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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.