An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for instance the Egyptian fraction above sums to . Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including and as summands, were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations into medieval times. In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation. However, Egyptian fractions continue to be an object of study in modern number theory and recreational mathematics, as well as in modern historical studies of ancient mathematics.
The system of ancient Egyptian numerals was used in Ancient Egypt from around 3000 BC until the early first millennium AD. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs. The Egyptians had no concept of a positional notation such as the decimal system. The hieratic form of numerals stressed an exact finite series notation, ciphered one-to-one onto the Egyptian alphabet.
Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt c. 3000 to c. 300 BCE, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplication and fractions. Evidence for Egyptian mathematics is limited to a scarce amount of surviving sources written on papyrus. From these texts it is known that ancient Egyptians understood concepts of geometry, such as determining the surface area and volume of three-dimensional shapes useful for architectural engineering, and algebra, such as the false position method and quadratic equations.
El Lahun. It was known as Ptolemais Hormos in Ptolemaic Egypt. There are multiple areas at El Lahun including the Pyramid of Senwosret II, cemeteries, the Valley temple, and the town of Kahun. It contains many artifacts of daily life like pottery from the Middle Kingdom and evidence of administrative procedures seen on papyri and seals.
Sekhemre Khutawy Amenemhat Sobekhotep was an Egyptian pharaoh of the early 13th Dynasty in the late Middle Kingdom.
The Moscow Mathematical Papyrus, also named the Golenishchev Mathematical Papyrus after its first non-Egyptian owner, Egyptologist Vladimir Golenishchev, is an ancient Egyptian mathematical papyrus containing several problems in arithmetic, geometry, and algebra. Golenishchev bought the papyrus in 1892 or 1893 in Thebes. It later entered the collection of the Pushkin State Museum of Fine Arts in Moscow, where it remains today.
In mathematics, ancient Egyptian multiplication, one of two multiplication methods used by scribes, is a systematic method for multiplying two numbers that does not require the multiplication table, only the ability to multiply and divide by 2, and to add. It decomposes one of the multiplicands into a set of numbers of powers of two and then creates a table of doublings of the second multiplicand by every value of the set which is summed up to give result of multiplication.
The Berlin Papyrus 6619, simply called the Berlin Papyrus when the context makes it clear, is one of the primary sources of ancient Egyptian mathematics. One of the two mathematics problems on the Papyrus may suggest that the ancient Egyptians knew the Pythagorean theorem.
Neferuptah or Ptahneferu was a daughter of the Egyptian king Amenemhat III of the 12th Dynasty. Her sister was the Pharaoh Sobekneferu.
The Egyptian Mathematical Leather Roll (EMLR) is a 10 × 17 in (25 × 43 cm) leather roll purchased by Alexander Henry Rhind in 1858. It was sent to the British Museum in 1864, along with the Rhind Mathematical Papyrus, but it was not chemically softened and unrolled until 1927 (Scott, Hall 1927).
The Reisner Papyri date to the reign of Senusret I, who was king of ancient Egypt in the 19th century BCE. The documents were discovered by G.A. Reisner during excavations in 1901–04 in Naga ed-Deir in southern Egypt. A total of four papyrus rolls were found in a wooden coffin in a tomb.
The Akhmim wooden tablets, also known as the Cairo wooden tablets are two wooden writing tablets from ancient Egypt, solving arithmetical problems. They each measure around 18 by 10 inches and are covered with plaster. The tablets are inscribed on both sides. The hieroglyphic inscriptions on the first tablet include a list of servants, which is followed by a mathematical text. The text is dated to year 38 of an otherwise unnamed king's reign. The general dating to the early Egyptian Middle Kingdom combined with the high regnal year suggests that the tablets may date to the reign of the 12th Dynasty pharaoh Senusret I, c. 1950 BC. The second tablet also lists several servants and contains further mathematical texts.
The Rhind Mathematical Papyrus is one of the best known examples of ancient Egyptian mathematics.
The Kahun Papyri are a collection of ancient Egyptian texts discussing administrative, mathematical and medical topics. Its many fragments were discovered by Flinders Petrie in 1889 and are kept at the University College London. This collection of papyri is one of the largest ever found. Most of the texts are dated to ca. 1825 BC, to the reign of Amenemhat III. In general the collection spans the Middle Kingdom of Egypt.
The Kahun Gynaecological Papyrus is the oldest known medical text in Egyptian history, dated to c. 1825 BCE, during the Twelfth Dynasty. The Papyrus addresses gynecological health concerns, pregnancy, fertility, and various treatments.
The Rhind Mathematical Papyrus, an ancient Egyptian mathematical work, includes a mathematical table for converting rational numbers of the form 2/n into Egyptian fractions, the form the Egyptians used to write fractional numbers. The text describes the representation of 50 rational numbers. It was written during the Second Intermediate Period of Egypt by Ahmes, the first writer of mathematics whose name is known. Aspects of the document may have been copied from an unknown 1850 BCE text.
The Heqanakht Papyri or Heqanakht letters are a group of papyri dating to the early Middle Kingdom of Ancient Egypt that were found in the tomb complex of Vizier Ipi. Their find was located in the burial chamber of a servant named Meseh, which was to the right side of the courtyard of Ipi's burial complex. It is believed that the papyri were accidentally mixed into debris used to form a ramp to push the coffin of Meseh into the chamber. The papyri contain letters and accounts written by Heqanakht, a ka-priest of Ipi. Heqanakht himself was obliged to stay in the Theban area, and thus wrote letters to his family, probably located somewhere near the capital of Egypt at that time, near the Faiyum. These letters and accounts were somehow lost and thus preserved. The significance of the papers is that they give rare and valuable information about lives of ordinary members of the lower upper class of Egypt during this period.
Kheti was an ancient Egyptian vizier of the Twelfth Dynasty under king Amenemhet III, who ruled around 1800 BC.
Egyptian geometry refers to geometry as it was developed and used in Ancient Egypt. Their geometry was a necessary outgrowth of surveying to preserve the layout and ownership of farmland, which was flooded annually by the Nile river.
Mathematics in Ancient Egypt: A Contextual History is a book on ancient Egyptian mathematics by Annette Imhausen. It was published by the Princeton University Press in 2016.
