Library / Mathematics / The golden mean / Braille
The golden mean ⠃⠗⠋ 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.
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1,037,698 braille cells · 1,501 embossed pages at 40×25 · 2 unrepresentable characters omitted
⠠⠹⠊⠎⠀⠊⠎⠀⠮⠀⠛⠕⠇⠙⠢⠀⠗⠁⠞⠊⠕⠂⠀⠶⠼⠁⠎⠟⠗⠞⠶⠼⠑⠶⠶⠸⠌⠃⠂⠀ ⠾⠀⠼⠁⠲⠚⠚⠚⠲⠚⠚⠚⠀⠙⠊⠛⠊⠞⠎⠲⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠀⠊⠎⠀⠃⠁⠎⠫⠀ ⠕⠝⠀⠎⠟⠥⠜⠑⠀⠗⠕⠕⠞⠀⠷⠀⠼⠑⠀⠉⠕⠍⠏⠥⠞⠫⠀⠃⠽⠀⠠⠗⠕⠃⠻⠞⠀ ⠠⠝⠑⠍⠊⠗⠷⠋⠀⠯⠀⠠⠚⠻⠗⠽⠀⠠⠃⠕⠝⠝⠑⠇⠇⠲⠀⠀⠀⠀⠠⠮⠀⠛⠕⠇⠙⠢⠀ ⠗⠁⠞⠊⠕⠀⠀⠀⠀⠀⠀⠀ ⠼⠁⠲⠋⠁⠓⠚⠉⠉⠊⠓⠓⠛⠙⠊⠓⠊⠙⠓⠙⠓⠃⠚⠙⠑⠓⠋⠓⠉⠙⠉⠋⠑⠋⠉⠓⠁⠁⠛⠛ ⠃⠚⠉⠚⠊⠁⠛⠊⠓⠚⠑⠛⠋⠃⠓⠋⠃⠁⠉⠑⠙⠙⠓⠋⠃⠃⠛⠚⠑⠃⠋⠚⠙⠋⠃⠓⠁⠓⠊⠀ ⠼⠚⠃⠙⠙⠊⠛⠚⠛⠃⠚⠛⠃⠚⠙⠁⠓⠊⠉⠊⠁⠁⠉⠛⠙⠓⠙⠛⠑⠙⠚⠓⠓⠚⠛⠑⠉⠓⠋⠓ ⠊⠁⠛⠑⠃⠁⠃⠋⠋⠉⠉⠓⠋⠃⠃⠃⠉⠑⠉⠋⠊⠉⠁⠛⠊⠉⠁⠓⠚⠚⠋⠚⠛⠋⠋⠛⠃⠋⠉⠑ ⠙⠀⠀ ⠼⠙⠉⠉⠉⠓⠊⠚⠓⠋⠑⠊⠑⠊⠉⠊⠑⠓⠃⠊⠚⠑⠋⠉⠓⠉⠃⠃⠋⠋⠁⠉⠁⠊⠊⠃⠓⠃⠊⠚ ⠃⠋⠛⠓⠓⠚⠋⠛⠑⠃⠚⠓⠛⠋⠋⠓⠊⠃⠑⠚⠁⠛⠁⠁⠋⠊⠋⠃⠚⠛⠚⠉⠃⠃⠃⠁⠚⠙⠉⠃ ⠁⠀⠀ ⠼⠋⠃⠋⠊⠑⠙⠓⠋⠃⠋⠃⠊⠋⠉⠁⠉⠋⠁⠙⠙⠉⠓⠁⠙⠊⠛⠑⠓⠛⠚⠁⠃⠃⠚⠉⠙⠚⠓⠚ ⠑⠓⠓⠛⠊⠑⠙⠙⠑⠙⠛⠙⠊⠃⠙⠋⠁⠓⠑⠋⠊⠑⠉⠋⠙⠓⠋⠙⠙⠙⠊⠃⠙⠁⠚⠙⠙⠉⠃⠚ ⠛⠀⠀ ⠼⠛⠁⠉⠙⠙⠊⠙⠛⠚⠙⠊⠑⠋⠑⠓⠙⠋⠛⠓⠓⠑⠚⠊⠓⠛⠙⠉⠉⠊⠙⠙⠃⠃⠁⠃⠑⠙⠙⠓ ⠛⠛⠚⠋⠋⠙⠛⠓⠚⠊⠁⠑⠓⠓⠙⠋⠚⠛⠙⠊⠊⠓⠓⠛⠁⠃⠙⠚⠚⠛⠋⠑⠃⠁⠛⠚⠑⠛⠑⠁ ⠛⠀⠀ ⠼⠊⠛⠓⠓⠉⠙⠁⠋⠋⠃⠑⠋⠃⠙⠊⠙⠚⠛⠑⠓⠊⠚⠋⠊⠛⠚⠙⠚⠚⠚⠃⠓⠁⠃⠁⠚⠙⠃⠛ ⠋⠃⠁⠛⠛⠁⠁⠁⠛⠛⠛⠓⠚⠑⠉⠁⠑⠉⠁⠛⠁⠙⠁⠚⠁⠁⠛⠚⠙⠋⠋⠋⠑⠊⠊⠁⠙⠋⠋⠊ ⠛⠀⠀ ⠼⠊⠓⠛⠉⠁⠛⠋⠁⠉⠑⠋⠚⠚⠋⠛⠚⠓⠛⠙⠓⠚⠛⠁⠚⠁⠉⠁⠛⠊⠑⠃⠉⠋⠓⠊⠙⠃⠛⠑ ⠃⠁⠊⠙⠓⠙⠉⠑⠉⠚⠑⠋⠛⠓⠉⠚⠚⠃⠃⠓⠛⠓⠑⠋⠊⠊⠛⠓⠃⠊⠛⠛⠓⠉⠙⠛⠓⠙⠑⠓ ⠛⠀⠀
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