Ango A. Matematika dlja elektro i radioinzhenerov Nauka, 1965ruT779sMC. М Baerwolff G. Hoehere Mathematik fuer Naturwissenschaftler und. Computing the optimal road trip across the U. S. Last week, Tracy Staedter from Discovery News proposed an interesting idea to me Why not use the same algorithm from my Wheres Waldo article to compute the optimal road trip across every state in the U. S. Visiting every U. S. state has long been on my bucket list, so I jumped on the opportunity and opened up my machine learning tool box for another quick weekend project. Note If youre not interested in the technical details of the project, skip down to the Road trip stopping at major U. Numerical Methods For Mathematics John H Mathews Pdf To Jpg' title='Numerical Methods For Mathematics John H Mathews Pdf To Jpg' />S. Planning the road trip. One of the hardest parts of planning a road trip is deciding where to stop along the way. Given how large and diverse the U. S. is, its especially difficult to make a road trip that will appeal to everyone. To stand a chance at making an interesting road trip, Tracy and I laid out a few rules from the beginning The trip must make at least one stop in all 4. Numerical Methods For Mathematics John H Mathews Pdf To Jpg' title='Numerical Methods For Mathematics John H Mathews Pdf To Jpg' />U. S. The trip would only make stops at National Natural Landmarks, National Historic Sites, National Parks, or National Monuments. The trip must be taken by car and never leave the U. S. With those objectives in mind, Tracy compiled a list of 5. U. S. landmarks one in each state excluding AlaskaHawaii and including D. C., and two in California. Tracy wrote about that process on Discovery News here. The result was an epic itinerary with a mix of inner city exploration, must see historical sites, and beautiful natural landscapes. All that was left was to figure out the path that would minimize our time spent driving and maximize our time spent enjoying the landmarks. Numerical Methods For Mathematics John H Mathews Pdf To Jpg' title='Numerical Methods For Mathematics John H Mathews Pdf To Jpg' />1 I celebrate myself, and sing myself, And what I assume you shall assume, For every atom belonging to me as good belongs to you. I loafe and invite my soul. The Maya civilization was a Mesoamerican civilization developed by the Maya peoples, and noted for its hieroglyphic scriptthe only known fully developed writing. Gravitational waves are ripples in the curvature of spacetime that are generated in certain gravitational interactions and propagate as waves outward from their. Numerical Methods For Mathematics John H Mathews Pdf To Jpg' title='Numerical Methods For Mathematics John H Mathews Pdf To Jpg' />Randy Olson shows you how to compute an epic road trip across the U. S. Image credit Dean Franklin. Computing the optimal road trip across the U. S. With the list of landmarks in hand, the next step was to find the true distance between all of the landmarks by car. Since we cant just drive a straight line between every landmark driving by car has this pesky limitation of having to stay on roads we needed to find the shortest route by road between every landmark. If youve ever used Google Maps to get the directions between two addresses, thats basically what we had to do here. Except this time, we needed to look up 2,4. Thankfully, the Google Maps API makes this information freely available, so all it took was a short Python script to calculate the distance and time driven for all 2,4. Now with the 2,4. We needed to order the list of landmarks such that the total distance traveled between them is as small as possible if we visited them in order. This means finding the route that backtracks as little as possible, which is especially difficult when visiting Florida and the Northeast. Archimate Visio Stencil. If you read my Wheres Waldo article, youre already aware of how difficult it can be to solve route optimization problems like this one. With 5. 0 landmarks to put in order, we would have to exhaustively evaluate 3 x 1. To provide some context If you started computing this problem on your home computer right now, youd find the optimal route in about 9. Sun has entered its red giant phase and devoured the Earth. This complication is why Google Maps route optimization service only optimizes routes of up 1. The traveling salesman problem is so notoriously difficult to solve that even xkcd poked fun at it Clearly, we need a smarter solution if we want to take this epic road trip in our lifetime. Thankfully, the traveling salesman problem has been well studied over the years and there are many ways for us to solve it in a reasonable amount of time. If were willing to accept that we dont need the absolute best route between all of the landmarks, then we can turn to smarter techniques such as genetic algorithms to find a solution thats good enough for our purposes. Instead of exhaustively looking at every possible solution, genetic algorithms start with a handful of random solutions and continually tinkers with these solutions always trying something slightly different from the current solutions and keeping the best ones until they cant find a better solution any more. Ive included a visualization of a genetic algorithm solving a similar routing problem below. Road trip stopping at major U. S. landmarks. After less than a minute, the genetic algorithm reached a near perfect solution that makes a complete trip around the U. S. in only 1. 3,6. Ive mapped that route below. Note Theres an extra stop in Cleveland to force the route between Vermont and Michigan to stay in the U. S. rather than go through Canada. If youre able to drive through Canada without issue, then take the direct route through Canada instead. Click here for the interactive version. Assuming no traffic, this road trip will take about 2. The best part is that this road trip is designed so that you can start anywhere on the route as long as you follow it from then on. Youll hit every major area in the U. S. on this trip, and as an added bonus, you wont spend too long driving through the endless corn fields of Nebraska. Heres the Google Maps of the route 123456Note that Google maps itself only allows 1. Maps links. Heres the full list of landmarks in order Grand Canyon, AZBryce Canyon National Park, UTCraters of the Moon National Monument, IDYellowstone National Park, WYPikes Peak, COCarlsbad Caverns National Park, NMThe Alamo, TXThe Platt Historic District, OKToltec Mounds, ARElvis Presleys Graceland, TNVicksburg National Military Park, MSFrench Quarter, New Orleans, LAUSS Alabama, ALCape Canaveral Air Force Station, FLOkefenokee Swamp Park, GAFort Sumter National Monument, SCLost World Caverns, WVWright Brothers National Memorial Visitor Center, NCMount Vernon, VAWhite House, Washington, DCColonial Annapolis Historic District, MDNew Castle Historic District, Delaware. Cape May Historic District, NJLiberty Bell, PAStatue of Liberty, NYThe Mark Twain House Museum, CTThe Breakers, RIUSS Constitution, MAAcadia National Park, MEMount Washington Hotel, NHShelburne Farms, VTFox Theater, Detroit, MISpring Grove Cemetery, OHMammoth Cave National Park, KYWest Baden Springs Hotel, INAbraham Lincolns Home, ILGateway Arch, MOC. W. Parker Carousel Museum, KSTerrace Hill Governors Mansion, IATaliesin, WIFort Snelling, MNAshfall Fossil Bed, NEMount Rushmore, SDFort Union Trading Post, NDGlacier National Park, MTHanford Site, WAColumbia River Highway, ORSan Francisco Cable Cars, CASan Andreas Fault, CAHoover Dam, NVBonus Road trip stopping at popular U. S. cities. If youre more of a city slicker, the road trip above may not look very appealing to you because it involves spending a lot of time outdoors. But worry not, for I created a second road trip just for you The road trip below stops at the Trip. Advisor rated Best City to Visit in every contiguous U. S. state. Note Again, theres an extra stop in Cleveland to force the route between New Hampshire and Michigan to stay in the U. S. rather than go through Canada. If youre able to drive through Canada without issue, then take the direct route through Canada instead. But really, Cleveland is a nice city to stop in ranked 5. Trip. Advisor. Click here for the interactive version. This road trip will more or less follow the same path as the major U. S. landmarks trip, covering a slightly shorter 1. U. S. Some larger states like California and Texas may have multiple cities youd like to visit, so its probably worthwhile to stop at other larger cities along the route. You may note that cities from North Dakota, Vermont, and West Virginia are missing. Maya civilization Wikipedia. The Maya civilization was a Mesoamericancivilization developed by the Maya peoples, and noted for its hieroglyphic scriptthe only known fully developed writing system of the pre Columbian Americasas well as for its art, architecture, mathematics, calendar, and astronomical system. The Maya civilization developed in an area that encompasses southeastern Mexico, all of Guatemala and Belize, and the western portions of Honduras and El Salvador. This region consists of the northern lowlands encompassing the Yucatn Peninsula, and the highlands of the Sierra Madre, running from the Mexican state of Chiapas, across southern Guatemala and onwards into El Salvador, and the southern lowlands of the Pacific littoral plain. The Archaic period, prior to 2. BC, saw the first developments in agriculture and the earliest villages. The Preclassic period c. BC to 2. 50 AD saw the establishment of the first complex societies in the Maya region, and the cultivation of the staple crops of the Maya diet, including maize, beans, squashes, and chili peppers. The first Maya cities developed around 7. BC, and by 5. 00 BC these cities possessed monumental architecture, including large temples with elaborate stucco faades. Hieroglyphic writing was being used in the Maya region by the 3rd century BC. In the Late Preclassic a number of large cities developed in the Petn Basin, and Kaminaljuyu rose to prominence in the Guatemalan Highlands. Beginning around 2. AD, the Classic period is largely defined as when the Maya were raising sculpted monuments with Long Count dates. This period saw the Maya civilization develop a large number of city states linked by a complex trade network. In the Maya Lowlands two great rivals, Tikal and Calakmul, became powerful. The Classic period also saw the intrusive intervention of the central Mexican city of Teotihuacan in Maya dynastic politics. In the 9th century, there was a widespread political collapse in the central Maya region, resulting in internecine warfare, the abandonment of cities, and a northward shift of population. The Postclassic period saw the rise of Chichen Itza in the north, and the expansion of the aggressive Kiche kingdom in the Guatemalan Highlands. In the 1. 6th century, the Spanish Empire colonized the Mesoamerican region, and a lengthy series of campaigns saw the fall of Nojpetn, the last Maya city, in 1. Classic period rule was centred on the concept of the divine king, who acted as a mediator between mortals and the supernatural realm. Kingship was patrilineal, and power would normally pass to the eldest son. A prospective king was also expected to be a successful war leader. Maya politics was dominated by a closed system of patronage, although the exact political make up of a kingdom varied from city state to city state. By the Late Classic, the aristocracy had greatly increased, resulting in the corresponding reduction in the exclusive power of the divine king. The Maya civilization developed highly sophisticated artforms, and the Maya created art using both perishable and non perishable materials, including wood, jade, obsidian, ceramics, sculpted stone monuments, stucco, and finely painted murals. Maya cities tended to expand haphazardly, and the city centre would be occupied by ceremonial and administrative complexes, surrounded by an irregular sprawl of residential districts. Different parts of a city would often be linked by causeways. The principal architecture of the city consisted of palaces, pyramid temples, ceremonial ballcourts, and structures aligned for astronomical observation. The Maya elite were literate, and developed a complex system of hieroglyphic writing that was the most advanced in the pre Columbian Americas. The Maya recorded their history and ritual knowledge in screenfold books, of which only three uncontested examples remain, the rest having been destroyed by the Spanish. There are also a great many examples of Maya text found on stelae and ceramics. The Maya developed a highly complex series of interlocking ritual calendars, and employed mathematics that included one of the earliest instances of the explicit zero in the world. As a part of their religion, the Maya practised human sacrifice. Mesoamerica. The Maya civilization developed within the Mesoamerican cultural area, which covers a region that spreads from northern Mexico southwards into Central America. Mesoamerica was one of six cradles of civilization worldwide. The Mesoamerican area gave rise to a series of cultural developments that included complex societies, agriculture, cities, monumental architecture, writing, and calendrical systems. The set of traits shared by Mesoamerican cultures also included astronomical knowledge, blood and human sacrifice, and a cosmovision that viewed the world as divided into four divisions aligned with the cardinal directions, each with different attributes, and a three way division of the world into the celestial realm, the earth, and the underworld. By 6. BC, the early inhabitants of Mesoamerica were experimenting with the domestication of plants, a process that eventually led to the establishment of sedentaryagricultural societies. The diverse climate allowed for wide variation in available crops, but all regions of Mesoamerica cultivated the base crops of maize, beans, and squashes. All Mesoamerican cultures used Stone Age technology after c. Manual De Psicoterapia Cognitiva Ruiz Cano. AD copper, silver and gold were worked. Mesoamerica lacked draft animals, did not use the wheel, and possessed few domesticated animals the principal means of transport was on foot or by canoe. Mesoamericans viewed the world as hostile and governed by unpredictable deities. The ritual Mesoamerican ballgame was widely played. Mesoamerica is linguistically diverse, with most languages falling within a small number of language families the major families are Mayan, MixeZoquean, Otomanguean, and Uto Aztecan there are also a number of smaller families and isolates. The Mesoamerican language area shares a number of important features, including widespread loanwords, and use of a vigesimal number system. The territory of the Maya covered a third of Mesoamerica,1. Maya were engaged in a dynamic relationship with neighbouring cultures that included the Olmecs, Mixtecs, Teotihuacan, the Aztecs, and others. During the Early Classic period, the Maya cities of Tikal and Kaminaljuyu were key Maya foci in a network that extended beyond the Maya area into the highlands of central Mexico. At around the same time, there was a strong Maya presence at the Tetitla compound of Teotihuacan. Centuries later, during the 9th century AD, murals at Cacaxtla, another site in the central Mexican highlands, were painted in a Maya style. This may have been either an effort to align itself with the still powerful Maya area after the collapse of Teotihuacan and ensuing political fragmentation in the Mexican Highlands,1. Maya origin of the inhabitants. The Maya city of Chichen Itza and the distant Toltec capital of Tula had an especially close relationship. Geography. Maximum extent of the Maya civilization. The Maya civilization occupied a wide territory that included southeastern Mexico and northern Central America. This area included the entire Yucatn Peninsula and all of the territory now incorporated into the modern countries of Guatemala and Belize, as well as the western portions of Honduras and El Salvador.