Fractal Geometry

A free, expert breakdown of this official LSAT Reading Comprehension question.

TopicsInferenceScience

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Passage

Fractal geometry is a mathematical theory devoted to the study of complex shapes called fractals. Although an exact definition of fractals has not been established, fractals commonly exhibit the property of self-similarity: the reiteration of irregular details or patterns at progressively smaller scales so that each part, when magnified, looks basically like and then the process is repeated indefinitely on the segments at each stage of the construction.

Self-similarity is built into the construction process by treating segments at each stage the same way as the original segment was treated. Since the rules for getting from one stage to another are fully explicit and always the same, images of successive stages of the process can be generated by computer. Theoretically, illustrates a major attraction of fractal geometry: simple processes can be responsible for incredibly complex patterns.

A worldwide public has become captivated by fractal geometry after viewing astonishing computer-generated images of fractals; enthusiastic practitioners in the field of fractal geometry consider it a new language for describing complex natural and mathematical forms. They anticipate that fractal geometry's significance will rival that of calculus and expect that proficiency in in mathematics only if it becomes a precise language supporting a system of theorems and proofs.

What this question is testing

Inference

Your task

Find what must be true based on what the passage or stimulus states.

Common trap

Answers that are plausible or likely but not actually guaranteed by the text.

Winning move

Keep only the choice the statements fully support — eliminate anything that requires an extra assumption.

Reading along? Open the full official question in LawHub — we show a fragment here and keep the reasoning in our own words.

The question

25.

Each of the following statements about the Koch curve can be properly deduced from the information given in

Answer choices

Correct53% picked this
The total number of protrusions in the Koch curve at any stage of the construction depends on the length of the initial
Why this is right
The absolute length of the line is irrelevant to the total number of protrusions. You could start a Koch curve with a 10 foot line or a 1 foot line. The rules for making the curve involve dividing up that starting line into thirds, over and over again, infinitely. After the first round of division, both the 10 foot line and the 1 foot line will have one protrusion. There's no such thing as a total number when you're dividing infinitely. You end up with infinite number of protrusions, no matter how big your starting line is.
Skill tested: Inference · how this choice captures the passage's function is the move to repeat next time.
53%
Supported11% picked this
The line segments at each successive stage of the construction of the Koch curve are shorter than the
Since the instructions for making the Koch curve involve taking every line segment you can find and dividing it into three equal parts, as you build this curve, you're dealing with ever-smaller parts. If you started with a 9 ft line, you'd divide it into three 3 ft. segments. ___ ___ ___ 3 3 3 Then you'd copy that middle segment to make a protrusion. ___ / ___ All four of those segments are 3ft. long. Next, you take each of those 3ft. long segments and chop them into 3rd's. _ _ _ / ___ 1 1 1 At the first stage, we were dealing with 3ft segments. Now we're dealing with 1ft segments. And so on.
11%
Supported4% picked this
Theoretically, as the Koch curve is constructed its line segments become
In the middle of the 2nd paragraph it says: Theoretically, the Koch curve is the result of infinitely many steps in the construction process.
4%
Supported27% picked this
At every stage of constructing the Koch curve, all the line segments composing it are
As illustrated in the explanation for (B), if you start with a 9 ft. line, then the first stage involves a bunch of 3 ft. segments. At the second stage, you have all 1 ft. segments. At the third stage, you have all 1/3 ft. segments. The first paragraph explains: one begins with a straight line. The middle third of the line is removed and replaced with two line segments, each as long as the removed piece. Because it says "the middle third", it implies that we have divided the original straight line into thirds, which implies that all three segments are 1/3 the length of the original line. And then the passage explicitly says that the middle third is replaced with two segments that are each as long as the removed middle third.
27%
Supported4% picked this
The length of the line segments in the Koch curve at any stage of its construction depends on the length of the
As we've considered in (B) and (D), START: 9 ft. line STAGE 1: 3 ft segments STAGE 2: 1 ft segments STAGE 3: 1/3 ft segments Meanwhile, if we chose a different length of the initial line, we'd have different lengths at corresponding stages. START: 36 ft. line STAGE 1: 12 ft segments STAGE 2: 4 ft segments STAGE 3: 4/3 ft segments
4%

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