In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0,
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, together with Ancient Egypt and Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.
Electrum is a naturally occurring alloy of gold and silver, with trace amounts of copper and other metals. The ancient Greeks called it "gold" or "white gold", as opposed to "refined gold". Its colour ranges from pale to bright yellow, depending on the proportions of gold and silver. It has been produced artificially, and is also known as "green gold".
Hero of Alexandria was a Greco-Egyptian mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He is often considered the greatest experimenter of antiquity and his work is representative of the Hellenistic scientific tradition.
The lyre is a string instrument known for its use in Greek classical antiquity and later periods. The lyre is similar in appearance to a small harp but with distinct differences.
Gerrha was an ancient city of Eastern Arabia, on the west side of the Persian Gulf.
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to it from known points.
Mathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building; from the Pythagoreans of the sixth century BC onwards, to create forms considered harmonious, and thus to lay out buildings and their surroundings according to mathematical, aesthetic and sometimes religious principles; to decorate buildings with mathematical objects such as tessellations; and to meet environmental goals, such as to minimise wind speeds around the bases of tall buildings.
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.
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.
Scholia are grammatical, critical, or explanatory comments — original or copied from prior commentaries — which are inserted in the margin of the manuscript of ancient authors, as glosses. One who writes scholia is a scholiast. The earliest attested use of the word dates to the 1st century BC.
The history of science and technology in the Indian subcontinent begins with prehistoric human activity in the Indus Valley Civilization to early states and empires. Following independence, science and technology in the Republic of India has included automobile engineering, information technology, communications as well as space, polar, and nuclear sciences.
During the growth of the ancient civilizations, ancient technology was the result from advances in engineering in ancient times. These advances in the history of technology stimulated societies to adopt new ways of living and governance.
The ancient Egyptian units of measurement are those used by the dynasties of ancient Egypt prior to its incorporation in the Roman Empire and general adoption of Roman, Greek, and Byzantine units of measurement. The units of length seem to have originally been anthropic, based on various parts of the human body, although these were standardized using cubit rods, strands of rope, and official measures maintained at some temples.
A knotted cord was a primitive surveyor's tool for measuring distances. It is a length of cord with knots at regular intervals. They were eventually replaced by surveyor's chains, which being made of metal were less prone to stretching and thus were more accurate and consistent.
A measuring rod is a tool used to physically measure lengths and survey areas of various sizes. Most measuring rods are round or square sectioned; however, they can also be flat boards. Some have markings at regular intervals. It is likely that the measuring rod was used before the line, chain or steel tapes used in modern measurement.
This is a timeline of ancient Greek mathematicians.
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios such as sine.
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.
