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Published byRhoda Joseph Modified over 8 years ago
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17 Sides By Mike Frost
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What Can You Construct with Straight Edge and Compass? Lengths can be multiplied
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Lengths can be halved by Dropping a Perpendicular
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Angles can be Halved
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Square Roots can be taken But you can’t: Trisect an Angle or take Cube Roots
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Constructing the Pentagon
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Carl Friedrich Gauss To construct a Polygon with a prime number of sides n, n must be a Fermat Prime, of the form: F 0 = 3 F 1 = 5 F 2 = 17 F 3 = 257 F 4 = 65, 537 Five known Fermat Primes N=0,1,2,3,4
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“Dr Euler’s Fabulous Formula” – by Paul Nahin
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Cos (2 π / 17)... Cos (2 π / 3) = -0.5 Cos (2 π / 5) = (-1 + sqrt(5) ) / 4 Cos (2 π / 257) ?
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...and Cos (2π/65,537) ??
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The Biggest Constructible Odd-Numbered Polygon 3. 5. 17. 257. 65537 = 4, 294, 967, 295 Sides
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Constructing the 17-Gon
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