Han Dynasty (202 BC – 220 AD) paintings on tile of Chinese guardian spirits representing 11 pm to 1 am (left) and 5 am to 7 am (right); the ancient Chinese, although discussing it in supernatural terms, acknowledged circadian rhythm within the human body
Circadian rhythm in humans: The observation of a circadian or diurnal process in humans is mentioned in Chinese medical texts dated to around the 13th century, including the Noon and Midnight Manual and the Mnemonic Rhyme to Aid in the Selection of Acu-points According to the Diurnal Cycle, the Day of the Month and the Season of the Year.
Diabetes, recognition and treatment of: The Huangdi Neijing compiled by the 2nd century BC during the Han Dynasty identified diabetes as a disease suffered by those who had made an excessive habit of eating sweet and fatty foods, while the Old and New Tried and Tested Prescriptions written by the Tang Dynasty physician Zhen Quan (died 643) was the first known book to mention an excess of sugar in the urine of diabetic patients.
Equal temperament: During the Han Dynasty (202 BC–220 AD), the music theorist and mathematician Jing Fang (78–37 BC) extended the 12 tones found in the 2nd century BC Huainanzi to 60. While generating his 60-divisional tuning, he discovered that 53 just fifths is approximate to 31 octaves, calculating the difference at ; this was exactly the same value for 53 equal temperament calculated by the German mathematician Nicholas Mercator (c. 1620–1687) as 353/284, a value known as Mercator's Comma. The Ming Dynasty (1368–1644) music theorist Zhu Zaiyu (1536–1611) elaborated in three separate works beginning in 1584 the tuning system of equal temperament. In an unusual event in music theory's history, the Flemish mathematician Simon Stevin (1548–1620) discovered the mathematical formula for equal temperament at roughly the same tim, yet he did not publish his work and it remained unknown until 1884 (whereas the Harmonie Universelle written in 1636 by Marin Mersenne is considered the first publication in Europe outlining equal temperament); therefore, it is debatable who discovered equal temperament first, Zhu or Stevin. In order to obtain equal intervals, Zhu divided the octave (each octave with a ratio of 1:2, which can also be expressed as 1:212/12) into twelve equal semitones while each length was divided by the 12th root of 2. He did not simply divide the string into twelve equal parts (i.e. 11/12, 10/12, 9/12, etc.) since this would give unequal temperament; instead, he altered the ratio of each semitone by an equal amount (i.e. 1:2 11/12, 1:210/12, 1:29/12, etc.) and determined the exact length of the string by dividing it by 12√2 (same as 21/12).
Aware of underground minerals associated with certain plants by at least the 5th century BC, the Chinese extracted trace elements of copper from Oxalis corniculata, pictured here, as written in the 1421 text Precious Secrets of the Realm of the King of Xin.
Geomorphology: In his Dream Pool Essays of 1088, Shen Kuo (1031–1095) wrote about a landslide (near modern Yan'an) where petrified bamboos were discovered in a preserved state underground, in the dry northern climate zone of Shanbei, Shaanxi; Shen reasoned that since bamboo was known only to grow in damp and humid conditions, the climate of this northern region must have been different in the very distant past, postulating that climate change occurred over time. Shen also advocated a hypothesis in line with geomorphology after he observed a stratum of marine fossils running in a horizontal span across a cliff of the Taihang Mountains, leading him to believe that it was once the location of an ancient shoreline that had shifted hundreds of km (mi) east over time (due to deposition of silt and other factors).
Grid reference: Although professional map-making and use of the grid had existed in China before, the Chinese cartographer and geographer Pei Xiu of the Three Kingdoms period was the first to mention a plotted geometrical grid reference and graduated scale displayed on the surface of maps to gain greater accuracy in the estimated distance between different locations. Historian Howard Nelson asserts that there is ample written evidence that Pei Xiu derived the idea of the grid reference from the map of Zhang Heng (78–139 CE), a polymath inventor and statesman of the Eastern Han dynasty.
Jia Xian triangle: This triangle was the same as Pascal's Triangle, discovered by Jia Xian in the first half of the 11th century, about six centuries before Pascal. Jia Xian used it as a tool for extracting square and cubic roots. The original book by Jia Xian titled Shi Suo Suan Shu was lost; however, Jia's method was expounded in detail by Yang Hui, who explicitly acknowledged his source: "My method of finding square and cubic roots was based on the Jia Xian method in Shi Suo Suan Shu." A page from the Yongle Encyclopedia preserved this historic fact.
Leprosy, first description of its symptoms: The Feng zhen shi 封診式 (Models for sealing and investigating), written between 266 and 246 BC in the State of Qin during the Warring States period (403–221 BC), is the earliest known text which describes the symptoms of leprosy, termed under the generic word li 癘 (for skin disorders). This text mentioned the destruction of the nasal septum in those suffering from leprosy (an observation that would not be made outside of China until the writings of Avicenna in the 11th century), and according to Katrina McLeod and Robin Yates it also stated lepers suffered from "swelling of the eyebrows, loss of hair, absorption of nasal cartilage, affliction of knees and elbows, difficult and hoarse respiration, as well as anaesthesia." Leprosy was not described in the West until the writings of the Roman authors Aulus Cornelius Celsus (25 BC – 37 AD) and Pliny the Elder (23–79 AD). Although it is alleged that the Indian Sushruta Samhita, which describes leprosy, is dated to the 6th century BC, India's earliest written script (besides the then long extinct Indus script)—the Brāhmī script—is thought to have been created no earlier than the 3rd century BC.
Magic squares: The earliest magic square is the Lo Shu square, dating to 4th century BCE China. The square was viewed as mystical, and according the Chinese mythology, and "was first seen by Emperor Yu."
Map scaling: The foundations for quantitative map scaling goes back to ancient China with textual evidence that the idea of map scaling was understood by the second century BC. Ancient Chinese surveyors and cartographers had ample technical resources used to produce maps such as counting rods, carpenter's square's, plumb lines, compasses for drawing circles, and sighting tubes for measuring inclination. Reference frames postulating a nascent coordinate system for identifying locations were hinted by ancient Chinese astronomers that divided the sky into various sectors or lunar lodges. The Chinese cartographer and geographer Pei Xiu of the Three Kingdoms period created a set of large-area maps that were drawn to scale. He produced a set of principles that stressed the importance of consistent scaling, directional measurements, and adjustments in land measurements in the terrain that was being mapped.
True north, concept of: The Song Dynasty (960–1279) official Shen Kuo (1031–1095), alongside his colleague Wei Pu, improved the orifice width of the sighting tube to make nightly accurate records of the paths of the moon, stars, and planets in the night sky, for a continuum of five years. By doing so, Shen fixed the outdated position of the pole star, which had shifted over the centuries since the time Zu Geng (fl. 5th century) had plotted it; this was due to the precession of the Earth's rotational axis. When making the first known experiments with a magnetic compass, Shen Kuo wrote that the needle always pointed slightly east rather than due south, an angle he measured which is now known as magnetic declination, and wrote that the compass needle in fact pointed towards the magnetic north pole instead of true north (indicated by the current pole star); this was a critical step in the history of accurate navigation with a compass.
Culturing Chlamydia trachomatis bacteria: Chlamydia trachomatis agent was first cultured in the yolk sacs of eggs by Chinese scientists in 1957 
Feathered theropods: The first feathered dinosaur outside of Avialae, Sinosauropteryx, meaning "Chinese reptilian wing," was discovered in the Yixian Formation by Chinese paleontologists in 1996. The discovery is seen as evidence that dinosaurs originated from birds, a theory proposed and supported decades earlier by paleontologists like Gerhard Heilmann and John Ostrom, but "no true dinosaur had been found exhibiting down or feathers until the Chinese specimen came to light." The dinosaur was covered in what are dubbed 'protofeathers' and considered to be homologous with the more advanced feathers of birds, although some scientists disagree with this assessment.
Heterosis in rice, three-line hybrid rice system: A team of agricultural scientists headed by Yuan Longping applied heterosis to rice, developing the three-line hybrid rice system in 1973. The innovation allowed for roughly 12,000 kg (26,450 lbs) of rice to be grown per hectare (10,000 m2). Hybrid rice has proven to be greatly beneficial in areas where there is little arable land, and has been adopted by several Asian and African countries. Yuan won the 2004 Wolf Prize in agriculture for his work.
Ky Fan norms: The sum of the k largest singular values of M is a matrix norm, the Ky Fank-norm of M.The first of the Ky Fan norms, the Ky Fan 1-norm is the same as the operator norm of M as a linear operator with respect to the Euclidean norms of Km and Kn. In other words, the Ky Fan 1-norm is the operator norm induced by the standard l2 Euclidean inner product.
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