of self-similarity.

Using the Koch █████ ██ █ ██████ ███████ █████████ ████ █████████ █ ███ ████████████ ████████ ████ ██ ██████████ ██████ ██ █████████████ ████████ ███████ ██ ████ ███ ████ ██ █████████

The author doesn’t suggest fractal geometry is useful due to lack of reliance on theorems.

Though fractal geometry ███ ████ ███ ████ ██ █████ █████ ███ ███ ████████ ██ ██████ ████████ ████████████ ███████ ██ ██ ███ ████████ ██ ██ ██████ ███ ███ ███████████ ██ ████████ ███████ ███████

Actually, the author says some mathematicians believe it will be useful for describing natural shapes.

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PrepTest 129 - Section 4 - Passage 4 - Question 20

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