Library / Mathematics / The golden mean / Braille
The golden mean ⠃⠗⠋ 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.
Download .brf — Grade 2 Download .brf — Grade 1 Plain-text reader .txt
1,037,698 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.