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Gnomon
A gnomon (; ) is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields, typically to measure directions, position, or time. History A painted stick dating from 2300 BC that was excavated at the archeological site of Taosi is the oldest gnomon known in China. The gnomon was widely used in ancient China from the second millennium BC onward in order to determine the changes in seasons, orientation, and geographical latitude. The ancient Chinese used shadow measurements for creating calendars that are mentioned in several ancient texts. According to the collection of Zhou Chinese poetic anthologies ''Classic of Poetry'', one of the distant ancestors of King Wen of the Zhou dynasty used to measure gnomon shadow lengths to determine the orientation around the 14th century BC. The ancient Greek philosopher Anaximander (610–546 BC) is credited with introducing this Babylonian instrument to the Ancient Greeks. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zhoubi Suanjing
The ''Zhoubi Suanjing'', also known by many other names, is an ancient Chinese astronomical and mathematical work. The ''Zhoubi'' is most famous for its presentation of Chinese cosmology and a form of the Pythagorean theorem. It claims to present 246 problems worked out by the Duke of Zhou as well as members of his court, placing its composition during the 11th century BC. However, the present form of the book does not seem to be earlier than the Eastern Han (25–220 AD), with some additions and commentaries continuing to be added for several more centuries. The book was included as part of the '' Ten Computational Canons''. Names The work's original title was simply the ''Zhoubi'': the character is a literary term for the femur or thighbone but in context only refers to one or more gnomons, large sticks whose shadows were used for Chinese calendrical and astronomical calculations. Because of the ambiguous nature of the character , it has been alternatel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Figurate Number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The ancient Greek mathematicians already considered triangular numbers, polygonal numbers, tetrahedral numbers, and pyramidal numbers, ReprintedG. E. Stechert & Co., 1934 and AMS Chelsea Publishing, 1944. and subsequent mathematicians have included other classes of these numbers including numbers defined from other types of polyhedra and from their analogs in other dimensions. Terminology Some kinds of figurate number were discussed in the 16th and 17th centuries under the name "figural number". In historical works about Greek mathematics the preferred term used to be ''figured number''. In a use going back to Jacob Bernoulli's Ars Conjectandi, the term ''figurate number'' is used for triangular numbers made up of successive integers, tetrahedral numbers made ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sundial Taganrog
A sundial is a horology, horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by the position of the Sun, apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a flat plate (the ''dial'') and a gnomon, which casts a shadow onto the dial. As the Sun diurnal motion, appears to move through the sky, the shadow aligns with different hour-lines, which are marked on the dial to indicate the time of day. The ''style'' is the time-telling edge of the gnomon, though a single point or ''nodus'' may be used. The gnomon casts a broad shadow; the shadow of the style shows the time. The gnomon may be a rod, wire, or elaborately decorated metal casting. The style must be polar alignment, parallel to the axis of the Earth's rotation for the sundial to be accurate throughout the year. The style's angle from horizontal is equal to the sundial's geographical latitude. The term ''sundial'' can r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taosi
Taosi () is an archaeological site in Xiangfen County, Shanxi, China. Taosi is considered to be part of the late phase of the Longshan culture in southern Shanxi, also known as the Taosi phase (2300 BC to 1900 BC). Archaeology Taosi was surrounded by a gigantic rammed-clay enclosure. This was discovered from 1999 to 2001 by the archaeologists from the Institute of Archaeology, Chinese Academy of Social Sciences; they attributed this wall to the Middle Taosi period (4,100 to 4,000 BP). Rectangular in form with an inner area of 280 ha. An internal rammed-earth wall separated the residential and ceremonial areas of the elite from the areas inhabited by commoners, signifying the development of a stratified society. The Huaxia settlement outgrew the perimeter of the wall. The settlement is the largest Longshan site discovered in the Linfen basin of the Yellow River, and is possibly a regional center. The settlement represents the most politically organized system on the Central Pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anaximander
Anaximander ( ; ''Anaximandros''; ) was a Pre-Socratic philosophy, pre-Socratic Ancient Greek philosophy, Greek philosopher who lived in Miletus,"Anaximander" in ''Chambers's Encyclopædia''. London: George Newnes Ltd, George Newnes, 1961, Vol. 1, p. 403. a city of Ionia (in modern-day Turkey). He belonged to the Milesian school and learned the teachings of his master Thales. He succeeded Thales and became the second master of that school where he counted Anaximenes of Miletus, Anaximenes and, arguably, Pythagoras amongst his pupils. Little of his life and work is known today. According to available historical documents, he is the first philosopher known to have written down his studies, although only one fragment of his work remains. Fragmentary testimonies found in documents after his death provide a portrait of the man. Anaximander was an early proponent of science and tried to observe and explain different aspects of the universe, with a particular cosmogony, interest in its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Numbers
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The usual notation for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name ''square'' number comes from the name of the shape. The unit of area is defined as the area of a unit square (). Hence, a square with side length has area . If a square number is represented by ''n'' points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of ''n''; thus, square numbers are a type of figurate numbers (other examples being cube numbers and triangular numbers). In the real number system, square numbers are non-negative. A non-negative integer is a square number when its square root is again an integer. For example, \s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paolo Toscanelli
Paolo dal Pozzo Toscanelli (1397 – 10 May 1482) was an Italian mathematician, astronomer, and cosmographer. Life Paolo dal Pozzo Toscanelli was born in Florence, the son of the physician Domenico Toscanelli and Biagia Mei. There is no precise information on his education and background. Gustavo Uzielli claimed in 1894 that Toscanelli studied at the University of Padua, but modern authors consider this pure conjecture., pp. 333–335 Toscanelli lived most of his life in Florence, with occasional excursions to Todi and Rome. He is said to have entered into correspondence with scholars around Europe, but his writings have yet to be thoroughly researched. Thanks to his long life, his intelligence and his wide interests, Toscanelli was one of the central figures in the intellectual and cultural history of Renaissance Florence in its early years. His circle of friends included Filippo Brunelleschi, the architect of the Florence Cathedral, and the philosopher Marsilio Ficino. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nine Chapters On The Mathematical Art
''The Nine Chapters on the Mathematical Art'' is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 1st century CE. This book is one of the earliest surviving mathematical texts from China, the others being the '' Suan shu shu'' (202 BCE – 186 BCE) and '' Zhoubi Suanjing'' (compiled throughout the Han until the late 2nd century CE). It lays out an approach to mathematics that centres on finding the most general methods of solving problems, which may be contrasted with the approach common to ancient Greek mathematicians, who tended to deduce propositions from an initial set of axioms. Entries in the book usually take the form of a statement of a problem, followed by the statement of the solution and an explanation of the procedure that led to the solution. These were commented on by Liu Hui in the 3rd century. The book was later included in the early Tang collection, the '' Ten Computational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shadow
A shadow is a dark area on a surface where light from a light source is blocked by an object. In contrast, shade occupies the three-dimensional volume behind an object with light in front of it. The cross-section of a shadow is a two-dimensional silhouette, or a reverse projection of the object blocking the light. Point and non-point light sources A point source of light casts only a simple shadow, called an "umbra". For a non-point or "extended" source of light, the shadow is divided into the umbra, penumbra, and antumbra. The wider the light source, the more blurred the shadow becomes. If two penumbras overlap, the shadows appear to attract and merge. This is known as the shadow blister effect. The outlines of the shadow zones can be found by tracing the rays of light emitted by the outermost regions of the extended light source. The umbra region does not receive any direct light from any part of the light source and is the darkest. A viewer located in the umbra regi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
