Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic).
In geometry, a frustum ; is the portion of a solid that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal. A right frustum is a right pyramid or a right cone truncated perpendicularly to its axis; otherwise, it is an oblique frustum. In a truncated cone or truncated pyramid, the truncation plane is not necessarily parallel to the cone's base, as in a frustum. If all its edges are forced to become of the same length, then a frustum becomes a prism.
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.
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 In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation.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.
In geometry, a square pyramid is a pyramid with a square base, having a total of five faces. If the apex of the pyramid is directly above the center of the square, it is a right square pyramid with four isosceles triangles; otherwise, it is an oblique square pyramid. When all of the pyramid's edges are equal in length, its triangles are all equilateral. It is called an equilateral square pyramid, an example of a Johnson solid.
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.
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. A pyramid is a conic solid with a polygonal base. Many types of pyramids can be found by determining the shape of bases, either by based on a regular polygon or by cutting off the apex. It can be generalized into higher dimensions, known as hyperpyramid. All pyramids are self-dual.
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.
In mathematics, the Heronian meanH of two non-negative real numbers A and B is given by the formula
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 Rhind Mathematical Papyrus is one of the best known examples of ancient Egyptian mathematics.
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 following is a timeline of key developments of geometry:
Seked is an ancient Egyptian term describing the inclination of the triangular faces of a right pyramid. The system was based on the Egyptians' length measure known as the royal cubit. It was subdivided into seven palms, each of which was sub-divided into four digits.
The Lahun Mathematical Papyri is an ancient Egyptian mathematical text. It forms part of the Kahun Papyri, which was discovered at El-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.
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.
In the history of mathematics, Egyptian algebra, as that term is used in this article, refers to algebra as it was developed and used in ancient Egypt. Ancient Egyptian mathematics as discussed here spans a time period ranging from c. 3000 BCE to c. 300 BCE.
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.
