answer:I. Introduction A. Definition of chess as a strategic board game B. Importance and popularity of chess throughout history II. Ancient origins of chess A. Chaturanga: ancient Indian game (circa 6th century) 1. Four divisions of the military: infantry, cavalry, elephants, chariots 2. Two-player game with an 8x8 grid B. Shatranj: Persian adaptation of Chaturanga (circa 7th century) 1. Simplification of pieces and rules 2. Introduction of "shah" (king) and "farzin" (counselor) III. Key milestone 1: Arrival in Europe (circa 9th-10th centuries) A. Transmission through Islamic conquests and trade routes B. Adaptation to European culture 1. Piece names changed to reflect feudal society 2. Development of distinct regional variations IV. Key milestone 2: Major rule changes in Europe (15th century) A. Increased power of queen and bishop B. Introduction of castling and pawn moves (en passant, double-step) C. Emergence of modern chess strategies and tactics V. Key milestone 3: Birth of competitive chess (19th century) A. First international chess tournament (London, 1851) B. Establishment of World Chess Championship (1886) C. Development of chess clubs, associations, and literature VI. Key milestone 4: Technological advancements and chess (20th-21st centuries) A. Creation of chess engines and computer programs 1. Deep Blue vs. Garry Kasparov (1997) 2. AI advancements and their impact on chess strategy B. Online chess platforms and global connectivity C. Use of technology in chess education and training VII. Modern-day variations of chess A. Chess960 (Fischer Random Chess) 1. Invented by Bobby Fischer to reduce reliance on memorization 2. Randomized starting positions for pieces B. Three-check chess 1. Objective is to check the opponent's king three times 2. Encourages aggressive play and tactics C. Bughouse and Crazyhouse 1. Team-based chess variant with captured pieces returning to play 2. Increased complexity and collaboration VIII. Conclusion A. Continued evolution and adaptation of chess over time B. Enduring popularity and cultural significance

answer:Here's a CoffeeScript script that converts temperature values between Celsius, Fahrenheit, and Kelvin scales: ```coffeescript class TemperatureConverter celsiusToFahrenheit: (celsius) -> (celsius * 9 / 5) + 32 fahrenheitToCelsius: (fahrenheit) -> (fahrenheit - 32) * 5 / 9 celsiusToKelvin: (celsius) -> celsius + 273.15 kelvinToCelsius: (kelvin) -> kelvin - 273.15 fahrenheitToKelvin: (fahrenheit) -> @celsiusToKelvin(@fahrenheitToCelsius(fahrenheit)) kelvinToFahrenheit: (kelvin) -> @celsiusToFahrenheit(@kelvinToCelsius(kelvin)) converter = new TemperatureConverter() console.log "25°C to Fahrenheit:", converter.celsiusToFahrenheit(25) console.log "77°F to Celsius:", converter.fahrenheitToCelsius(77) console.log "25°C to Kelvin:", converter.celsiusToKelvin(25) console.log "298.15K to Celsius:", converter.kelvinToCelsius(298.15) console.log "77°F to Kelvin:", converter.fahrenheitToKelvin(77) console.log "298.15K to Fahrenheit:", converter.kelvinToFahrenheit(298.15) ``` This script defines a `TemperatureConverter` class with methods for converting temperatures between Celsius, Fahrenheit, and Kelvin. It then creates an instance of the class and demonstrates how to use it to perform various conversions. You can run this script using a CoffeeScript compiler like `coffee`, or you can compile it to JavaScript and run it in any JavaScript environment.

answer:1. The Legend of Bloody Mary: Origin: The urban legend of Bloody Mary has its roots in various historical figures and folklore tales. One possible source is the story of Queen Mary I of England, who was nicknamed "Bloody Mary" due to her brutal persecution of Protestants during her reign in the 16th century. Another potential origin is the tale of a witch named Mary Worth, who was allegedly executed for practicing dark magic. Possible Sources: As mentioned earlier, one of the sources could be Queen Mary I of England. Her violent actions against Protestants led to many gruesome stories about her, which may have contributed to the development of the Bloody Mary myth. Another possibility is that the legend originated from older European folklore involving mirror divination, where people would gaze into mirrors to see their future or communicate with spirits. How it spread: The legend of Bloody Mary has been passed down through generations by word of mouth, often as a cautionary tale or a game played at sleepovers and parties. In this game, participants stand in front of a mirror, usually in a dimly lit room, and chant "Bloody Mary" multiple times. According to the legend, doing so will summon the spirit of Bloody Mary, who will appear in the mirror and either reveal the participant's future or attack them. This game has helped perpetuate the legend and ensure its continued popularity. 2. The Legend of the Vanishing Hitchhiker: Origin: The vanishing hitchhiker is an urban legend in which a driver picks up a hitchhiker, only for the passenger to mysteriously disappear before reaching their destination. This legend has been told in various forms across different cultures and dates back centuries. Possible Sources: One possible source of the vanishing hitchhiker legend is the ancient Greek myth of Baucis and Philemon, in which two hospitable peasants offer shelter to disguised gods Zeus and Hermes. As a reward, the gods save them from a devastating flood and turn their home into a temple. This story shares similarities with the vanishing hitchhiker legend, as both involve mysterious travelers who disappear after being helped by kind strangers. Another possible source is the widespread belief in ghosts and spirits across different cultures. The idea of encountering a ghostly figure on a lonely road has been a common theme in folklore and literature for centuries. How it spread: The vanishing hitchhiker legend has been passed down through generations via word of mouth, often as a cautionary tale or an eerie campfire story. As automobiles became more popular and accessible in the 20th century, stories about haunted roads and ghostly hitchhikers gained traction. These tales were further popularized by radio programs, books, and films that featured variations of the vanishing hitchhiker story. Today, this urban legend continues to be shared and adapted, reflecting society's fascination with the supernatural and unexplained phenomena.

answer:To prove that the function f(x) = x^3 - 6x^2 + 9x is increasing for all x in the interval [0, infinity), we need to show that its derivative is positive for all x in this interval. Let's find the derivative of f(x): f'(x) = d/dx (x^3 - 6x^2 + 9x) = 3x^2 - 12x + 9 Now let's analyze the sign of f'(x). We can factor out a common term: f'(x) = 3(x^2 - 4x + 3) Further factoring gives: f'(x) = 3(x - 1)(x - 3) Since both factors (x - 1) and (x - 3) are linear functions, their signs depend only on whether x is greater or less than 1 and 3, respectively. Let's consider three cases: 1. If x < 1, then both (x - 1) and (x - 3) are negative, so their product is positive. Thus, f'(x) > 0. 2. If 1 < x < 3, then (x - 1) is positive while (x - 3) is negative, so their product is negative. However, since we're considering the interval [0, infinity), this case doesn't affect our conclusion. 3. If x > 3, then both (x - 1) and (x - 3) are positive, so their product is positive. Thus, f'(x) > 0. So, for all x in the interval [0, infinity), f'(x) > 0, which means that the function f(x) = x^3 - 6x^2 + 9x is increasing.