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Rhind Mathematical Papyrus

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The Rhind Mathematical Papyrus is a vital artifact of ancient Egyptian mathematics.

Egyptian A'h-mosè or Rhind Papyrus (1065x1330)
Egyptian A'h-mosè or Rhind Papyrus (1065x1330)

It serves as a detailed record of how ancient people calculated quantities and measured space. The document is one of two famous mathematical papyri, the other being the Moscow Mathematical Papyrus. While the Moscow version is well-known, the Rhind Papyrus is the larger and more recent of the two. It provides a window into the mathematical reasoning used during the Second Intermediate Period of Egypt. This collection of problems helped ancient scribes manage resources and solve practical challenges.

The papyrus was copied by a scribe named Ahmes around 1550 BC. Ahmes stated that his work provided "accurate reckoning" for inquiring into mysteries and secrets. He copied this text from an even older manuscript created during the reign of King Nimaatre.

Rhind Papyrus Recto and Verso
Rhind Papyrus Recto and Verso

The document also contains historical notes on its verso, or back side. One entry mentions a date in the regnal year 11 of the Hyksos king Khamudi. This note describes an event where "he of the South" broke into Tjaru. Historians like Thomas Schneider and Irene Forstner-Mueller believe "he of the South" refers to the Theban king Ahmose I. Such details allow researchers to connect mathematical records to specific political eras.

Mathematical content in the papyrus is organized into three distinct books. Book I focuses on arithmetic and algebra through 91 different problems. It begins with reference tables, such as a 2/n table for odd numbers. This table expresses fractions like 2/n as sums of unit fractions. For example, the scribe decomposes fractions into parts that are never more than four terms long. Book I also contains "aha" problems, which are early forms of linear equations.

Rhind Papyrus Unit Concordance
Rhind Papyrus Unit Concordance

These problems require finding an unknown value to make an equation true.

Book II transitions into geometry, which is the study of shapes and their measurements. Scholars often call these "mensuration problems" because they involve measuring physical dimensions. The scribe provides methods to calculate the volume of cylindrical and rectangular granaries. To find the volume of a cylinder, the scribe uses the diameter and height. This calculation includes an approximation of pi, the constant used for circles. The papyrus uses the fraction 256/81, which is about 3.1605. This value is remarkably accurate, with an error of less than one percent.

Rhind Papyrus Problem 81
Rhind Papyrus Problem 81

Geometry in the Rhind Papyrus also covers the area of various shapes. The scribe shows how to calculate the areas of rectangles, triangles, and trapezoids. A notable method involves finding the area of a circle by using a specific ratio. The text states that a circle's area relates to its circumscribing square by a ratio of 64/81. Additionally, the papyrus addresses the slopes of pyramids. This is done through a concept called the seked. The seked is the ratio of the run to the rise of the pyramid's face. It helps builders maintain a consistent angle as they construct the monument.

Book III serves as a miscellany, or a collection of various unrelated items. It contains more complex data tables and problems involving food preparation. Some of these are called pefsu problems, which involve the strength of bread and beer. One famous item is problem 79, which functions like a mathematical riddle. It describes a sequence: seven houses, 49 cats, 343 mice, 2401 ears of spelt, and 16807 hekats. This problem demonstrates an early understanding of geometric progressions.

Rhind Papyrus Number 85
Rhind Papyrus Number 85

Such problems show that math was used for both utility and intellectual play.

The discovery and preservation of the papyrus involve several historical figures. In 1858, a Scottish antiquarian named Alexander Henry Rhind purchased two parts of the document. He found it near the Ramesseum in Luxor, Egypt. In 1865, the British Museum acquired the majority of the papyrus. Other fragments were purchased by the American Egyptologist Edwin Smith in the mid-1860s. These pieces are now held by the Brooklyn Museum. Through the work of scholars like T. Eric Peet and Arnold Buffum Chace, the text has been translated and studied for decades. This ongoing research continues to reveal the sophistication of ancient Egyptian thought.

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🖼️ Images & Media (5)
File:Egyptian A'h-mosè or Rhind Papyrus (1065x1330).png
Egyptian A'h-mosè or Rhind Papyrus (1065x1330).png
File:Rhind Papyrus Unit Concordance.png
Rhind Papyrus Unit Concordance.png
File:Rhind Papyrus Recto and Verso.png
Rhind Papyrus Recto and Verso.png
File:Rhind Papyrus Problem 81.png
Rhind Papyrus Problem 81.png
File:Rhind Papyrus Number 85.png
Rhind Papyrus Number 85.png
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