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Understanding Root 2 as a Continued Fraction and Geometric Constructions

This text explores the mathematical properties of the square root of 2 expressed as a continued fraction, as discussed in J. H. Conway and R. K. Guy's "The Book of Numbers." It also delves into classic geometric problems such as squaring the circle, doubling the cube, and trisecting the angle. The relationships between pi, circumference, diameter, and radius of a circle are outlined, providing key insights into these essential mathematical concepts. Ideal for those interested in the interplay of numbers and geometry, this resource offers foundational knowledge and stimulating connections.

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Understanding Root 2 as a Continued Fraction and Geometric Constructions

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Presentation Transcript

  1. Root 2 as a continued fraction

  2. J. H. Conway, R. K. Guy, The Book of Numbers, Copernicus, 1996

  3. Squaring the circle Doubling the cube Trisecting the angle

  4. p = circumference/diameter

  5. Pi =circumference/diameter Circumference=pi x diameter Diameter=2 x radius Circumference =2 pi r For a unit diameter circle circumference = pi

  6. Nova Infinite Secrets Interactive

  7. Link

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