![]() It can now move in three directions: left and right (x-direction), up and down (y-direction) and back and forth (z-direction).”Īllowing the point more freedom, beyond our 3D world, moves it in four directions: left and right (x-direction), up and down (y-direction), back and forth (z-direction), ana and kata (w-direction). The point is happy because it can travel even more. Moving the square perpendicular to itself results in a cube. The point can now travel left and right as well as up and down. “Now we move the line perpendicular to itself in a plane and we get a square. It is now possible for the zero-dimensional point to travel within the line in a left and right manner. If we put another point at the right side beside the first one and connect them we get a line. It only exists in itself and has no possibilities to move anywhere. “To get an idea of the fourth dimension maybe it would be a good start to begin with a point. The extra dimension is added due to the geometrical laws found in the first three…” It is constructed with mathematical means by analyzing three-dimensional space and how the three dimensions relate to each other. Try to think of it as geometrical extravaganza. It’s a concept of an artificial space that bears no direct similarity to real space. “There is no fourth dimension in reality. The resulting film, titled The Hypercube: Projections and Slicing, was constructed with the real-time interactive computer graphics of the era, a technological milestone for 4-dimensional geometry.īeginning at the 1-minute mark, the film observes and annotates a rotating cube in three ways: orthogonal or straight projection, central or perspective projection, and finally with hyperplane slices coming from four different directions. “The tesseract can be unfolded into eight cubes into 3D space, just as the cube can be unfolded into six squares into 2D space.” Orthogonal column Latin hypercubes and their application in computer experiments.In 1978, mathematics professor Thomas Banchoff and computer scientist Charles Strauss teamed up to create an animated visualization of a 3-dimensional cube rotating in four-dimensional space, also known as a hypercube or tesseract. Construction of orthogonal and nearly orthogonal Latin hypercube designs from orthogonal designs. Monte Carlo and Quasi-Monte Carlo Methods. In: Niederreiter H, Zinterhof P, Hellekalek P, eds. Nearly orthogonal Latin hypercube designs for many design columns. Construction of orthogonal symmetric Latin hypercube designs. A general rotation method for orthogonal Latin hypercubes. Construction of column-orthogonal designs for computer experiments. Construction of orthogonal Latin hypercube designs with flexible run sizes. Construction of orthogonal Latin hypercube designs. A construction method for orthogonal Latin hypercube designs. A construction method for orthogonal Latin hypercube designs with prime power levels. Controlling correlations in Latin hypercube samples. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Handbook of Design and Analysis of Experiments. In: Dean A, Morris M, Stufken J, et al., eds. Latin hypercubes and space-filling designs. Construction of orthogonal and nearly orthogonal Latin hypercubes. A general construction for space-filling Latin hypercubes. A new and flexible method for constructing designs for computer experiments. Orthogonal-maximin Latin hypercube designs. An efficient algorithm for constructing optimal design of computer experiments. Orthogonal Arrays: Theory and Applications. Some classes of orthogonal Latin hypercube designs. Singapore-Beijing: Springer and Science Press, 2018 Theory and Application of Uniform Experimental Designs. Construction of nearly orthogonal Latin hypercube designs. J Statist Plann Inference, 2012, 142: 2809–2818Įfthimiou I, Georgiou S D, Liu M Q. Some new classes of orthogonal Latin hypercube designs.
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