Recreational mathematics is mathematics carried out for recreation rather than as a research and application-based professional activity. Although it is not limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games appealing to children and untrained adults, inspiring their further study of the subject; the Mathematical Association of America includes Recreational Mathematics as one of its seventeen Special Interest Groups, commenting: Recreational mathematics is not defined because it is more than mathematics done as a diversion or playing games that involve mathematics. Recreational mathematics is inspired by deep ideas that are hidden in puzzles and other forms of play; the aim of the SIGMAA on Recreational Mathematics is to bring together enthusiasts and researchers in the myriad of topics that fall under recreational math. We will share results and ideas from our work, show that real, deep mathematics is there awaiting those who look, welcome those who wish to become involved in this branch of mathematics.
Mathematical competitions are categorized under recreational mathematics. Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, logic puzzles and mathematical chess problems, but this area of mathematics includes the aesthetics and culture of mathematics, peculiar or amusing stories and coincidences about mathematics, the personal lives of mathematicians. Mathematical games are multiplayer games whose rules and outcomes can be studied and explained using mathematics; the players of the game may not need to use explicit mathematics in order to play mathematical games. For example, Mancala is studied in the mathematical field of combinatorial game theory, but no mathematics is necessary in order to play it. Mathematical puzzles require mathematics, they have specific rules, as do multiplayer games, but mathematical puzzles don't involve competition between two or more players. Instead, in order to solve such a puzzle, the solver must find a solution that satisfies the given conditions.
Logic puzzles and classical ciphers are common examples of mathematical puzzles. Cellular automata and fractals are considered mathematical puzzles though the solver only interacts with them by providing a set of initial conditions; as they include or require game-like features or thinking, mathematical puzzles are sometimes called mathematical games. Other curiosities and pastimes of non-trivial mathematical interest include: patterns in juggling the sometimes profound algorithmic and geometrical characteristics of origami patterns and process in creating string figures such as Cat's cradles, etc. fractal-generating software There are many online blogs devoted to recreational mathematics. Among them Cut-the-knot by Alexander Bogomolny Futility Closet by Greg Ross Numberphile by Brady Haran The journal Eureka published by the mathematical society of the University of Cambridge is one of the oldest publications in recreational mathematics, it has been published 60 times since 1939 and authors have included many famous mathematicians and scientists such as Martin Gardner, John Conway, Roger Penrose, Ian Stewart, Timothy Gowers, Stephen Hawking and Paul Dirac.
The Journal of Recreational Mathematics was the largest publication on this topic from its founding in 1968 until 2014 when it ceased publication. Mathematical Games was the title of a long-running Scientific American column on recreational mathematics by Martin Gardner, he inspired several generations of mathematicians and scientists through his interest in mathematical recreations. "Mathematical Games" was succeeded by 25 "Metamagical Themas" columns, a distinguished, but shorter-running, column by Douglas Hofstadter by 78 "Mathematical Recreations" and "Computer Recreations" columns by A. K. Dewdney by 96 "Mathematical Recreations" columns by Ian Stewart, most "Puzzling Adventures" by Dennis Shasha; the Recreational Mathematics Magazine, published by the Ludus Association, is electronic and semiannual, focuses on results that provide amusing, witty but nonetheless original and scientifically profound mathematical nuggets. The issues are published in the exact moments of the equinox. Prominent practitioners and advocates of recreational mathematics have included: List of recreational number theory topics W. W. Rouse Ball and H.
S. M. Coxeter. Mathematical Recreations and Essays, Thirteenth Edition, Dover. ISBN 0-486-25357-0. Henry E. Dudeney. 536 Puzzles and Curious Problems. Charles Scribner's sons. ISBN 0-684-71755-7. Sam Loyd. in Martin Gardner: The Mathematical Puzzles of Sam Loyd. Dover. OCLC 5720955. Raymond M. Smullyan; the Lady or the Tiger? And Other Logic Puzzles. Oxford University Press. ISBN 0-19-286136-0. Recreational Mathematics from MathWorld at Wolfram Research The Unreasonable Utility of Recreational Mathematics by David Singmaster
Sudóva Výšnja is a town of Mostyska Raion in Lviv Oblast of Ukraine. Population: 6,461 ; the town has a number of Catholic cathedrals, a secondary school, is a market centre for surrounding agricultural area. In the past the town contained a horse farm, providing horse stud service for the area, some of the horse studs being expensive. On outskirts there is a hippodrome. Sudova Vyshnia is located about 50 km west of Lviv, on the highway M11 and railroad to Przemyśl in Poland. In the city terminates a route P40 that stretches all the way to Rava-Ruska; the Vishnya river flows through the town in a westerly direction joining San in Poland. The railway line leads to Kraków and Silesia in Poland, being a main route carrying coal to the former USSR. Sudova Vyshnia was first mentioned in Galician–Volhynian Chronicle for 1230 as Vyshnia. In 1340, together with whole Red Ruthenia, it was annexed by the Kingdom of Poland; until the 1772 Partitions of Poland, Sądowa Wisznia, as it was called, was part of Przemyśl Land, Ruthenian Voivodeship.
Sudova Vyshnia received its Magdeburg rights town charter in 1368. It was called Vyshnia, after the river Wisznia, a tributary of the San; the adjective Sudova was added in 1545, when it became the seat of the general sejmiks of the Ruthenian szlachta of Lesser Poland Province of the Polish Crown. In 1772, the town was annexed by the Habsburg Empire, as part of Habsburg Austrian Galicia, where it remained until late 1918. In the Second Polish Republic, Sądowa Wisznia belonged to Lwów Voivodeship. During the September 1939 Invasion of Poland, the Battle of Jaworów took place in the area of the town; when captured by the USSR in the Second World War, the town had a large main square and with a podium – suitable for public meetings. Under Communism, the square was planted over by bushes -- no more public meetings. In 1940–41 and 1944–59 Sudova Vyshnia was a district seat of the Sudova Vyshnia Raion, merged with Mostyska Raion; when under Nazi Germany administration during the Second World War, being in the area called Galicia since ancient times, it was not considered occupied but a part of the German Reich.
The currency at that time was the Reichsmark, whereas in occupied territories German administration was using Ostmark. German armed forces included a number of SS divisions, considered to be elite units, and there was a division SS Galicia. Before the war the town had had a Jewish population. After World War II, the Soviet regime used a Catholic temple that existed since the 14th century as a warehouse until 1989. Today, Sudova Vyshnia is one of the centers of the Poles in Ukraine, with a local office of the Association of Polish Culture of the Lviv Land. Ivan Vyshenskyi, an Eastern Orthodox monk Stefan Czmil, an Eastern Catholic bishop Bohdan Shust, a professional football player Jan Mars, an owner of Sudova Vyshnia Marcin Krowicki, a priest who converted from Catholicism to Unitiarianism Brief info at the Verkhovna Rada website Sudova Vyshnia at the Castles and temples of Ukraine
HMS Tigris was a T-class submarine of the Royal Navy. She was laid down at Chatham Dockyard and launched in October 1939. Tigris had a active career, serving in the North Sea and the Mediterranean. Tigris was active in the Bay of Biscay under the command of Commander Howard Bone, she sank the French fishing vessels Sancte Michael, Charles Edmond and Rene Camaleyre, the French merchantmen Jacobsen and Guilvinec, the German tanker Thorn. She unsuccessfully attacked a number of submarines, including the German submarine U-58 On 5 October 1940, Tigris made an unsuccessful attack on two Italian submarines off Bordeaux, Reginaldo Giuliani and Maggiore Barracca. On 5 July 1941 Tigris torpedoed and sank the Italian submarine Michele Bianchi 150 nm off the Gironde estuary as the Italian submarine was on passage to the Atlantic, she was assigned to operate in the North Sea near the Scandinavian coast in mid-1941. Off the coast of Finnmark, she sank the Norwegian passenger/cargo ships Haakon Jarl and Richard With, In the case of Richard With, the ship sank in less than a minute, killing two of the three German soldiers on board and claiming the lives of 101 Norwegian civilians.
Post-war, the Norwegian public was told. She attacked and badly damaged the German auxiliary submarine chaser Uj-1201 off the Rolvsøy Fjord; the bow of the ship sank but the stern was towed to port and the ship was rebuilt, entering service again in April 1944. In addition, Tigris unsuccessfully attacked the German merchant ship Bessheim and a merchantman of 3,000 tons. Tigris was reassigned to the Mediterranean, was active there from late 1942. On 6 December, she torpedoed and sank the Italian submarine Porfido, for which her commander, George Colvin, was awarded the Distinguished Service Order. On 21 January 1943, she sank the Italian merchant ship Citta di Genova in the Strait of Otranto; this ship was carrying Greek officers. Tigris left Malta on 18 February 1943 to patrol off Naples. On 22 February the Italian merchant ship Teramo was attacked by a British submarine, believed to have been Tigris, she was last sighted at 0730 on 24 February, 39 miles from Capri. On the morning of 27 February, the German submarine chaser Uj-2210, commanded by Otto Pollmann, was escorting a convoy six miles southeast of Capri.
She made contact with a submarine and carried out three depth charge attacks, the third attack brought oil to the surface and the contact was noted to be stationary. A fourth attack of fifteen depth charges brought a huge bubble of air up. On 6 March, Tigris there was no reply to this signal, she was declared overdue on that date. It is believed that Tigris was the submarine sunk on 27 February by Uj-2210; the submarine had been adopted by the town of Newbury during the Second World War as part of Warship Week. The plaque from this adoption is held by the National Museum of the Royal Navy in Portsmouth; each year there is an annual Remembrance Service for the submarine and the crew lost at St Nicolas Church, Berkshire, on the Sunday nearest 27 February. In 2016, the Remembrance Service was held on 24 July at 11.45 a.m. to allow descendants of her last commander, George Colvin, to attend. In 2017, it will be on 26 February. In 2018, the 75th and final commemoration is scheduled for 8 July From 2019 onwards a small memorial service will be held at the Royal British Legion Newbury branch on the Sunday nearest 27 February.
Colledge, J. J.. Ships of the Royal Navy: The Complete Record of all Fighting Ships of the Royal Navy. London: Chatham Publishing. ISBN 978-1-86176-281-8. Hutchinson, Robert. Jane's Submarines: War Beneath the Waves from 1776 to the Present Day. London: HarperCollins. ISBN 978-0-00-710558-8. OCLC 53783010. Kemp, Paul J.. The T-Class Submarine: The Claasic British Design. Annapolis, Maryland, USA: Naval Institute Press. ISBN 9781557508263. Rohwer, Jürgen. Chronology of the War at Sea 1939–1945. London: Greenhill Books. ISBN 1-85367-117-7
The European Train Control System is the signalling and control component of the European Rail Traffic Management System. It is a replacement for legacy train protection systems and designed to replace the many incompatible safety systems used by European railways; the standard was adopted outside Europe and is an option for worldwide application. In technical terms it is a kind of positive train control. ETCS is implemented with standard trackside equipment and unified controlling equipment within the train cab. In its advanced form, all lineside information is passed to the driver wireless inside the cab, removing the need for lineside signals watched by the driver; this will give the foundation for a to be defined automatic train operation. Trackside equipment aims to exchange information with the vehicle for safely supervising train circulation; the information exchanged between track and trains can be either continuous or intermittent according to the ERTMS/ETCS level of application and to the nature of the information itself.
The need for a system like ETCS stems from more and longer running trains resulting from economic integration of the European Union and the liberalisation of national railway markets. At the beginning of the 1990s there were some national high speed train projects supported by the EU which lacked interoperability of trains; this catalysed the Directive 1996/48 about the interoperability of high-speed trains, followed by Directive 2001/16 extending the concept of interoperability to the conventional rail system. ETCS specifications have become part of, or are referred to, the Technical Specifications for Interoperability for control-command systems, pieces of European legislation managed by the European Union Agency for Railways, it is a legal requirement that all new, upgraded or renewed tracks and rolling stock in the European railway system should adopt ETCS keeping legacy systems for backward compatibility. Many networks outside the EU have adopted ETCS for high-speed rail projects; the main goal of achieving interoperability had mixed success in the beginning.
Deployment has been slow, as there is no business case for replacing existing train protection systems in Germany and France which had advanced train protection systems installed in most mainlines. Though these legacy systems were developed in the 1960s, they provided similar performance to ETCS Level 2, thus the reluctance of infrastructure managers to replace these systems with ETCS. There are significant problems regarding compatibility of the latest software releases or baselines with older on-board equipment, forcing in many cases the train operating companies to install new on-board equipment. Switzerland, an early adopter of ETCS Limited Supervision, has introduced a moratorium on its planned roll-out of ETCS Level 2 due to cost and capacity concerns, added to fears about GSM-R obsolence starting in 2030; the European railway network grew from separate national networks with little more in common than standard gauge. Notable differences include voltages, loading gauge, couplings and control systems.
By the end of the 1980s there were 14 national standard train control systems in use across the EU, the advent of high-speed trains showed that signalling based on lineside signals is insufficient. Both factors led to efforts to reduce the cost of cross-border traffic. On 4 and 5 December 1989, a working group including Transport Ministers resolved a master plan for a trans-European high-speed rail network, the first time that ETCS was suggested; the Commission communicated the decision to the European Council, which approved the plan in its resolution of 17 December 1990. This led to a resolution on 91/440/EEC as of 29 July 1991, which mandated the creation of a requirements list for interoperability in high-speed rail transport; the rail manufacturing industry and rail network operators had agreed on creation of interoperability standards in June 1991. Until 1993 the organizational framework was created to start technical specifications that would be published as Technical Specifications for Interoperability.
The mandate for TSI was resolved by 93/38/EEC. In 1995 a development plan first mentioned the creation of the European Rail Traffic Management System; because ETCS is in many parts implemented in software, some wording from software technology is used. Versions are called system requirements specifications; this is a bundle of documents. A main version is called baseline; the specification was written in 1996 in response to EU Council Directive 96/48/EC99 of 23 July 1996 on interoperability of the trans-European high-speed rail system. First the European Railway Research Institute was instructed to formulate the specification and about the same time the ERTMS User Group was formed from six railway operators that took over the lead role in the specification; the standardisation went on for the next two years and it was felt to be slow for some industry partners – 1998 saw the formation of Union of Signalling Industry, including Alstom, Bombardier, Invensys and Thales that were to take over the finalisation of the standard.
In July 1998 SRS 5a documents were published that formed the first baseline for technical specifications. UNISIG provided for corrections and enhancements of the baseline specification leading to the Class P specification in April 1999; this baseline specification has been tested by six railways since 1999 as part of the ERTMS. The railway companies defined some extended requirements that were included to ETCS, leading to the Class 1 SRS 2.0.0 specification of ETCS (published in Apr
The Pascoe River is a river located in Far North Queensland, Australia. The headwaters rise under Mount Yangee in the Table Range, part of the Great Dividing Range at the northern end of Cape York Peninsula; the river flows south west past the Sir William Thompson Range veers north through the uninhabited country. Flowing past Hamilton Hill the river heads east past Wattle Hill and runs parallel with the Goddard Hills forming the northern border of Iron Range National Park; the river discharges into Weymouth Bay and onto the Coral Sea. From source to mouth, the Pascoe River is joined by eight tributaries including the Little Pascoe River; the river has a catchment area of 2,124 square kilometres of which an area of 33 square kilometres is composed of riverine wetlands. The traditional owners of the area are the Kuuku Ya’u, Kaanju and Umpila people who maintain a strong spiritual connection to the land. List of rivers of Queensland
Michael F. Dowd is a former New York City Police Department officer, drug distributor, associate of the Diaz organization, arrested in 1992 for running a drug ring out of Suffolk County, Long Island, New York, he is the subject of the 2014 documentary film The Seven Five directed by Tiller Russell and produced by Eli Holzman. Dowd was born on January 10, 1961 in Brooklyn, New York City, the third of seven children in an Irish Catholic family, he grew up in Brentwood, Long Island, on a block populated by the families of police officers and firefighters. According to Dowd, he was a good student in high school. According to Dowd, he was advised to become a physician, lawyer, or an accountant after high school, but he took the police test and the firefighter test. Dowd graduated from the New York City Police Academy in 1982 and was assigned to the 75th Precinct, which at that time was one of the most violent in the country. In the course of his career, Dowd committed a "host of crimes," including conspiring with drug traffickers to distribute cocaine, warning drug dealers about upcoming raids, providing them with guns and badges, planning to abduct a woman in Queens, stealing food meant for the needy at a church.
Dowd located a man who robbed the Diaz drug cartel and instead of arresting him turned him over to Diaz. He pocketed several thousand dollars a week as a result of corrupt arrangements. Dowd was arrested in 1992. After investigations by the Suffolk County Police, the DEA, NYPD's internal affairs, Dowd was convicted of racketeering and conspiracy to distribute narcotics and sent to prison for his crimes, he cooperated with the Mollen Commission, which investigated allegations of corruption in the NYPD. In the 12 years and 5 months he was in prison, Dowd claimed he worked as a peer counselor, worked out and ran the addiction and suicide prevention programs. Dowd has been featured on podcasts, broadcast radio and television programs, was the subject of the documentary film The Seven Five. A narrative feature adaptation by Sony Pictures is being produced by John Lesher and Megan Ellison