Library / Mathematics / Four-Dimensional Vistas / Braille
Four-Dimensional Vistas ⠃⠗⠋ 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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155,153 braille cells · 164 embossed pages at 40×25 · 505 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.