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Unit cube

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The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics
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whose sides are 1 unit long. The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.
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Ball, Keith (2010), "High-dimensional geometry and its probabilistic analogues", in
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Sometimes the term "unit cube" refers in specific to the set of all
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and the (Euclidean) length of the vector (1,1,1,....1,1) in
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The length of the longest diagonal of a unit hypercube of
90: 144:, an infinite-dimensional analogue of the unit cube 271: 217:Gardner, Martin (2001), "Chapter 13: Hypercubes", 100: 247:, Holt Rinehart & Winston, 2001, p. 74, 292: 223:, W. W. Norton & Company, pp. 162–174, 187:, Princeton University Press, pp. 670–680, 18: 216: 293: 184:The Princeton Companion to Mathematics 272: 212: 210: 208: 172: 170: 168: 77:-tuples of numbers in the interval . 176: 13: 205: 165: 14: 322: 265: 42: 70:other than 3 and edge length 1. 237: 1: 158: 245:Geometry: Reteaching Masters 7: 119: 101:{\displaystyle {\sqrt {n}}} 10: 327: 16:Cube with edge length one 301:Euclidean solid geometry 102: 24: 108:, the square root of 103: 22: 198:. See in particular 116:-dimensional space. 88: 64:-dimensional spaces 274:Weisstein, Eric W. 98: 31:, more formally a 25: 126:Doubling the cube 96: 55:is also used for 318: 287: 286: 259: 257: 241: 235: 233: 214: 203: 197: 174: 136:Robbins constant 107: 105: 104: 99: 97: 92: 66:, for values of 59:, or "cubes" in 326: 325: 321: 320: 319: 317: 316: 315: 291: 290: 268: 263: 262: 255: 243: 242: 238: 231: 215: 206: 195: 179:Gowers, Timothy 175: 166: 161: 122: 91: 89: 86: 85: 45: 17: 12: 11: 5: 324: 314: 313: 308: 303: 289: 288: 267: 266:External links 264: 261: 260: 253: 236: 229: 204: 193: 163: 162: 160: 157: 156: 155: 150: 145: 142:Tychonoff cube 139: 133: 128: 121: 118: 95: 84:dimensions is 53:unit hypercube 44: 43:Unit hypercube 41: 33:cube of side 1 15: 9: 6: 4: 3: 2: 323: 312: 309: 307: 304: 302: 299: 298: 296: 284: 283: 278: 275: 270: 269: 256: 254:9780030543289 250: 246: 240: 232: 230:9780393020236 226: 222: 221: 213: 211: 209: 201: 196: 194:9781400830398 190: 186: 185: 180: 173: 171: 169: 164: 154: 151: 149: 146: 143: 140: 137: 134: 132: 129: 127: 124: 123: 117: 115: 111: 93: 83: 78: 76: 71: 69: 65: 63: 58: 54: 50: 40: 38: 34: 30: 21: 280: 244: 239: 219: 182: 113: 109: 81: 79: 74: 72: 67: 61: 52: 48: 46: 32: 28: 26: 277:"Unit cube" 200:p. 671 153:Unit sphere 148:Unit square 306:1 (number) 295:Categories 159:References 57:hypercubes 282:MathWorld 49:unit cube 47:The term 29:unit cube 23:Unit cube 120:See also 181:(ed.), 35:, is a 251:  227:  191:  131:K-cell 311:Cubes 249:ISBN 225:ISBN 189:ISBN 37:cube 51:or 297:: 279:. 207:^ 167:^ 27:A 285:. 258:. 234:. 202:. 114:n 110:n 94:n 82:n 75:n 68:n 62:n

Index


cube
hypercubes
n-dimensional spaces
Doubling the cube
K-cell
Robbins constant
Tychonoff cube
Unit square
Unit sphere



Gowers, Timothy
The Princeton Companion to Mathematics
ISBN
9781400830398
p. 671



The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics
ISBN
9780393020236
ISBN
9780030543289
Weisstein, Eric W.
"Unit cube"
MathWorld
Categories

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