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Consider the problem of inscribing an equilateral pentagon in a square. There are two ways to do this; the figure below shows one method, where equilateral pentagon AEFGH is inscribed in square ABCD. B F E A H

Consider the problem of inscribing an equilateral pentagon in a square. There are two ways to do this; the figure below shows one method, where equilateral pentagon AEFGH is inscribed in square ABCD. B F E A H

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Inscribing an Equilateral Pentagon in a Square** Consider the problem of inscribing an equilateral pentagon in a square. There are two ways to do this; the figure below shows one method, where an equilateral pentagon AEFGH is inscribed in square ABCD. **Diagram Explanation:** - The square ABCD is illustrated with vertices labeled clockwise: A, B, C, and D. - The equilateral pentagon AEFGH is inscribed within the square. - The vertices of the pentagon are labeled as A, E, F, G, and H. - The pentagon shares vertex A with the square. - AE is drawn from A to E, which lies on line segment BE. - F is on BC, creating line segment EF, and the shape continues similarly to complete the pentagon. **Historical Context:** In the 10th century, Abu Kamil solved this problem. **Solution Approach:** His solution begins with: - Let AB = 10. - Let AE = x. **Challenge:** Complete Abu Kamil’s solution, and give an exact value for the length of AE.
Transcribed Image Text:**Inscribing an Equilateral Pentagon in a Square** Consider the problem of inscribing an equilateral pentagon in a square. There are two ways to do this; the figure below shows one method, where an equilateral pentagon AEFGH is inscribed in square ABCD. **Diagram Explanation:** - The square ABCD is illustrated with vertices labeled clockwise: A, B, C, and D. - The equilateral pentagon AEFGH is inscribed within the square. - The vertices of the pentagon are labeled as A, E, F, G, and H. - The pentagon shares vertex A with the square. - AE is drawn from A to E, which lies on line segment BE. - F is on BC, creating line segment EF, and the shape continues similarly to complete the pentagon. **Historical Context:** In the 10th century, Abu Kamil solved this problem. **Solution Approach:** His solution begins with: - Let AB = 10. - Let AE = x. **Challenge:** Complete Abu Kamil’s solution, and give an exact value for the length of AE.
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