A Curious Construction
Project: Constructing π (Pi)
Many mathematicians have been interested in ways to construct the number pi (π).
Here is one such geometric construction:
In the drawing, triangles ABC and ADE are right triangles. The length of AB = 1.
The length of AD equals the length of AC and FB is parallel to EG.
The length of BG gives a decimal approximation of pi (π) to six decimal places.
Complete all calculations to 7 decimal places.
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1. Use the length of BC and the Pythagorean theorem to find the length of AC. |
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2. Find the length of AD. |
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3. Use the length of AD and the Pythagorean theorem to find the length of AE. |
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4. The sides of the similar triangles FED and DEA are in proportion. So, FE/0.5 = 0.5/AE. Find the length of FE. 
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5. Find the length of AF. |
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6. The sides of the similar triangles AFB and AEG are in proportion. So, AF/AE = AB/AG. Find the length of AG. 
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7. Now, find the length of BG. |
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8. The value of pi (π) to seven decimal places is 3.1415927. Compare the fractional part of pi (π) with the length of BG. |
According to the teacher's manual, BG = 0.1415929
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Geometry memories: Why were the triangles in Step 4 and in Step 6 similar? |
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