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61-521: Diophantine means pertaining to the ancient Greek mathematician Diophantus . A number of concepts bear this name: [REDACTED] Look up diophantine in Wiktionary, the free dictionary. Diophantine approximation Diophantine equation Diophantine quintuple Diophantine set Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with

122-505: A chain holding the chandelier in place and causing the castle to collapse. Everyone makes it out in time before the building falls into the mine, caving in the exposed mine shaft in the basement. Layton explains that when the mine was discovered fifty years ago, it released a hallucinatory gas that affected everyone in Folsense; as the gas disperses, Anton is revealed to be an old man, and Folsense an abandoned, desolate town . Layton suspects

183-498: A circle around a specific part, or entering the answer through character recognition on the Nintendo DS 's touchscreen. If the player is correct, the picarats are added to their total score, and they are sometimes rewarded with an item. If the player is incorrect, they can retry the puzzle indefinitely, though the first two times they are wrong, the value of the puzzle will decrease by approximately ten percent each time. Optionally,

244-719: A comprehensive commentary written by the earlier Greek scholar Maximos Planudes (1260 – 1305), who produced an edition of Diophantus within the library of the Chora Monastery in Byzantine Constantinople . In addition, some portion of the Arithmetica probably survived in the Arab tradition (see above). In 1463 German mathematician Regiomontanus wrote: No one has yet translated from the Greek into Latin

305-630: A feature in which passwords are exchanged between Curious Village and Diabolical Box for bonuses in both games. In March 2009, at the Game Developers Conference , Akihiro Hino listed Professor Layton and the Diabolical Box as an English title for the game. At an interview following the conference, he confirmed that the name was the official English title and that the localization was currently being worked on, which he hoped to be finished in about six months. The game

366-490: A new vein of gold, strange incidents began to occur around town, and many of its citizens left. Fredrich left with his part of the family fortune and founding the Molentary Express, changing his name to hide his identity. They also learn that Dropstone's founder Sophia was also a former resident, evacuating with several of the citizens to form the nearby village. The remaining citizens point to the central castle over

427-607: A player can quit a puzzle at no cost and try another, though certain puzzles are mandatory to progress. Once a puzzle is completed, the player may retry it at any time via the game's menus. As a reward for completing a puzzle, the player may earn one of three categories of item. Hamster toys are collected to help Luke give a morbidly obese hamster a workout; pieces of a shattered camera that Sammy accidentally dropped can be assembled to repair it; and players can earn tea ingredients to brew new recipes and serve cups of tea to Luke, Layton and people they meet. By completing all 138 puzzles in

488-539: A quantity of the gas was in the Elysian Box, causing those that believed in the myth to actually succumb to death. Anton is suddenly reminded of his fiancée, Sophia, and that he has commissioned the box to hold a message to be sent to Sophia in Dropstone after her departure, but it had been stolen so many times he had lost hope Sophia received it. Luke opens the special compartment and reveals that Sophia had gotten

549-452: A score of two nines and two eights for a total of 34 out of 40. The A.V. Club gave it an A− and said that "even if the relatively short game doesn't have much replay value, there’s an incentive to keep picking it up for some brain exercise." Wired gave it a score of eight out of ten and said, "While Diabolical Box 's gameplay, animation and plot are quite a bit like its predecessor's, slight improvements make this installment of

610-424: A symbol for a general number n . Where we would write ⁠ 12 + 6 n / n − 3 ⁠ , Diophantus has to resort to constructions like: "... a sixfold number increased by twelve, which is divided by the difference by which the square of the number exceeds three". Algebra still had a long way to go before very general problems could be written down and solved succinctly. "But what we really want to know

671-488: A temporary coma from his exposure to the gas from the box, and has now fully recovered. After the credits, the game ends showing "to be continued" along with a picture of Layton and Luke standing in front of a time machine, alluding to the premise of Professor Layton and the Unwound Future . The Professor Layton series was announced to be a trilogy immediately following the announcement of Professor Layton and

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732-408: A third game, Professor Layton and the Unwound Future . The game follows Professor Layton and his self-proclaimed apprentice Luke as they travel cross-country by train to solve the mystery behind a mysterious box that is said to kill anyone who opens it. An enhanced mobile port of Diabolical Box , subtitled "HD for Mobile", was released on December 5, 2018. Professor Layton and the Diabolical Box

793-537: A value of 84 years. However, the accuracy of the information cannot be confirmed. In popular culture, this puzzle was the Puzzle No.142 in Professor Layton and Pandora's Box as one of the hardest solving puzzles in the game, which needed to be unlocked by solving other puzzles first. Arithmetica is the major work of Diophantus and the most prominent work on premodern algebra in Greek mathematics. It

854-572: Is a collection of problems giving numerical solutions of both determinate and indeterminate equations . Of the original thirteen books of which Arithmetica consisted only six have survived, though there are some who believe that four Arabic books discovered in 1968 are also by Diophantus. Some Diophantine problems from Arithmetica have been found in Arabic sources. It should be mentioned here that Diophantus never used general methods in his solutions. Hermann Hankel , renowned German mathematician made

915-479: Is also known to have written on polygonal numbers , a topic of great interest to Pythagoras and Pythagoreans . Fragments of a book dealing with polygonal numbers are extant. A book called Preliminaries to the Geometric Elements has been traditionally attributed to Hero of Alexandria . It has been studied recently by Wilbur Knorr , who suggested that the attribution to Hero is incorrect, and that

976-655: Is an adventure/puzzle game. The player controls the movements of the eponymous Professor Layton and his young assistant Luke through several locations, unlike in the previous game which is confined to just one town. Along with completing many different types of puzzles, players must explore different areas, solve mysteries, and aid the Professor on his quest. The puzzle menus for this game are very similar to those in Curious Village. Puzzles include brain teasers , sliding puzzles , logic puzzles and others. The player

1037-453: Is based on algebra. How much he affected India is a matter of debate. Diophantus has been considered "the father of algebra" because of his contributions to number theory, mathematical notations and the earliest known use of syncopated notation in his book series Arithmetica . However this is usually debated, because Al-Khwarizmi was also given the title as "the father of algebra", nevertheless both mathematicians were responsible for paving

1098-459: Is believed that Fermat did not actually have the proof he claimed to have. Although the original copy in which Fermat wrote this is lost today, Fermat's son edited the next edition of Diophantus, published in 1670. Even though the text is otherwise inferior to the 1621 edition, Fermat's annotations—including the "Last Theorem"—were printed in this version. Fermat was not the first mathematician so moved to write in his own marginal notes to Diophantus;

1159-412: Is entirely lost. Although The Porisms is lost, we know three lemmas contained there, since Diophantus refers to them in the Arithmetica . One lemma states that the difference of the cubes of two rational numbers is equal to the sum of the cubes of two other rational numbers, i.e. given any a and b , with a > b , there exist c and d , all positive and rational, such that Diophantus

1220-411: Is presented with each puzzle and its value in "picarats", and is given unlimited time to solve it. Each puzzle has three hints available for it, but the player must spend one "hint coin" to see each hint. Hint coins are limited; the player starts with ten, and more can be found by searching the game's locales. Once the player feels they have the answer, they enter it, either by selecting an answer, drawing

1281-498: Is that he did not have any notion for zero and he avoided negative coefficients by considering the given numbers a , b , c to all be positive in each of the three cases above. Diophantus was always satisfied with a rational solution and did not require a whole number which means he accepted fractions as solutions to his problems. Diophantus considered negative or irrational square root solutions "useless", "meaningless", and even "absurd". To give one specific example, he calls

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1342-510: Is to what extent the Alexandrian mathematicians of the period from the first to the fifth centuries C.E. were Greek. Certainly, all of them wrote in Greek and were part of the Greek intellectual community of Alexandria. And most modern studies conclude that the Greek community coexisted [...] So should we assume that Ptolemy and Diophantus, Pappus and Hypatia were ethnically Greek, that their ancestors had come from Greece at some point in

1403-465: Is unreasonable to portray them with purely European features when no physical descriptions exist." "Diophantos was most likely a Hellenized Babylonian." Professor Layton and Pandora%27s Box Professor Layton and the Diabolical Box , known in Australia and Europe as Professor Layton and Pandora's Box , is the second game in the Professor Layton series by Level-5 . It was followed by

1464-620: The Academy of Interactive Arts & Sciences nominated Professor Layton and the Diabolical Box for " Portable Game of the Year " and " Outstanding Achievement in Original Story ". As of July 9, 2008, the game sold 815,369 copies in Japan, according to Famitsu . IGN gave the game Editor's Choice Award, and rated it the eleventh best Nintendo DS game as of 2010. GameTrailers gave

1525-546: The Professor Layton saga even more enjoyable than the last." However, The Daily Telegraph gave it a score of seven out of ten and said that it "still has more charm and character than most and—despite the hiccups—provides a challenging, fun and satisfying puzzle experience for players young, old—and everything in between." 1Up.com gave the game an A+ and said that, while the developers could have given gamers Curious Village again, " Diabolical Box shows that

1586-510: The Byzantine scholar John Chortasmenos (1370–1437) had written "Thy soul, Diophantus, be with Satan because of the difficulty of your other theorems and particularly of the present theorem" next to the same problem. Diophantus wrote several other books besides Arithmetica , but only a few of them have survived. Diophantus himself refers to a work which consists of a collection of lemmas called The Porisms (or Porismata ), but this book

1647-528: The Curious Village within Japan. By this time, Level-5 had already decided upon the Japanese names of Curious Village and Professor Layton and the Unwound Future , but were originally planning to entitle the second game " Layton-kyōju to Yū-rei Jima no Himitsu ". ( ゆうれい島のひみつ , – Yū-rei Jima no Himitsu , lit. " Professor Layton and the Secret of Ghost Island ") These plans were eventually cancelled due to

1708-415: The Diabolical Box was released in Japan during November 2007, nine months after the release of Curious Village . Following this, Nintendo began to localize the series internationally; Curious Village was released in 2008, though Nintendo had not officially announced the localization of Diabolical Box . The manual of Curious Village , however, implied an eventual release of the second game while mentioning

1769-512: The additional content, since the Nintendo Wi-Fi Connection service was terminated on that date. There are also two bonuses in "The Hidden Door" that are only available after the player finds one unique code each in the game's predecessor and sequel . Other bonuses include a soundtrack, cut-scenes, soundbites, character profiles, and scenes from the game. Dr. Schrader, Professor Layton's mentor, reportedly has come across

1830-460: The box and left her own note to Anton, stating her love for him and Katia's relationship to her. Anton welcomes Katia with open arms, wanting to love her as much as he had Sophia, stating that he has to get to know Katia before he can join Sophia in death. The group returns to Dropstone, where Flora is located. As Layton and his friends return to London, they learn that Dr. Schrader had only fallen into

1891-448: The box is completely empty, so Layton eventually suggests visiting Anton to solve the mystery. At the castle, the surprisingly young Anton initially welcomes them as his guests, but when they start to ask about the Elysian Box, he becomes suspicious and at one point ties the pair up, though they are able to escape. During the escape, the pair find a large hole in the basement of the castle, along with some strange machinery. Layton discovers

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1952-514: The crime, and Flora, who sneaks aboard the train but is eventually discovered by the pair. The train makes a stop in Dropstone, a town celebrating the fiftieth anniversary of its founding. As they enjoy the celebration, Layton and Luke learn that the town's founder, Sophia, also had an interest in the Elysian Box, but she died the year before, and her granddaughter Katia continues to seek it out. Don Paolo, Layton's arch-rival, kidnaps Flora and disguises himself as her, leaving her behind in Dropstone as

2013-399: The development of algebra by Arabs, and his equations influenced modern work in both abstract algebra and computer science . The first five books of his work are purely algebraic. Furthermore, recent studies of Diophantus's work have revealed that the method of solution taught in his Arithmetica matches later medieval Arabic algebra in its concepts and overall procedure. Diophantus was

2074-522: The earliest, the Arithmetica has the best-known use of algebraic notation to solve arithmetical problems coming from Greek antiquity, and some of its problems served as inspiration for later mathematicians working in analysis and number theory . In modern use, Diophantine equations are algebraic equations with integer coefficients for which integer solutions are sought. Diophantine geometry and Diophantine approximations are two other subareas of number theory that are named after him. Diophantus

2135-650: The equation 4 = 4 x + 20 'absurd' because it would lead to a negative value for x . One solution was all he looked for in a quadratic equation. There is no evidence that suggests Diophantus even realized that there could be two solutions to a quadratic equation. He also considered simultaneous quadratic equations. Diophantus made important advances in mathematical notation, becoming the first person known to use algebraic notation and symbolism. Before him everyone wrote out equations completely. Diophantus introduced an algebraic symbolism that used an abridged notation for frequently occurring operations, and an abbreviation for

2196-471: The first Greek mathematician who recognized positive rational numbers as numbers, by allowing fractions for coefficients and solutions. He coined the term παρισότης ( parisotēs ) to refer to an approximate equality. This term was rendered as adaequalitas in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Although not

2257-416: The first Latin edition that was widely available. Pierre de Fermat owned a copy, studied it and made notes in the margins. A later 1895 Latin translation by Paul Tannery was said to be an improvement by Thomas L. Heath , who used it in the 1910 second edition of his English translation. The 1621 edition of Arithmetica by Bachet gained fame after Pierre de Fermat wrote his famous " Last Theorem " in

2318-451: The following remark regarding Diophantus: Our author (Diophantos) not the slightest trace of a general, comprehensive method is discernible; each problem calls for some special method which refuses to work even for the most closely related problems. For this reason it is difficult for the modern scholar to solve the 101st problem even after having studied 100 of Diophantos's solutions. Like many other Greek mathematical treatises, Diophantus

2379-580: The founding of Alexandria, small numbers of Egyptians were admitted to the privileged classes in the city to fulfill numerous civic roles. Of course, it was essential in such cases for the Egyptians to become "Hellenized," to adopt Greek habits and the Greek language. Given that the Alexandrian mathematicians mentioned here were active several hundred years after the founding of the city, it would seem at least equally possible that they were ethnically Egyptian as that they remained ethnically Greek. In any case, it

2440-430: The game was composed by Tomohito Nishiura with the entire soundtrack later released on an album titled Layton Kyouju to Akuma no Hako Original Soundtrack, in Japan only. The puzzle theme is similar to the original but with additional percussion. The ending theme song "Iris" was sung by Salyu , though it was omitted from the album. The international release of the game utilizes an instrumental version, though it similarly

2501-403: The game's developers aren't content to just sit on their laurels – they take a wonderful game, and make it even better." VideoGamer.com gave the game a 8/10, stating: "If you liked Mysterious Village and need more, or if you just want something genuinely fresh and original for your DS, Pandora's Box is the answer you're looking for." During the 13th Annual Interactive Achievement Awards ,

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2562-432: The game's narrative. The puzzles within the series from Diabolical Box onward tended to use English more than Japanese. This was coincidental, but allowed the game to be translated without replacing as many puzzles. Level-5 also tried to update existing systems within the game, such as the Professor's suitcase and minigames; ultimately, Diabolical Box used up nearly twice as much data than its predecessor. The music of

2623-542: The main game and each of these additional puzzles, the player could access 15 bonus puzzles for 153 puzzles total (excluding the downloadable puzzles). The game was compatible with Nintendo Wi-Fi Connection , allowing players to connect to the internet and download new weekly puzzles. The first unlockable puzzle was made available on the day of the game's Japanese release, and one new key had been released every week thereafter for 33 weeks, with new keys being released on Sunday. Since May 20, 2014, it has been impossible to download

2684-455: The margins of his copy: If an integer n is greater than 2, then a + b = c has no solutions in non-zero integers a , b , and c . I have a truly marvelous proof of this proposition which this margin is too narrow to contain. Fermat's proof was never found, and the problem of finding a proof for the theorem went unsolved for centuries. A proof was finally found in 1994 by Andrew Wiles after working on it for seven years. It

2745-665: The mine, which is connected to the castle basement, but finds the effects of the nausea worsen as they get closer to it. In spite of this, the two return to Anton and find Katia along the way. Upon mistaking her for Sophia, Anton challenges Layton to a fencing duel. Anton eventually tires from the duel: this leads Katia to break it up, revealing Anton to be her grandfather in the process. She also tells everyone that her grandmother left Folsense to protect her and Anton's unborn child (who would grow up to be Katia's mother) and that Sophia and this child had died some time ago. Unfortunately, Anton lashes out with his saber in rage and disbelief, cutting

2806-448: The mines, where they claim that Anton remains to this day as a vampire. On returning to the hotel, Layton and Luke find that the remainder of the train's contingent has arrived, and Chelmey has arrested a conductor named Sammy as a suspect in the theft of the box and Schrader's death. Layton proves him wrong, revealing Don Paolo after exposing his disguise. Don Paolo escapes but leaves behind the Elysian Box. Layton and Luke open it but find

2867-514: The mysterious Elysian Box, fabled to kill anyone who opens it. When Layton and Luke pay Dr. Schrader a visit, they find him unconscious on the floor and no sign of the box. A train ticket for the Molentary Express is the only clue of the box's theft, and the two prepare to follow on the next train out to head towards the town of Folsense, listed in Schrader's diary as the origin of the Elysian Box. They are followed by Inspector Chelmey, tracking down

2928-406: The necessary notation to express more general methods. This caused his work to be more concerned with particular problems rather than general situations. Some of the limitations of Diophantus' notation are that he only had notation for one unknown and, when problems involved more than a single unknown, Diophantus was reduced to expressing "first unknown", "second unknown", etc. in words. He also lacked

2989-436: The past but had remained effectively isolated from the Egyptians? It is, of course, impossible to answer this question definitively. But research in papyri dating from the early centuries of the common era demonstrates that a significant amount of intermarriage took place between the Greek and Egyptian communities [...] And it is known that Greek marriage contracts increasingly came to resemble Egyptian ones. In addition, even from

3050-482: The staff thinking that it was too strange for an English gentleman to try and survive on a desert island, and the story was changed to that of Diabolical Box . Level-5 learned several lessons from the critical response to Curious Village . Critics had often claimed that the puzzles in the games were too disjointed from the game's plot, so in Diabolical Box , they attempted to make the puzzles more relevant to

3111-503: The stone tells how old: 'God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his father's life chill fate took him. After consoling his fate by the science of numbers for four years, he ended his life.' This puzzle implies that Diophantus' age x can be expressed as which gives x

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3172-442: The thirteen books of Diophantus, in which the very flower of the whole of arithmetic lies hidden. Arithmetica was first translated from Greek into Latin by Bombelli in 1570, but the translation was never published. However, Bombelli borrowed many of the problems for his own book Algebra . The editio princeps of Arithmetica was published in 1575 by Xylander . The Latin translation of Arithmetica by Bachet in 1621 became

3233-479: The title Diophantine . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Diophantine&oldid=553884646 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Diophantus His Arithmetica influenced

3294-518: The train departs. En route to Folsense, Layton, Luke, and "Flora" are knocked out with sleeping gas by the train's conductor. They awake to find their train car separated from the rest of the engine at the Folsense station. As they enter the town, they are struck by a brief wave of nausea, and "Flora" feigns illness to stay at the hotel. Layton and Luke explore the town and learn it was founded on top of rich mine deposits by Duke Herzen and his sons, Anton and Fredrich. Some fifty years ago, upon discovery of

3355-509: The true author is Diophantus. Diophantus' work has had a large influence in history. Editions of Arithmetica exerted a profound influence on the development of algebra in Europe in the late sixteenth and through the 17th and 18th centuries. Diophantus and his works also influenced Arab mathematics and were of great fame among Arab mathematicians. Diophantus' work created a foundation for work on algebra and in fact much of advanced mathematics

3416-481: The unknown and for the powers of the unknown. Mathematical historian Kurt Vogel states: The symbolism that Diophantus introduced for the first time, and undoubtedly devised himself, provided a short and readily comprehensible means of expressing an equation... Since an abbreviation is also employed for the word 'equals', Diophantus took a fundamental step from verbal algebra towards symbolic algebra. Although Diophantus made important advances in symbolism, he still lacked

3477-642: The way for algebra today. Today, Diophantine analysis is the area of study where integer (whole-number) solutions are sought for equations, and Diophantine equations are polynomial equations with integer coefficients to which only integer solutions are sought. It is usually rather difficult to tell whether a given Diophantine equation is solvable. Most of the problems in Arithmetica lead to quadratic equations . Diophantus looked at 3 different types of quadratic equations: ax + bx = c , ax = bx + c , and ax + c = bx . The reason why there were three cases to Diophantus, while today we have only one case,

3538-531: Was born into a Greek family and is known to have lived in Alexandria , Egypt , during the Roman era , between AD 200 and 214 to 284 or 298. Much of our knowledge of the life of Diophantus is derived from a 5th-century Greek anthology of number games and puzzles created by Metrodorus . One of the problems (sometimes called his epitaph) states: Here lies Diophantus, the wonder behold. Through art algebraic,

3599-698: Was forgotten in Western Europe during the Dark Ages , since the study of ancient Greek, and literacy in general, had greatly declined. The portion of the Greek Arithmetica that survived, however, was, like all ancient Greek texts transmitted to the early modern world, copied by, and thus known to, medieval Byzantine scholars. Scholia on Diophantus by the Byzantine Greek scholar John Chortasmenos (1370–1437) are preserved together with

3660-504: Was not included on the album either due to not have being created at the time. The album scored slightly higher than its predecessor. Square Enix Music Online gave it a score of 7 out of 10, criticizing that "there are no masterpieces on this score, even though the variety and entertainment is much more enhanced [over Curious Village' s]." RPGFan Music stated "At 75 minutes, this one disc is packed with goodies, though one might also argue that it's packed with filler." Professor Layton and

3721-650: Was released in North America during August 2009, as Professor Layton and the Diabolical Box . It would be released in PAL regions during September of the same year, as Professor Layton and Pandora's Box , where it would become the fastest-selling Nintendo DS game ever released within the United Kingdom . Professor Layton and the Diabolical Box received "favorable" reviews according to video game review aggregator Metacritic . In Japan, Famitsu gave it

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