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🔗 Mathematics

The shoelace formula or shoelace algorithm (also known as Gauss's area formula and the surveyor's formula) is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. The user cross-multiplies corresponding coordinates to find the area encompassing the polygon, and subtracts it from the surrounding polygon to find the area of the polygon within. It is called the shoelace formula because of the constant cross-multiplying for the coordinates making up the polygon, like tying shoelaces. It is also sometimes called the shoelace method. It has applications in surveying and forestry, among other areas.

The formula was described by Meister (1724–1788) in 1769 and by Gauss in 1795. It can be verified by dividing the polygon into triangles, and can be considered to be a special case of Green's theorem.

The area formula is derived by taking each edge AB, and calculating the area of triangle ABO with a vertex at the origin O, by taking the cross-product (which gives the area of a parallelogram) and dividing by 2. As one wraps around the polygon, these triangles with positive and negative area will overlap, and the areas between the origin and the polygon will be cancelled out and sum to 0, while only the area inside the reference triangle remains. This is why the formula is called the surveyor's formula, since the "surveyor" is at the origin; if going counterclockwise, positive area is added when going from left to right and negative area is added when going from right to left, from the perspective of the origin.

The area formula can also be applied to self-overlapping polygons since the meaning of area is still clear even though self-overlapping polygons are not generally simple. Furthermore, a self-overlapping polygon can have multiple "interpretations" but the Shoelace formula can be used to show that the polygon's area is the same regardless of the interpretation.

🔗 Languages 🔗 Ottoman Empire 🔗 Western Asia

The language of the court and government of the Ottoman Empire was Ottoman Turkish, but many other languages were in contemporary use in parts of the empire. Although the minorities of the Ottoman Empire were free to use their language amongst themselves, if they needed to communicate with the government they had to use Ottoman Turkish.

The Ottomans had three influential languages: Turkish, spoken by the majority of the people in Anatolia and by the majority of Muslims of the Balkans except in Albania, Bosnia, and various Aegean Sea islands; Persian, initially used by the educated in northern portions of the Ottoman Empire before being displaced by Ottoman Turkish; and Arabic, used in southern portions of the Ottoman Empire; Arabic was spoken mainly in Arabia, North Africa, Mesopotamia and the Levant. Throughout the vast Ottoman bureaucracy Ottoman Turkish language was the official language, a version of Turkish, albeit with a vast mixture of both Arabic and Persian grammar and vocabulary.

Virtually all intellectual and literate pursuits were taken in Turkish language. Some ordinary people had to hire special "request-writers" (arzuhâlcis) to be able to communicate with the government. The ethnic groups continued to speak within their families and neighborhoods (mahalles) with their own languages (e.g., Jews, Greeks, Armenians, etc.) In villages where two or more populations lived together, the inhabitants would often speak each other's language. In cosmopolitan cities, people often spoke their family languages, many non-ethnic Turks spoke Turkish as a second language. Educated Ottoman Turks spoke Arabic and Persian, as these were the main foreign languages in the pre-Tanzimat era, with the former being used for science and the latter for literary affairs.

In the last two centuries, French and English emerged as popular languages, especially among the Christian Levantine communities. The elite learned French at school, and used European products as a fashion statement. The use of Ottoman Turkish for science and literature grew steadily under the Ottomans, while Persian declined in those functions. Ottoman Turkish, during the period, gained many loanwords from Arabic and Persian. Up to 88% of the vocabulary of a particular work would be borrowed from those two languages.

Linguistic groups were varied and overlapping. In the Balkan Peninsula, Slavic, Greek and Albanian speakers were the majority, but there were substantial minorities of Turks and Romance-speaking Vlachs. In most of Anatolia, Turkish was the majority language, but Greek, Armenian and, in the east and southeast, Kurdish were also spoken. In Syria, Iraq, Arabia, Egypt and north Africa, most of the population spoke varieties of Arabic with, above them, a Turkish-speaking elite. However, in no province of the Empire was there a unique language.

🔗 Philosophy 🔗 Philosophy/Contemporary philosophy 🔗 Philosophy/Ethics

The trolley problem is a thought experiment in ethics. It is generally considered to represent a classic clash between two schools of moral thought, utilitarianism and deontological ethics. The general form of the problem is this:

There is a runaway trolley barreling down the railway tracks. Ahead, on the tracks, there are five people tied up and unable to move. The trolley is headed straight for them. You are standing some distance off in the train yard, next to a lever. If you pull this lever, the trolley will switch to a different set of tracks. However, you notice that there is one person on the side track. You have two options:

1. Do nothing and allow the trolley to kill the five people on the main track.
2. Pull the lever, diverting the trolley onto the side track where it will kill one person.

Which is the more ethical option? Or, more simply: What is the right thing to do?

Philippa Foot introduced this modern form of the problem in 1967. Judith Thomson, Frances Kamm, and Peter Unger have also analysed the dilemma extensively.

Earlier forms of the problem predated Foot's publication. Frank Chapman Sharp included a version in a moral questionnaire given to undergraduates at the University of Wisconsin in 1905. In this variation, the railway's switchman controlled the switch, and the lone individual to be sacrificed (or not) was the switchman's child. The German legal scholar Hans Welzel discussed a similar problem in 1951. In his commentary on the Talmud, published long before his death in 1953, Avrohom Yeshaya Karelitz discussed the similar question of whether it is ethical to deflect a projectile from a larger crowd toward a smaller one.

Beginning in 2001, the trolley problem and its variants have been used extensively in empirical research on moral psychology. Trolley problems have also been a topic of popular books. The problem arises in discussing the ethics of autonomous vehicle design, which may require programming to choose whom or what to strike when a collision appears to be unavoidable.

🔗 Philosophy 🔗 Philosophy/Logic 🔗 Philosophy/Contemporary philosophy 🔗 Philosophy/Philosophy of mind 🔗 Philosophy/Analytic philosophy

The Chinese room argument holds that a digital computer executing a program cannot be shown to have a "mind", "understanding" or "consciousness", regardless of how intelligently or human-like the program may make the computer behave. The argument was first presented by philosopher John Searle in his paper, "Minds, Brains, and Programs", published in Behavioral and Brain Sciences in 1980. It has been widely discussed in the years since. The centerpiece of the argument is a thought experiment known as the Chinese room.

The argument is directed against the philosophical positions of functionalism and computationalism, which hold that the mind may be viewed as an information-processing system operating on formal symbols. Specifically, the argument is intended to refute a position Searle calls strong AI: "The appropriately programmed computer with the right inputs and outputs would thereby have a mind in exactly the same sense human beings have minds."

Although it was originally presented in reaction to the statements of artificial intelligence (AI) researchers, it is not an argument against the behavioural goals of AI research, because it does not limit the amount of intelligence a machine can display. The argument applies only to digital computers running programs and does not apply to machines in general.

🔗 Biology 🔗 Physics 🔗 Biophysics

Magnetosomes are membranous structures present in magnetotactic bacteria (MTB). They contain iron-rich magnetic particles that are enclosed within a lipid bilayer membrane. Each magnetosome can often contain 15 to 20 magnetite crystals that form a chain which acts like a compass needle to orient magnetotactic bacteria in geomagnetic fields, thereby simplifying their search for their preferred microaerophilic environments. Recent research has shown that magnetosomes are invaginations of the inner membrane and not freestanding vesicles. Magnetite-bearing magnetosomes have also been found in eukaryotic magnetotactic algae, with each cell containing several thousand crystals.

Overall, magnetosome crystals have high chemical purity, narrow size ranges, species-specific crystal morphologies and exhibit specific arrangements within the cell. These features indicate that the formation of magnetosomes is under precise biological control and is mediated biomineralization.

Magnetotactic bacteria usually mineralize either iron oxide magnetosomes, which contain crystals of magnetite (Fe₃O₄), or iron sulfide magnetosomes, which contain crystals of greigite (Fe₃S₄). Several other iron sulfide minerals have also been identified in iron sulfide magnetosomes—including mackinawite (tetragonal FeS) and a cubic FeS—which are thought to be precursors of Fe₃S₄. One type of magnetotactic bacterium present at the oxic-anoxic transition zone (OATZ) of the southern basin of the Pettaquamscutt River Estuary, Narragansett, Rhode Island, United States is known to produce both iron oxide and iron sulfide magnetosomes.

🔗 Military history 🔗 Military history/Military science, technology, and theory 🔗 Books 🔗 Classical Greece and Rome 🔗 Greece 🔗 Middle Ages 🔗 Middle Ages/History 🔗 Military history/Roman and Byzantine military history 🔗 Military history/Medieval warfare 🔗 Greece/Byzantine world 🔗 Military history/Balkan military history 🔗 Military history/European military history

The Strategikon or Strategicon (Greek: Στρατηγικόν) is a manual of war traditionally regarded as written in the late 6th century and usually attributed to the Byzantine Emperor Maurice. It is moreover a practical manual, "a rather modest elementary handbook" in the words of its introduction, "for those devoting themselves to generalship". This book gives a general guide, handbook, of the Byzantine military's strategies. In his introduction to his 1984 translation of the text, George T. Dennis noted "The Strategikon is written in a very straightforward and generally uncomplicated Greek."

The Strategikon may have been written in an effort to codify the military reforms brought about by the soldier-emperor Maurice. There is debate in academic circles as to the true author of the Strategikon. Maurice may have only commissioned it; perhaps his brother Peter, or another general of his court, was the true author. The dating is also debated. If it was written in the 6th century, the Strategikon may have been produced to codify the experience of the Balkan and Persian campaigns, or the campaigns may have been carried out in compliance with the manual. However, starting in the late 19th century, some historians have argued for a later date in the eighth or ninth century, on philological or technological grounds. In any case, it is considered one of the most important military texts of the medieval years, along with the 10th century military treatises attributed to the Byzantine emperors Leo VI (Tactica) and Nicephorus Phocas (De velitatione and Praecepta Militaria); Leo's Tactica in particular drew heavily from the Strategikon.

The text consists of 12 chapters, or "books", on various aspects of the tactics employed by the Byzantine military of the 6th and 7th century A.D. It is primarily focused on cavalry tactics and formations, yet it also elaborates on matters of infantry, sieges, baggage trains, drilling and marching. The author was familiar with classical military treatises, especially Onasander and Aelian, which he used as conceptional models rather than sources of content. Each book has a general topic to be discussed, and each book goes into great detail even separating each book further into subsections and including maps. These maps are not large and extravagant but more symbols to show positions and a standard design of the formations the Byzantine military used at this time. Books seven and eight contain practical advice to the General in the form of instructions and maxims. The eleventh book has ethnographic interest, with its portrayal of various Byzantine enemies (Franks, Lombards, Avars, Turks, and Slavs). The Strategikon also belongs to Byzantine legal literature, since it contains a list of military infractions and their suitable penalties.

🔗 Professional sound production 🔗 Stagecraft

The Schaffer–Vega diversity system (SVDS) was a wireless guitar system developed in 1975–76, engineered and prototyped by Ken Schaffer in New York City, and manufactured by the Vega Corporation, El Monte, California. A handheld microphone version was introduced in 1977.

The system was the first cordless system to be adopted by major rock acts because it solved technical problems common to earlier wireless systems. The reliable sound and freedom of movement it provided paved the way for bands to tour with large multi-level stages in arenas. Schaffer-Vegas were used in the late 1970s and early 1980s by many rock bands such as Pink Floyd (namely guitarist David Gilmour), the Rolling Stones, AC/DC and Kiss.

🔗 Aviation 🔗 Military history 🔗 Military history/Military aviation 🔗 Military history/North American military history 🔗 Military history/United States military history 🔗 Aviation/aircraft 🔗 Smithsonian Institution-related 🔗 Smithsonian Institution

The Goodyear Inflatoplane was an inflatable experimental aircraft made by the Goodyear Aircraft Company, a subsidiary of Goodyear Tire and Rubber Company, well known for the Goodyear blimp. Although it seemed an improbable project, the finished aircraft proved to be capable of meeting its design objectives, although orders were never forthcoming from the military. A total of 12 prototypes were built between 1956 and 1959, and testing continued until 1972, when the project was finally cancelled.

🔗 Mathematics

The interesting number paradox is a semi-humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting. The "proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a contradiction.

In a discussion between the mathematicians G. H. Hardy and Srinivasa Ramanujan about interesting and uninteresting numbers, Hardy remarked that the number 1729 of the taxicab he had ridden seemed "rather a dull one", and Ramanujan immediately answered that it is interesting, being the smallest number that is the sum of two cubes in two different ways.

🔗 United States 🔗 Spaceflight 🔗 Telecommunications

The Iridium satellite constellation provides L-band voice and data information coverage to satellite phones, pagers and integrated transceivers over the entire Earth surface. Iridium Communications owns and operates the constellation, additionally selling equipment and access to its services. It was originally conceived by Bary Bertiger, Raymond J. Leopold and Ken Peterson in late 1987 (in 1988 protected by patents Motorola filed in their names) and then developed by Motorola on a fixed-price contract from July 29, 1993, to November 1, 1998, when the system became operational and commercially available.

The constellation consists of 66 active satellites in orbit, required for global coverage, and additional spare satellites to serve in case of failure. Satellites are in low Earth orbit at a height of approximately 781 km (485 mi) and inclination of 86.4°. Orbital velocity of the satellites is approximately 27,000 km/h (17,000 mph). Satellites communicate with neighboring satellites via K_a band inter-satellite links. Each satellite can have four inter-satellite links: one each to neighbors fore and aft in the same orbital plane, and one each to satellites in neighboring planes to either side. The satellites orbit from pole to same pole with an orbital period of roughly 100 minutes. This design means that there is excellent satellite visibility and service coverage especially at the North and South poles. The over-the-pole orbital design produces "seams" where satellites in counter-rotating planes next to one another are traveling in opposite directions. Cross-seam inter-satellite link hand-offs would have to happen very rapidly and cope with large Doppler shifts; therefore, Iridium supports inter-satellite links only between satellites orbiting in the same direction. The constellation of 66 active satellites has six orbital planes spaced 30° apart, with 11 satellites in each plane (not counting spares). The original concept was to have 77 satellites, which is where the name Iridium came from, being the element with the atomic number 77 and the satellites evoking the Bohr model image of electrons orbiting around the Earth as its nucleus. This reduced set of six planes is sufficient to cover the entire Earth surface at every moment.

Because of the shape of the original Iridium satellites' reflective antennas, the first generation satellites focus sunlight on a small area of the Earth surface in an incidental manner. This results in an effect called Iridium flares, where the satellite momentarily appears as one of the brightest objects in the night sky and can be seen even during daylight. Newer Iridium satellites do not produce flares.