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On Machin-like formulas and Gaussian integers

On Machin-like formulas and Gaussian integers. Carl Friedrich Gauss – John Machin – Colin Wright. Gaussian machin-ations. Full Puzzle. The first rule of mathsjam. “ Don ’ t tell them the answer ” - Colin Wright. Show that

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On Machin-like formulas and Gaussian integers

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  1. On Machin-like formulas and Gaussian integers

  2. Carl Friedrich Gauss – John Machin – Colin Wright Gaussianmachin-ations Full Puzzle

  3. The first rule of mathsjam “Don’t tell them the answer” - Colin Wright

  4. Show that 𝛼 =β+ 𝛾

  5. THE ATTACK OF THE GAUSSIAN INTEGERS

  6. Machin’s formula John Machin (1686-1751) Used this, and the Taylor series for arctan, to compute π to 100 decimal places (1706)

  7. Gauss’s machin-like formula Gauss’s formula is a whole 2% faster for calculating π.

  8. summary • The 1-2-3 puzzle is linked to approximations of π • You can create machin-like formulas by factorising gaussian integers • What would machin have thought?

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