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.