Library / Mathematics / The Golden Mean or Ratio[(1+sqrt(5))/2] / Braille
The Golden Mean or Ratio[(1+sqrt(5))/2] ⠃⠗⠋ braille edition
Grade 2 — contracted English braille (EBAE-compatible subset). Translated on this server by our own braille engine (BRF — Braille Ready Format, Library of Congress fdd000551). View Grade 1 instead.
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265,406 braille cells · 292 embossed pages at 40×25 · 21 unrepresentable characters omitted
⠼⠉⠉⠓⠋⠛⠛⠑⠁⠃⠓⠑⠉⠁⠁⠓⠑⠙⠃⠊⠋⠊⠉⠓⠚⠊⠙⠙⠋⠉⠋⠃⠋⠉⠙⠃⠓⠋⠛⠓ ⠃⠉⠋⠊⠃⠑⠚⠚⠑⠑⠃⠊⠃⠑⠚⠋⠚⠁⠋⠓⠋⠃⠙⠛⠃⠋⠃⠁⠋⠁⠁⠃⠁⠓⠉⠃⠃⠓⠉⠀ ⠼⠚⠉⠁⠃⠋⠓⠙⠛⠁⠋⠋⠓⠛⠊⠚⠑⠑⠙⠊⠚⠙⠁⠙⠙⠃⠋⠋⠑⠁⠚⠋⠊⠁⠊⠛⠑⠊⠙⠋ ⠁⠉⠙⠑⠙⠚⠛⠙⠚⠚⠙⠋⠊⠋⠙⠛⠉⠁⠚⠓⠑⠓⠙⠁⠊⠑⠙⠓⠓⠛⠋⠁⠚⠊⠁⠉⠑⠙⠁⠀ ⠼⠁⠃⠛⠛⠃⠚⠛⠉⠉⠉⠃⠋⠚⠋⠃⠙⠓⠉⠑⠁⠑⠑⠚⠓⠑⠓⠁⠚⠛⠛⠛⠋⠓⠉⠙⠁⠃⠚⠑ ⠓⠋⠛⠁⠛⠑⠙⠛⠃⠑⠑⠃⠊⠓⠃⠙⠑⠙⠚⠊⠚⠊⠑⠛⠁⠙⠑⠊⠑⠃⠛⠙⠙⠁⠉⠙⠊⠋⠃⠀ ⠼⠑⠚⠙⠁⠉⠊⠛⠋⠙⠛⠊⠙⠓⠚⠃⠉⠃⠙⠚⠛⠁⠊⠉⠋⠛⠑⠊⠓⠊⠃⠑⠑⠃⠃⠑⠁⠉⠉⠑ ⠃⠊⠃⠃⠉⠛⠃⠁⠓⠛⠋⠛⠁⠓⠛⠃⠚⠓⠙⠓⠁⠋⠁⠓⠁⠁⠚⠋⠙⠋⠑⠁⠚⠋⠓⠓⠛⠃⠙⠀ ⠼⠁⠙⠃⠙⠃⠚⠁⠊⠋⠚⠉⠁⠛⠓⠁⠊⠙⠉⠓⠋⠓⠑⠚⠊⠁⠃⠑⠚⠑⠃⠃⠓⠛⠑⠛⠑⠛⠓⠚ ⠚⠚⠛⠊⠊⠋⠋⠁⠉⠁⠓⠁⠊⠚⠋⠋⠊⠛⠃⠛⠁⠊⠉⠃⠑⠃⠚⠓⠚⠓⠊⠊⠑⠉⠓⠙⠙⠋⠚⠀ ⠼⠚⠃⠁⠁⠉⠋⠊⠙⠃⠋⠃⠓⠃⠁⠉⠑⠃⠋⠓⠋⠊⠉⠚⠑⠙⠁⠛⠉⠛⠙⠁⠛⠛⠉⠉⠑⠛⠉⠓ ⠙⠛⠉⠁⠛⠋⠉⠚⠛⠁⠃⠙⠃⠃⠃⠑⠋⠃⠙⠓⠊⠛⠁⠓⠁⠁⠚⠛⠛⠑⠃⠙⠑⠙⠑⠃⠙⠃⠋⠀ ⠼⠃⠊⠙⠉⠚⠑⠁⠓⠃⠙⠋⠑⠃⠊⠋⠁⠃⠚⠓⠋⠃⠙⠑⠉⠁⠙⠋⠉⠚⠚⠓⠁⠑⠊⠙⠊⠊⠚⠃ ⠚⠉⠃⠋⠃⠓⠊⠓⠚⠃⠃⠁⠁⠁⠚⠁⠛⠓⠙⠃⠊⠋⠋⠓⠙⠃⠑⠑⠊⠃⠑⠉⠙⠁⠃⠑⠃⠁⠛⠀ ⠼⠃⠑⠊⠉⠉⠛⠙⠁⠛⠃⠛⠓⠁⠑⠛⠙⠚⠉⠉⠉⠃⠚⠋⠁⠓⠓⠑⠙⠃⠛⠑⠃⠋⠊⠙⠚⠓⠛⠃ ⠙⠋⠉⠊⠋⠊⠛⠙⠋⠛⠓⠚⠙⠓⠃⠑⠋⠃⠃⠚⠋⠋⠙⠃⠃⠉⠓⠉⠚⠑⠉⠉⠁⠑⠛⠃⠛⠚⠋⠀ ⠼⠁⠑⠋⠚⠉⠚⠉⠉⠓⠉⠉⠁⠉⠓⠊⠓⠋⠋⠉⠉⠑⠑⠙⠙⠑⠓⠓⠋⠃⠚⠓⠉⠚⠙⠑⠊⠋⠋⠚ ⠊⠉⠉⠑⠚⠃⠑⠑⠓⠓⠙⠑⠓⠓⠙⠓⠑⠓⠙⠁⠃⠑⠁⠁⠃⠑⠉⠋⠋⠛⠋⠁⠊⠚⠙⠋⠃⠁⠋⠀ ⠼⠙⠑⠋⠑⠉⠑⠑⠁⠁⠓⠋⠓⠊⠓⠚⠁⠙⠋⠛⠙⠋⠛⠋⠑⠃⠊⠋⠊⠁⠚⠙⠊⠓⠙⠁⠚⠁⠚⠃ ⠛⠊⠋⠛⠙⠙⠃⠛⠁⠙⠊⠑⠑⠁⠙⠛⠓⠋⠁⠃⠛⠛⠑⠃⠑⠁⠚⠋⠁⠚⠙⠊⠓⠑⠓⠉⠓⠁⠙⠀ ⠼⠉⠊⠙⠁⠁⠛⠚⠊⠙⠃⠑⠙⠙⠃⠚⠚⠑⠉⠊⠙⠃⠑⠙⠊⠚⠑⠁⠑⠊⠙⠁⠋⠛⠃⠛⠑⠃⠁⠊ ⠃⠊⠑⠑⠑⠙⠑⠃⠛⠓⠓⠚⠁⠑⠑⠑⠛⠛⠋⠉⠚⠓⠁⠑⠃⠑⠃⠋⠓⠓⠉⠃⠁⠋⠚⠊⠛⠚⠛⠀ ⠼⠋⠓⠑⠃⠓⠙⠊⠁⠋⠉⠚⠑⠉⠚⠁⠓⠛⠚⠃⠑⠉⠃⠑⠁⠊⠊⠁⠓⠙⠃⠃⠊⠉⠉⠋⠉⠛⠚⠛ ⠙⠉⠋⠚⠙⠛⠛⠛⠑⠃⠑⠉⠃⠉⠉⠓⠛⠉⠑⠓⠉⠊⠋⠑⠛⠚⠛⠚⠋⠑⠁⠉⠃⠁⠉⠓⠓⠚⠃⠀ ⠼⠊⠃⠓⠊⠋⠁⠊⠙⠛⠊⠓⠙⠃⠃⠚⠑⠉⠃⠉⠊⠙⠛⠓⠚⠁⠃⠑⠃⠉⠊⠚⠛⠋⠛⠙⠋⠛⠑⠙
These are the same pages the .brf download embosses — form-feed breaks and all. BRF opens in braille software (Duxbury, BrailleBlaster), on embossers, and on refreshable displays.