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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.16185 |
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| _version_ | 1866916537605029888 |
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| author | Kaushik, Khushi Murphy, Tommy Weed, David |
| author_facet | Kaushik, Khushi Murphy, Tommy Weed, David |
| contents | The FRACTRAN programs $\sqrt{2}$GAME and NR$\sqrt{2}$GAME are presented, both of which compute the decimal expansion of $\sqrt{2}$. Our $\sqrt{2}$GAME is analogous to Conway's PIGAME program. In fact, our proof carries over to PIGAME to produce a simpler proof of Conway's theorem as well as highlight how the efficiency of the program can be improved. NR$\sqrt{2}$GAME encodes the canonical example of the Newton--Raphson method in FRACTRAN. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16185 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing $\sqrt{2}$ with FRACTRAN Kaushik, Khushi Murphy, Tommy Weed, David Programming Languages 68N15 The FRACTRAN programs $\sqrt{2}$GAME and NR$\sqrt{2}$GAME are presented, both of which compute the decimal expansion of $\sqrt{2}$. Our $\sqrt{2}$GAME is analogous to Conway's PIGAME program. In fact, our proof carries over to PIGAME to produce a simpler proof of Conway's theorem as well as highlight how the efficiency of the program can be improved. NR$\sqrt{2}$GAME encodes the canonical example of the Newton--Raphson method in FRACTRAN. |
| title | Computing $\sqrt{2}$ with FRACTRAN |
| topic | Programming Languages 68N15 |
| url | https://arxiv.org/abs/2412.16185 |