Library / Mathematics / The golden mean / Braille
The golden mean ⠃⠗⠋ 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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1,037,718 braille cells · 1,501 embossed pages at 40×25 · 2 unrepresentable characters omitted
⠼⠓⠛⠙⠛⠊⠋⠛⠛⠊⠑⠋⠁⠊⠃⠊⠓⠃⠛⠙⠛⠙⠉⠑⠙⠁⠁⠁⠋⠛⠓⠃⠊⠚⠃⠑⠃⠑⠊⠃ ⠃⠉⠋⠛⠋⠓⠛⠛⠊⠛⠓⠓⠙⠚⠋⠃⠁⠛⠋⠊⠃⠃⠉⠛⠙⠙⠁⠋⠑⠑⠛⠑⠚⠛⠚⠁⠉⠚⠛⠛ ⠚⠀⠀ ⠼⠚⠚⠑⠃⠚⠑⠋⠛⠊⠚⠓⠃⠋⠑⠓⠃⠛⠃⠚⠚⠊⠊⠋⠑⠙⠊⠓⠙⠊⠋⠛⠛⠉⠋⠓⠑⠉⠓⠋ ⠊⠓⠃⠊⠊⠋⠉⠋⠊⠃⠑⠉⠊⠑⠁⠛⠊⠃⠑⠉⠁⠃⠙⠑⠓⠚⠉⠑⠑⠚⠊⠙⠋⠚⠛⠑⠓⠙⠊⠃ ⠋⠀⠀ ⠼⠚⠚⠊⠉⠛⠑⠓⠋⠛⠃⠁⠚⠙⠊⠁⠛⠊⠛⠁⠛⠙⠁⠛⠁⠋⠁⠚⠛⠙⠊⠉⠛⠋⠁⠚⠊⠃⠊⠙ ⠉⠋⠑⠊⠊⠉⠛⠙⠛⠃⠛⠉⠋⠁⠛⠓⠃⠚⠉⠁⠛⠁⠙⠉⠛⠓⠉⠚⠁⠁⠓⠋⠋⠊⠉⠁⠛⠁⠚⠙ ⠙⠀⠀ ⠼⠉⠑⠊⠛⠓⠃⠊⠓⠁⠁⠚⠛⠓⠊⠃⠋⠛⠃⠙⠉⠑⠊⠙⠃⠁⠓⠉⠓⠚⠋⠉⠃⠊⠉⠃⠁⠉⠉⠃ ⠚⠚⠓⠓⠙⠛⠛⠊⠁⠑⠓⠚⠛⠛⠉⠋⠉⠑⠉⠙⠊⠓⠙⠑⠛⠙⠊⠚⠚⠙⠛⠚⠙⠋⠙⠊⠛⠁⠙⠛ ⠙⠀⠀ ⠼⠙⠃⠓⠙⠚⠃⠃⠁⠊⠋⠋⠓⠚⠃⠃⠁⠃⠉⠑⠋⠙⠃⠛⠛⠉⠁⠋⠓⠑⠓⠙⠁⠁⠁⠛⠙⠙⠑⠓ ⠛⠊⠁⠑⠙⠋⠊⠑⠁⠃⠓⠚⠊⠚⠛⠚⠚⠚⠉⠙⠊⠚⠊⠓⠁⠊⠃⠓⠉⠃⠓⠃⠓⠙⠛⠋⠁⠊⠚⠚ ⠉⠀⠀ ⠼⠉⠑⠓⠑⠋⠛⠓⠙⠃⠊⠙⠃⠓⠛⠚⠁⠙⠊⠓⠃⠓⠊⠉⠉⠚⠚⠙⠛⠃⠉⠃⠊⠓⠚⠋⠛⠓⠋⠁ ⠛⠋⠓⠛⠁⠛⠉⠓⠁⠑⠋⠋⠛⠃⠚⠓⠛⠛⠁⠚⠙⠃⠑⠚⠚⠁⠛⠚⠁⠓⠚⠉⠊⠉⠛⠛⠛⠋⠃⠚ ⠙⠀⠀ ⠼⠓⠃⠋⠊⠋⠁⠃⠁⠚⠑⠚⠃⠙⠊⠃⠚⠛⠋⠚⠓⠚⠛⠙⠑⠑⠑⠙⠃⠚⠃⠃⠓⠓⠁⠊⠙⠛⠃⠓ ⠑⠚⠃⠁⠋⠚⠙⠃⠙⠉⠁⠃⠑⠑⠋⠊⠁⠑⠁⠛⠓⠁⠋⠋⠚⠚⠉⠙⠋⠉⠚⠁⠓⠛⠃⠊⠛⠃⠛⠉ ⠛⠀⠀ ⠼⠓⠉⠛⠛⠃⠉⠓⠋⠊⠊⠃⠃⠊⠑⠚⠓⠁⠃⠙⠊⠁⠋⠊⠁⠁⠃⠑⠑⠑⠛⠑⠚⠙⠃⠉⠊⠊⠉⠁ ⠙⠙⠊⠑⠚⠑⠋⠓⠑⠙⠛⠛⠑⠁⠛⠑⠓⠃⠙⠃⠚⠛⠁⠚⠊⠃⠚⠓⠉⠉⠛⠓⠛⠊⠑⠋⠑⠊⠋⠛ ⠊⠀⠀ ⠼⠁⠛⠚⠑⠛⠛⠓⠃⠚⠙⠑⠚⠙⠛⠓⠉⠉⠙⠛⠓⠃⠊⠉⠙⠉⠉⠉⠓⠁⠋⠃⠑⠓⠑⠚⠚⠚⠋⠑
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