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Inductive Reasoning and Deductive Reasoning
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Patterns and Inductive Reasoning (1)

Fold a square piece of paper into two as shown in the following figure:

Unfold it and count the number of nonoverlapping triangles formed. Do this four times [see figures (b) to (d) above] and record the results in a table similar to the following:

Results of Folding a Square Piece of Paper
Fold Number of
Nonoverlapping
Triangles Formed
First 2
Second
Third
Fourth

How many triangles do you think will be formed after the fifth fold? Can you fill out the rest of the entries in the table without further folding the sheet of paper? Do you see a pattern?

To answer these questions, use inductive reasoning. Inductive reasoning allows you to make generalizations based on patterns of specific examples or past events.


Definition

Inductive reasoning begins with specific cases or examples from which a generalization is drawn. A generalization reached using inductive reasoning is called a conjecture.