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The image shows a dilation of an equilateral triangle by scale factors of 1, 2, 3, and 4. At each stage, the dilated shape is partitioned into triangles congruent to the original. 1. Why is the difference in the number of original triangles that fit into the image between 2 successive scale factors always odd? 2. What does this image tell us about the sum of the first n odd numbers?

The image shows a dilation of an equilateral triangle by scale factors of 1, 2, 3, and 4. At each stage, the dilated shape is partitioned into triangles congruent to the original. 1. Why is the difference in the number of original triangles that fit into the image between 2 successive scale factors always odd? 2. What does this image tell us about the sum of the first n odd numbers?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The image shows a dilation of an equilateral triangle by scale factors of 1, 2, 3, and 4. At each stage, the dilated shape is partitioned into triangles congruent to the original. **Diagram Explanation:** This diagram features an equilateral triangle subdivided into smaller triangles. These smaller triangles are all congruent to the original triangle. As the scale factor increases, the number of smaller triangles increases, forming a larger composite triangle. 1. Why is the difference in the number of original triangles that fit into the image between 2 successive scale factors always odd? 2. What does this image tell us about the sum of the first n odd numbers?
Transcribed Image Text:The image shows a dilation of an equilateral triangle by scale factors of 1, 2, 3, and 4. At each stage, the dilated shape is partitioned into triangles congruent to the original. **Diagram Explanation:** This diagram features an equilateral triangle subdivided into smaller triangles. These smaller triangles are all congruent to the original triangle. As the scale factor increases, the number of smaller triangles increases, forming a larger composite triangle. 1. Why is the difference in the number of original triangles that fit into the image between 2 successive scale factors always odd? 2. What does this image tell us about the sum of the first n odd numbers?
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