Skip to contentSkip to Braille Studio

Library / Mathematics / The First 498 Bernoulli Numbers / Braille

The First 498 Bernoulli Numbers ⠃⠗⠋ 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.

Download .brf — Grade 2 Download .brf — Grade 1 Plain-text reader .txt

89,438 braille cells · 125 embossed pages at 40×25 · 4 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.