These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 Textbook into html format.
A Curious Construction
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Many mathematicians have been interested in ways to construct the number pi (π). In the drawing, triangles ABC and ADE are right triangles. The length of AB = 1. The length of BG gives a decimal approximation of pi (π) to six decimal places. Complete all calculations to 7 decimal places. |
1. Use the length of BC and the Pythagorean theorem to find the length of AC. | |
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 |
| Geometry memories: Why were the triangles in Step 4 and in Step 6 similar? | |
Copyright 1997-1999: html adaptation
Career Connection to Teaching with Technology