1 / 9

On Machin-like formulas and Gaussian integers

Explore the connections between Machin's formula, Gaussian integers, and Gauss's approach to calculating π efficiently. Learn how to create Machin-like formulas by factoring Gaussian integers and delve into the historical significance of these mathematical concepts.

casandrac
Download Presentation

On Machin-like formulas and Gaussian integers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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?

More Related