Skip to contentSkip to Braille Studio

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.

Download .brf — Grade 2 Download .brf — Grade 1 Plain-text reader .txt

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.