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<!doctype html> <html lang="en" class="historyandterminology mathworldcontributors"> <head> <title>Akhmim Wooden Tablet -- from Wolfram MathWorld</title> <meta name="DC.Title" content="Akhmim Wooden Tablet" /> <meta name="DC.Creator" content="Weisstein, Eric W." /> <meta name="DC.Description" content="The Akhmim wooden tablet, often called the Cairo wooden tablet, is a document dating to 2000 BC, near the beginning of the Egyptian Middle Kingdom. It is housed in the Egypt Museum in Cairo. The document was believed for nearly 100 years to define a unit known as a "ro" as being equal to 1/320th of a hekat, when in fact an exact computation was taking place that requires no additional units of the hekat. The "ro" operation was simply 5/320=1/64 as used to exactly complete..." /> <meta name="description" content="The Akhmim wooden tablet, often called the Cairo wooden tablet, is a document dating to 2000 BC, near the beginning of the Egyptian Middle Kingdom. It is housed in the Egypt Museum in Cairo. The document was believed for nearly 100 years to define a unit known as a "ro" as being equal to 1/320th of a hekat, when in fact an exact computation was taking place that requires no additional units of the hekat. The "ro" operation was simply 5/320=1/64 as used to exactly complete..." /> <meta name="DC.Date.Created" scheme="W3CDTF" content="2004-11-02" /> <meta name="DC.Subject" scheme="MathWorld" content="Mathematics:History and Terminology:History" /> <meta name="DC.Subject" scheme="MathWorld" content="Mathematics:MathWorld Contributors:Gardner" /> <meta name="DC.Subject" scheme="MSC_2000" content="01A" /> <meta name="DC.Rights" content="Copyright 1999-2025 Wolfram Research, Inc. 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It is housed in the Egypt Museum in Cairo. The document was believed for nearly 100 years to define a unit known as a "ro" as being equal to 1/320th of a hekat, when in fact an exact computation was taking place that requires no additional units of the hekat. The "ro" operation was simply 5/320=1/64 as used to exactly complete..."> <meta name="twitter:card" content="summary_large_image"> <meta name="twitter:site" content="@WolframResearch"> <meta name="twitter:title" content="Akhmim Wooden Tablet -- from Wolfram MathWorld"> <meta name="twitter:description" content="The Akhmim wooden tablet, often called the Cairo wooden tablet, is a document dating to 2000 BC, near the beginning of the Egyptian Middle Kingdom. It is housed in the Egypt Museum in Cairo. The document was believed for nearly 100 years to define a unit known as a "ro" as being equal to 1/320th of a hekat, when in fact an exact computation was taking place that requires no additional units of the hekat. The "ro" operation was simply 5/320=1/64 as used to exactly complete..."> <meta name="twitter:image:src" content="https://mathworld.wolfram.com/images/socialmedia/share/ogimage_AkhmimWoodenTablet.png"> <link rel="canonical" href="https://mathworld.wolfram.com/AkhmimWoodenTablet.html" /> <meta http-equiv="x-ua-compatible" content="ie=edge"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta charset="utf-8"> <script async src="/common/javascript/analytics.js"></script> <script async src="//www.wolframcdn.com/consent/cookie-consent.js"></script> <script async src="/common/javascript/wal/latest/walLoad.js"></script> <link rel="stylesheet" href="/css/styles.css"> <link rel="preload" href="//www.wolframcdn.com/fonts/source-sans-pro/1.0/global.css" as="style" onload="this.onload=null;this.rel='stylesheet'"> <noscript><link rel="stylesheet" href="//www.wolframcdn.com/fonts/source-sans-pro/1.0/global.css"></noscript> </head> <body id="topics"> <main id="entry"> <div 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History and Terminology </a> <a href="/topics/NumberTheory.html" id="sidebar-numbertheory"> Number Theory </a> <a href="/topics/ProbabilityandStatistics.html" id="sidebar-probabilityandstatistics"> Probability and Statistics </a> <a href="/topics/RecreationalMathematics.html" id="sidebar-recreationalmathematics"> Recreational Mathematics </a> <a href="/topics/Topology.html" id="sidebar-topology"> Topology </a> </nav> <nav class="secondary-nav"> <a href="/letters/"> Alphabetical Index </a> <a href="/whatsnew/"> New in MathWorld </a> </nav> </section> <section id="content">  <nav class="breadcrumbs"><ul class="breadcrumb"> <li> <a href="/topics/HistoryandTerminology.html">History and Terminology</a> </li> <li> <a href="/topics/History.html">History</a> </li> </ul><ul class="breadcrumb"> <li> <a href="/topics/MathWorldContributors.html">MathWorld Contributors</a> </li> <li> <a href="/topics/Gardner.html">Gardner</a> </li> </ul></nav>   <h1>Akhmim Wooden Tablet</h1>  <hr class="margin-t-1-8 margin-b-3-4">   <div class="entry-content"> <p> The Akhmim wooden tablet, often called the Cairo wooden tablet, is a document dating to 2000 BC, near the beginning of the Egyptian Middle Kingdom. It is housed in the Egypt Museum in Cairo. </p> <p> The document was believed for nearly 100 years to define a unit known as a "ro" as being equal to 1/320th of a hekat, when in fact an exact computation was taking place that requires no additional units of the hekat. The "ro" operation was simply <img src="/images/equations/AkhmimWoodenTablet/Inline1.svg" class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="106" height="21" alt="5/320=1/64" /> as used to exactly complete the remainder fraction component of the following divisions: </p> <div class="table-responsive"> <table align="center" class="mathworldtable"> <tr style=""><td align="left">fraction</td><td align="left">identity</td></tr><tr style=""><td align="left"><img src="/images/equations/AkhmimWoodenTablet/Inline2.svg" class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="125" height="21" alt="64/3=21+1/3" /></td><td align="left">5/(3 ro) = 5/960</td></tr><tr style=""><td align="left"><img src="/images/equations/AkhmimWoodenTablet/Inline3.svg" class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="116" height="21" alt="64/7=9+1/7" /></td><td align="left">5/(7 ro) = 5/2240</td></tr><tr style=""><td align="left"><img src="/images/equations/AkhmimWoodenTablet/Inline4.svg" class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="125" height="21" alt="64/10=6+2/5" /></td><td align="left">10/(10 ro) = 1/320</td></tr><tr style=""><td align="left"><img src="/images/equations/AkhmimWoodenTablet/Inline5.svg" class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="134" height="21" alt="64/11=5+9/11" /></td><td align="left">45/(11 ro) = 45/3520</td></tr><tr style=""><td align="left"><img src="/images/equations/AkhmimWoodenTablet/Inline6.svg" class="inlineformula" style="max-height:100%;max-width:100%" border="0" width="143" height="21" alt="64/13=4+12/13" /></td><td align="left">60/(13 ro) = 60/4160</td></tr> </table> </div> <p> The student scribe was then asked to prove his/her division by multiplying by 3, 7, 10, 11, 13, as required, to find the complete 1/64th unit. Since the student compiling this tablet made many arithmetic errors in the duplication arithmetic, even a 2002 translation of the document did not fully recognize the exact nature of all the division operations. The <a href="/RhindPapyrus.html">Rhind papyrus</a> also contains one of these problems, division by 3, leading to confusion by Gillings (1972) and others. </p> <p> The importance of the tablet is that the system of Egyptian fractions may have originated in trying to divide the smallest grain units or some other units in ancient Egyptian history. </p> </div>  <hr class="margin-b-1-1-4"> <div class="c-777 entry-secondary-content">  <h2>See also</h2><a href="/EgyptianFraction.html">Egyptian Fraction</a>, <a href="/EgyptianMathematicalLeatherRoll.html">Egyptian Mathematical Leather Roll</a>, <a href="/RhindPapyrus.html">Rhind Papyrus</a>     <p class="contributor"> <i>This entry contributed by <a target="_blank" href="/topics/Gardner.html">Milo Gardner</a></i> </p>   <h2>Explore with Wolfram|Alpha</h2> <div id="WAwidget"> <div class="WAwidget-wrapper"> <img alt="WolframAlpha" title="WolframAlpha" src="/images/wolframalpha/WA-logo.png" width="136" height="20"> <form name="wolframalpha" action="https://www.wolframalpha.com/input/" target="_blank"> <input type="text" name="i" class="search" placeholder="Solve your math problems and get step-by-step solutions" value=""> <button type="submit" title="Evaluate on WolframAlpha"></button> </form> </div> <div class="WAwidget-wrapper try"> <p class="text-align-r"> More things to try: </p> <ul> <li> <a target="_blank" href="http://www.wolframalpha.com/input/?i=derivative"> derivative </a> </li> <li> <a target="_blank" href="http://www.wolframalpha.com/input/?i=history"> history </a> </li> <li><a target="_blank" href="https://www.wolframalpha.com/input/?i=basket+bet+for+50+pounds+on+roulette">basket bet for 50 pounds on roulette</a></li> </ul> </div> </div>   <h2>References</h2><cite>Daressy, G. "Cairo Museum des Antiquities Egyptiennes." <i>Catalogue General Ostraca</i>, Volume No. 25001-25385, 1901.</cite><cite>Gillings, R. <i><a href="http://www.amazon.com/exec/obidos/ASIN/048624315X/ref=nosim/ericstreasuretro">Mathematics in the Time of the Pharaohs.</a></i> Boston, MA: MIT Press, pp. 202-205, 1972.</cite><cite>Peet, T. E. "Arithmetic in the Middle Kingdom." <i>J. Egyptian Arch.</i> <b>9</b>, 91-95, 1923.</cite><cite>Vymazalova, H. "The Wooden Tablets from Cairo: The Use of the Grain Unit HK3T in Ancient Egypt." Archiv Orientalai, Charles U., Prague, pp. 27-42, 2002.</cite><h2>Referenced on Wolfram|Alpha</h2><a href="http://www.wolframalpha.com/entities/mathworld/akhmim_wooden_tablet/m8/8g/jx/" title="Akhmim Wooden Tablet" target="_blank">Akhmim Wooden Tablet</a>   <h2>Cite this as:</h2> <p> <a href="/topics/Gardner.html">Gardner, Milo</a>. "Akhmim Wooden Tablet." From <a href="/"><i>MathWorld</i></a>--A Wolfram Web Resource, created by <a href="/about/author.html">Eric W. Weisstein</a>. <a href="https://mathworld.wolfram.com/AkhmimWoodenTablet.html">https://mathworld.wolfram.com/AkhmimWoodenTablet.html</a> </p>  <h2>Subject classifications</h2><nav class="breadcrumbs"><ul class="breadcrumb"> <li> <a href="/topics/HistoryandTerminology.html">History and Terminology</a> </li> <li> <a href="/topics/History.html">History</a> </li> </ul><ul class="breadcrumb"> <li> <a href="/topics/MathWorldContributors.html">MathWorld Contributors</a> </li> <li> <a href="/topics/Gardner.html">Gardner</a> </li> </ul></nav>  </div> </section> </section>  </div> </main> <aside id="bottom"> <style> #bottom { padding-bottom: 65px; } #acknowledgment { display:none; } .attribution { font-size: .75rem; font-style: italic; } footer ul li:not(:last-of-type)::after { background: #a3a3a3; margin-left: .3rem; margin-right: .1rem; } @media all and (max-width: 900px) { .attribution { font-size: 12px; } } @media (max-width: 600px) { footer { max-width: 360px; } footer ul { max-width: 360px; } footer ul:nth-child(1) li:nth-child(2):after { content: ""; height: 11px; } footer ul:nth-child(1) li:nth-child(3):after { content: ""; height: 0px; } } </style> <footer> <ul> <li><a href="/about/">About MathWorld</a></li> <li><a href="/classroom/">MathWorld Classroom</a></li> <li><a href="/contact/">Contribute</a></li> <li><a href="https://www.amazon.com/exec/obidos/ASIN/1420072218/ref=nosim/weisstein-20" target="_blank">MathWorld Book</a></li> <li class="display-n display-ib__600"><a href="https://www.wolfram.com" target="_blank">wolfram.com</a></li> </ul> <ul> <li class="display-n__600"><a href="/whatsnew/">13,246 Entries</a></li> <li class="display-n__600"><a href="/whatsnew/">Last Updated: Fri Feb 21 2025</a></li>  <li><a href="https://www.wolfram.com" target="_blank">©1999–2025 Wolfram Research, Inc.</a></li> <li><a href="https://www.wolfram.com/legal/terms/mathworld.html" target="_blank">Terms of Use</a></li> </ul> <ul class="wolfram"> <li class="display-n__600 display-n__900"><a href="https://www.wolfram.com" target="_blank" aria-label="Wolfram"><img src="/images/footer/wolfram-logo.png" alt="Wolfram" title="Wolfram" width="121" height="28"></a></li> <li class="display-n__600"><a href="https://www.wolfram.com" target="_blank">wolfram.com</a></li> <li class="display-n__600"><a href="https://www.wolfram.com/education/" target="_blank">Wolfram for Education</a></li> <li class="attribution">Created, developed and nurtured by Eric Weisstein at Wolfram Research</li> </ul> </footer> <section id="acknowledgment"> <i>Created, developed and nurtured by Eric Weisstein at Wolfram Research</i> </section> </aside> <script type="text/javascript" src="/scripts/scripts.js"></script> <script src="/common/js/c2c/1.0/WolframC2C.js"></script> <script src="/common/js/c2c/1.0/WolframC2CGui.js"></script> <script src="/common/js/c2c/1.0/WolframC2CDefault.js"></script> <link rel="stylesheet" href="/common/js/c2c/1.0/WolframC2CGui.css.en"> <style> .wolfram-c2c-wrapper { padding: 0px !important; border: 0px; } .wolfram-c2c-wrapper:active { border: 0px; } .wolfram-c2c-wrapper:hover { border: 0px; } </style> <script> let c2cWrittings = new WolframC2CDefault({'triggerClass':'mathworld-c2c_above', 'uniqueIdPrefix': 'mathworld-c2c_above-'}); </script> <style> #IPstripe-outer { background: #47a2af; } #IPstripe-outer:hover { background: #0095aa; } </style> <div id="IPstripe-wrap"></div> <script src="/common/stripe/stripe.en.js"></script> </body> </html>