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.