mathematics

Lahun Mathematical Papyri

Lahun Mathematical Papyri is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Lahun Mathematical Papyri rather than just read about it. In short: The Lahun Mathematical Papyri (also known as the Kahun Mathematical Papyri) is an ancient Egyptian mathematical text. It forms part of the Kahun Papyri, which was discovered at El-Lahun (also known as Lahun, Kahun or Il-Lahun) by Flinders Petrie during excavations of a workers' town near the pyramid of the Twelfth Dynasty pharaoh Sesostris II.

Key takeaways

Lahun Mathematical Papyri belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Lahun Mathematical Papyri to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Lahun Mathematical Papyri from memory before moving on to harder problems.

Reference excerpt

The Lahun Mathematical Papyri (also known as the Kahun Mathematical Papyri) is an ancient Egyptian mathematical text. It forms part of the Kahun Papyri, which was discovered at El-Lahun (also known as Lahun, Kahun or Il-Lahun) by Flinders Petrie during excavations of a workers' town near the pyramid of the Twelfth Dynasty pharaoh Sesostris II. The Kahun Papyri are a collection of texts including administrative texts, medical texts, veterinarian texts and six fragments devoted to mathematics.

Fragments The mathematical texts most commented on are usually named:

Lahun IV.2 (or Kahun IV.2) (UC 32159): This fragment contains a table of Egyptian fraction representations of numbers of the form 2/n. A more complete version of this table of fractions is given in the Rhind Mathematical Papyrus. Lahun IV.3 (or Kahun IV.3) (UC 32160) contains numbers in arithmetical progression and a problem very similar to Problem 40 of the Rhind Mathematical Papyrus. Another problem on this fragment computes the volume of a cylindrical granary. In this problem the scribe uses a formula which takes measurements in cubits and computes the volume and expresses it in terms of the unit khar. Given the diameter (d) and height (h) of the cylindrical granary. As was common for ancient Egyptian mathematics, the scribe did not necessarily generalize the result for arbitrary values of the diameter (d) and height (h). Instead, results were typically obtained empirically —even in problems that involved equations, often solved through the Regula falsi method— rather than through formalized geometric reasoning. In this particular case, the scribe presented the calculation for d = 12 and h = 8.

V = ( ( 1 + 1 / 3 ) d ) 2 ( ( 2 / 3 ) h ) {\displaystyle V=((1+1/3)d)^{2}\,((2/3)h)} . In modern mathematical notation this is equal to

V = 32 27 d 2 h = 128 27 r 2 h {\displaystyle V={\frac {32}{27}}d^{2}h={\frac {128}{27}}r^{2}h} (measured in khar). This problem resembles problem 42 of the Rhind Mathematical Papyrus. The formula is equivalent to V = 256 81 r 2 h {\displaystyle V={\frac {256}{81}}r^{2}h} measured in cubic-cubits as used in the other problems. Lahun XLV.1 (or Kahun XLV.1) (UC 32161) contains a group of very large numbers (hundreds of thousands). Lahun LV.3 (or Kahun LV.3) (UC 32134A and UC 32134B) contains a so-called aha problem which asks one to solve for a certain quantity. The problem resembles ones from the Rhind Mathematical Papyrus (problems 24–29). Lahun LV.4 (or Kahun LV.4) (UC 32162) contains what seems to be an area computation and a problem concerning the value of ducks, geese and cranes. The problem concerning fowl is a baku problem and most closely resembles problem 69 in the Rhind Mathematical Papyrus and problems 11 and 21 in the Moscow Mathematical Papyrus. Unnamed fragment (UC 32118B). This is a fragmentary piece.

2/n tables The Lahun papyrus IV.2 reports a 2/n table for odd n, n = 1, ..., 21. The Rhind Mathematical Papyrus reports an odd n table up to 101. These fraction tables were related to multiplication problems and the use of unit fractions, namely n/p scaled by LCM m to mn/mp. With the exception of 2/3, all fractions were represented as sums of unit fractions (i.e. of the form 1/n), first in red numbers. Multiplication algorithms and scaling factors involved repeated doubling of numbers, and other operations. Doubling a unit fraction with an even denominator was simple, dividing the denominator by 2. Doubling a fraction with an odd denominator however results in a fraction of the form 2/n. The RMP 2/n table and RMP 36 rules allowed scribes to find decompositions of 2/n into unit fractions for specific needs, most often to solve otherwise un-scalable rational numbers (i.e. 28/97 in RMP 31, and 30/53 n RMP 36 by substituting 26/97 + 2/97 and 28/53 + 2/53) and generally n/p by (n − 2)/p + 2/p. Decompositions were unique. Red auxiliary numbers selected divisors of denominators mp that best summed to numerator mn.

Worked examples

Example 1 — a first encounter with Lahun Mathematical Papyri

Start with the simplest possible case. Write down what Lahun Mathematical Papyri claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Lahun Mathematical Papyri before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Lahun Mathematical Papyri ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Lahun Mathematical Papyri

In research: Lahun Mathematical Papyri appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Lahun Mathematical Papyri in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Lahun Mathematical Papyri is common in secondary-school and first-year university syllabi. It links to neighbouring topics 2nd-millennium BC manuscripts, Ancient Egyptian mathematics, Egyptian fractions, so understanding it makes those chapters shorter.
In everyday life: Look for Lahun Mathematical Papyri outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Lahun Mathematical Papyri in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Lahun Mathematical Papyri means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Lahun Mathematical Papyri out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Lahun Mathematical Papyri in simple terms?

Why does Lahun Mathematical Papyri matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Lahun Mathematical Papyri?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Lahun Mathematical Papyri.