Library / Mathematics / The Golden Mean or Ratio[(1+sqrt(5))/2] / Braille
The Golden Mean or Ratio[(1+sqrt(5))/2] ⠃⠗⠋ braille edition
Grade 1 — uncontracted, letter-for-letter. Translated on this server by our own braille engine (BRF — Braille Ready Format, Library of Congress fdd000551). View Grade 2 instead.
Download .brf — Grade 2 Download .brf — Grade 1 Plain-text reader .txt
265,653 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.