Library / Mathematics / Catalan's Constant [Ramanujan's Formula] / Braille
Catalan's Constant [Ramanujan's Formula] ⠃⠗⠋ 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
310,440 braille cells · 311 embossed pages at 40×25 · 36 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.