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Originating in ancient India, Vastu Shastra (Sanskrit: वास्तु शास्त्र, vāstu śāstra – literally "science of architecture" [2]) is a traditional Hindu system of architecture [3] [4] based on ancient texts that describe principles of design, layout, measurements, ground preparation, space arrangement, and spatial geometry. [5]
With four colors, it can be colored in 24 + 4 × 12 = 72 ways: using all four colors, there are 4! = 24 valid colorings (every assignment of four colors to any 4-vertex graph is a proper coloring); and for every choice of three of the four colors, there are 12 valid 3-colorings. So, for the graph in the example, a table of the number of valid ...
Direction determination refers to the ways in which a cardinal direction or compass point can be determined in navigation and wayfinding.The most direct method is using a compass (magnetic compass or gyrocompass), but indirect methods exist, based on the Sun path (unaided or by using a watch or sundial), the stars, and satellite navigation.
In graph-theoretic terms, the theorem states that for loopless planar graph, its chromatic number is ().. The intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" – needs to be interpreted appropriately to be correct.
32-point compass rose. The points of the compass are a set of horizontal, radially arrayed compass directions (or azimuths) used in navigation and cartography.A compass rose is primarily composed of four cardinal directions—north, east, south, and west—each separated by 90 degrees, and secondarily divided by four ordinal (intercardinal) directions—northeast, southeast, southwest, and ...
The Aparajitaprccha (lit. "the questions of Aparajit") is a 12th-century Sanskrit text of Bhuvanadeva with major sections on architecture (Vastu Shastra) and arts (Kala). Predominantly a Hindu text, it largely reflects the north and western Indian traditions. The text also includes chapters on Jain architecture and arts.
The numbers of vertices in any two color classes differ by at most one. That is, the partition of vertices among the different colors is as uniform as possible. For instance, giving each vertex a distinct color would be equitable, but would typically use many more colors than are necessary in an optimal equitable coloring.
The Manasara is an ancient text, states Acharya, which was likely in its final form by about 700 CE, or by other estimates around the 5th-century CE. [13] Tarapada Bhattacharya, a historian specializing in Indian arts and crafts, in his book published in 1963, states that the Manasara is best viewed as a "recension of recensions" text that ...