Library / Mathematics / The golden mean / Braille
The golden mean ⠃⠗⠋ 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
1,037,718 braille cells · 1,501 embossed pages at 40×25 · 2 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.