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.
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310,440 braille cells · 311 embossed pages at 40×25 · 36 unrepresentable characters omitted
⠃⠁⠋⠉⠋⠋⠚⠁⠙⠛⠃⠙⠑⠑⠛⠊⠙⠉⠉⠋⠃⠁⠑⠉⠊⠚⠋⠊⠑⠓⠛⠑⠊⠙⠋⠃⠙⠃⠋⠀ ⠼⠋⠛⠊⠃⠉⠁⠑⠚⠁⠃⠑⠙⠋⠉⠁⠙⠋⠃⠉⠛⠑⠓⠙⠋⠋⠛⠁⠙⠙⠛⠃⠋⠚⠑⠛⠓⠊⠃⠛ ⠁⠛⠑⠃⠋⠊⠁⠃⠉⠋⠓⠁⠃⠙⠋⠃⠁⠉⠑⠃⠁⠚⠚⠊⠋⠃⠃⠑⠙⠃⠁⠚⠑⠛⠑⠋⠉⠃⠉⠀ ⠼⠑⠋⠋⠓⠋⠓⠊⠚⠉⠙⠚⠚⠋⠁⠓⠚⠑⠁⠋⠑⠓⠋⠃⠚⠓⠑⠋⠑⠋⠃⠉⠉⠁⠊⠁⠑⠊⠉⠃ ⠊⠙⠙⠋⠊⠙⠁⠑⠁⠋⠋⠃⠛⠛⠛⠙⠊⠚⠉⠚⠋⠛⠙⠓⠉⠚⠋⠙⠑⠙⠃⠃⠋⠑⠛⠋⠓⠚⠁⠀ ⠼⠁⠑⠉⠓⠓⠚⠓⠁⠓⠉⠉⠓⠓⠓⠊⠙⠓⠋⠃⠑⠊⠉⠃⠁⠊⠓⠓⠃⠁⠓⠁⠚⠑⠊⠙⠋⠓⠁⠑ ⠃⠓⠉⠛⠓⠑⠊⠙⠊⠙⠙⠁⠛⠋⠊⠊⠃⠊⠓⠊⠊⠁⠉⠋⠃⠚⠙⠙⠋⠊⠁⠑⠋⠚⠋⠋⠓⠓⠁⠀ ⠼⠊⠓⠙⠓⠃⠓⠋⠁⠑⠃⠛⠉⠊⠊⠋⠊⠁⠉⠛⠉⠑⠁⠉⠙⠋⠑⠁⠚⠓⠊⠓⠋⠉⠚⠋⠁⠊⠑⠛ ⠉⠓⠓⠉⠑⠑⠃⠋⠉⠃⠋⠙⠚⠙⠋⠑⠁⠉⠁⠉⠙⠛⠓⠙⠛⠑⠋⠛⠓⠓⠓⠑⠃⠙⠙⠊⠑⠃⠊⠀ ⠼⠓⠚⠓⠛⠋⠙⠙⠙⠋⠁⠁⠛⠓⠚⠋⠁⠑⠊⠑⠓⠊⠃⠁⠑⠙⠓⠁⠓⠉⠙⠉⠚⠙⠊⠑⠉⠛⠑⠊ ⠑⠃⠃⠑⠛⠓⠁⠃⠊⠁⠁⠚⠁⠛⠋⠁⠊⠊⠛⠑⠊⠁⠋⠁⠑⠛⠉⠛⠋⠑⠉⠊⠚⠋⠓⠓⠑⠛⠙⠀ ⠼⠙⠛⠉⠚⠚⠁⠉⠙⠁⠋⠁⠑⠑⠙⠑⠁⠁⠊⠚⠑⠓⠚⠑⠁⠑⠑⠊⠊⠚⠃⠙⠑⠁⠑⠋⠚⠚⠓⠛ ⠊⠙⠚⠛⠋⠉⠉⠁⠁⠁⠚⠑⠙⠑⠁⠛⠓⠓⠃⠓⠉⠙⠑⠃⠉⠚⠓⠋⠙⠓⠃⠊⠋⠉⠑⠊⠓⠚⠋⠀ ⠼⠑⠋⠊⠙⠁⠃⠋⠓⠓⠁⠊⠁⠁⠓⠙⠙⠊⠑⠑⠑⠃⠋⠙⠚⠙⠓⠁⠓⠙⠙⠙⠛⠑⠃⠛⠊⠑⠊⠚ ⠓⠓⠓⠑⠃⠊⠛⠁⠛⠛⠋⠋⠊⠉⠙⠊⠚⠋⠙⠋⠚⠛⠋⠚⠁⠁⠋⠓⠛⠑⠁⠛⠓⠛⠁⠉⠙⠙⠓⠀ ⠼⠁⠁⠃⠋⠚⠊⠉⠊⠓⠙⠊⠃⠙⠙⠃⠙⠓⠊⠋⠓⠉⠑⠓⠋⠙⠙⠁⠋⠁⠁⠚⠓⠁⠁⠚⠑⠃⠋⠋ ⠙⠁⠉⠁⠚⠚⠙⠑⠊⠑⠁⠃⠑⠁⠁⠉⠙⠉⠊⠙⠑⠑⠉⠁⠉⠛⠙⠃⠙⠋⠉⠁⠁⠊⠁⠋⠋⠑⠑⠀ ⠼⠉⠋⠛⠓⠋⠚⠋⠋⠁⠋⠚⠁⠑⠁⠛⠛⠃⠋⠊⠋⠉⠃⠚⠋⠃⠋⠃⠁⠓⠚⠃⠛⠊⠙⠁⠑⠉⠁⠋ ⠚⠃⠛⠃⠋⠉⠉⠁⠁⠋⠑⠃⠙⠑⠚⠋⠑⠓⠋⠃⠙⠚⠚⠉⠚⠊⠁⠓⠓⠙⠊⠉⠙⠛⠚⠓⠊⠛⠁⠀ ⠼⠚⠁⠓⠁⠃⠁⠑⠛⠃⠑⠃⠓⠃⠁⠋⠑⠋⠓⠊⠓⠛⠛⠊⠙⠛⠙⠁⠓⠑⠊⠁⠃⠁⠓⠉⠙⠛⠁⠑ ⠑⠙⠓⠙⠚⠚⠚⠑⠓⠚⠛⠋⠑⠙⠓⠑⠚⠚⠃⠛⠁⠛⠓⠑⠋⠃⠁⠊⠁⠚⠓⠃⠊⠉⠙⠁⠑⠃⠉⠀ ⠼⠙⠛⠁⠃⠃⠉⠊⠉⠑⠚⠛⠉⠑⠋⠉⠛⠋⠓⠚⠛⠛⠉⠙⠙⠚⠃⠑⠑⠃⠁⠋⠋⠋⠉⠑⠛⠚⠃⠓ ⠑⠚⠛⠛⠊⠛⠙⠛⠚⠛⠋⠃⠛⠙⠁⠓⠑⠊⠊⠑⠃⠃⠃⠃⠚⠃⠋⠉⠑⠋⠋⠙⠓⠋⠚⠑⠓⠉⠃⠀ ⠼⠊⠛⠉⠃⠓⠋⠛⠚⠚⠑⠚⠉⠊⠊⠙⠛⠃⠓⠊⠃⠙⠛⠃⠉⠃⠛⠊⠑⠙⠃⠚⠙⠛⠋⠉⠓⠚⠙⠁ ⠚⠚⠃⠑⠓⠙⠚⠙⠁⠚⠙⠓⠃⠉⠊⠃⠙⠚⠙⠁⠋⠃⠃⠊⠊⠑⠉⠛⠋⠓⠚⠋⠋⠓⠚⠉⠙⠉⠋⠀
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