mathematics

Archytas (/ˈɑːrkɪtəs/; Greek: Ἀρχύτας; 428–347 BC) was an Ancient Greek philosopher, mathematician, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato.

Numbers
- 英國牛津大學的研究員早前以放射性碳定年法，鑑定了在一八八一年出土的「巴赫沙利手稿」（Bakhshali Manuscripts），當中記載了數字的應用，學界一直認為該文件是在八至十二世紀期間寫下。研究結果出爐後，專家發現文件中含有的物質分別來自最少三個時期，年代最為久遠的物質可追溯至公元三世紀。領導研究的索托伊教授（Marcus du Sautoy）指出，過往大家理所當然認定「0」的存在，而在巴赫沙利手稿上的數字「0」，正是現在最早發現使用「0」作數字的古文件，亦是數學歷史的重大突破。orientaldaily 16sep17


Numberal system
- https://www.quora.com/Are-there-other-living-languages-that-use-a-numeral-system-similar-to-French
- The vigesimal or base 20 numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten). In a vigesimal place system, twenty individual numerals (or digit symbols) are used, ten more than in the usual decimal system. One modern method of finding the extra needed symbols is to write ten as the letter A₂₀ (the ₂₀ means base 20), to write nineteen as J₂₀, and the numbers between with the corresponding letters of the alphabet. This is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters "A–F". Another less common method skips over the letter "I", in order to avoid confusion between I₂₀ as eighteen and one, so that the number eighteen is written as J₂₀, and nineteen is written as K₂₀. The number twenty is written as 10₂₀.
- https://www.quora.com/Which-languages-count-in-the-most-interesting-ways
- https://www.quora.com/Are-numbers-universal-across-all-languages
- https://www.quora.com/Why-doesnt-French-have-a-word-for-the-number-90-They-literally-say-four-twenty-ten
- *******https://www.quora.com/Do-Arabic-numerals-actually-have-an-Arabic-origin
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• korean 하나hana한han

measurement units

- A bushel (abbreviation: bsh. or bu.) is an imperial and US customary unit of weight or massbased upon an earlier measure of dry capacity. The old bushel was equal to 2 kennings(obsolete), 4 pecks or 8 gallons and was used mostly for agricultural products such as wheat. In modern usage, the volume is nominal, with bushels denoting a mass defined differently for each commodity. The name comes from the Old Frenchboissiel and buissiel, meaning "little box".^[1]It may further derive from Old Frenchboise, thus meaning "little butt".The bushel is an intermediate value between the pound and ton or tun that was introduced to England following the Norman Conquest. Norman statutes made the London bushel part of the legal measure of English wine, ale, and grains. The Assize of Bread and Ale credited to Henry III c. 1266 defined this bushel in terms of the wine gallon,^[2] while the c. 1300 Assize of Weights and Measuresusually credited to Edward I or II defined the London bushel in terms of the larger corn gallon.^[3] In either case, the bushel was reckoned to contain 64 pounds of 12 ounces of 20 pence of 32 grains. These measures were based on the relatively light tower pound and were rarely used in Scotland, Ireland, or Wales during the Middle Ages. When the Tower system was abolished in the 16th century, the bushel was redefined as 56 avoirdupois pounds. The imperial bushel established by the Weights and Measures Act of 1824described the bushel as the volume of 80 avoirdupois pounds of distilled water in air at 62 °F (17 °C)^{[citation needed]} or 8 imperial gallons.^[1] This is the bushel in some use in the United Kingdom. The Winchester bushel was the volume of a cylinder 18.5 in (46.99 cm) in diameter and 8 in (20.32 cm) high, which gives an irrational number of cubic inches. The modern American or US bushel is a variant of this, rounded to exactly 2150.42 cubic inches, less than one part per ten million less. It is also somewhat in use in Canada.

• chinese counterpart 鬥

In mathematics, the Borromean rings^[a] consist of three topological circles which are linked and form a Brunnian link (i.e., removing any ring results in two unlinked rings). In other words, no two of the three rings are linked with each other as a Hopf link, but nonetheless all three are linked.The name "Borromean rings" comes from their use in the coat of arms of the aristocratic Borromeo family in Northern Italy. The link itself is much older and has appeared in the form of the valknut on Norse image stones dating back to the 7th century.The Borromean rings have been used in different contexts to indicate strength in unity, e.g., in religion or art. In particular, some have used the design to symbolize the Trinity. The psychoanalyst Jacques Lacan famously found inspiration in the Borromean rings as a model for his topology of human subjectivity, with each ring representing a fundamental Lacanian component of reality (the "real", the "imaginary", and the "symbolic").The rings were used as the logo of Ballantine beer, and are still used by the Ballantine brand beer, now distributed by the current brand owner, the Pabst Brewing Company.A stone pillar at Marundeeswarar Temple in Thiruvanmiyur, Chennai, Tamil Nadu, India, has such a figure dating to before 6th century.


Music
- In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa.^[1] For instance, the perfect fifth with ratio 3/2 (equivalent to 3¹/2¹) and the perfect fourth with ratio 4/3 (equivalent to 2²/3¹) are Pythagorean intervals. All the intervals between the notes of a scale are Pythagorean if they are tuned using the Pythagorean tuning system. However, some Pythagorean intervals are also used in other tuning systems. For instance, the above-mentioned Pythagorean perfect fifth and fourth are also used in just intonation.