Knowledge

Unit square

Source 📝

27: 58: 198: 303: 268: 360: 355: 86: 290:, Problem Books in Mathematics, vol. 1 (2nd ed.), Springer-Verlag, pp. 181–185, 248: 195:
Is there a point in the plane at a rational distance from all four corners of a unit square?
8: 350: 31: 323: 299: 264: 129: 102: 46: 161:. In this view, the four corners of the unit square are at the four complex numbers 291: 256: 205: 326: 283: 158: 295: 260: 344: 154: 114: 20: 227: 217: 38: 187: 331: 222: 26: 153:
The unit square can also be thought of as a subset of the
251:, in Crilly, A. J.; Earnshow, R. A.; Jones, H. (eds.), 249:"IFSs and the Interactive Design of Tiling Structures" 57:
unit square refers specifically to the square in the
321: 208:
distance from all four vertices of the unit square.
204:
It is not known whether any point in the plane is a
342: 189: 183: 80: 25: 199:(more unsolved problems in mathematics) 343: 157:, the topological space formed by the 148: 322: 246: 105:consisting of the points where both 282: 13: 288:Unsolved Problems in Number Theory 145:denotes the closed unit interval. 14: 372: 315: 255:, Springer-Verlag, p. 136, 101:, a unit square is defined as a 61:with corners at the four points 190:Unsolved problem in mathematics 276: 240: 128:That is, a unit square is the 1: 233: 7: 211: 87:Cartesian coordinate system 16:Square with side length one 10: 377: 247:Horn, Alastair N. (1991), 18: 296:10.1007/978-1-4899-3585-4 261:10.1007/978-1-4612-3034-2 184:Rational distance problem 361:Squares in number theory 49:whose sides have length 19:Not to be confused with 356:Types of quadrilaterals 30:The unit square in the 34: 81:Cartesian coordinates 29: 149:Complex coordinates 324:Weisstein, Eric W. 253:Fractals and Chaos 35: 305:978-1-4899-3587-8 270:978-1-4612-7770-5 130:Cartesian product 89:with coordinates 368: 337: 336: 309: 308: 280: 274: 273: 244: 191: 179: 172: 168: 164: 144: 140: 124: 120: 113:lie in a closed 112: 108: 100: 76: 72: 68: 64: 52: 376: 375: 371: 370: 369: 367: 366: 365: 341: 340: 318: 313: 312: 306: 284:Guy, Richard K. 281: 277: 271: 245: 241: 236: 214: 202: 201: 196: 193: 186: 174: 170: 166: 162: 159:complex numbers 151: 142: 132: 122: 118: 110: 106: 90: 83: 74: 70: 66: 62: 59:Cartesian plane 50: 24: 17: 12: 11: 5: 374: 364: 363: 358: 353: 339: 338: 317: 316:External links 314: 311: 310: 304: 275: 269: 238: 237: 235: 232: 231: 230: 225: 220: 213: 210: 197: 194: 188: 185: 182: 150: 147: 82: 79: 15: 9: 6: 4: 3: 2: 373: 362: 359: 357: 354: 352: 349: 348: 346: 334: 333: 328: 327:"Unit square" 325: 320: 319: 307: 301: 297: 293: 289: 285: 279: 272: 266: 262: 258: 254: 250: 243: 239: 229: 226: 224: 221: 219: 216: 215: 209: 207: 200: 181: 178: 160: 156: 155:complex plane 146: 139: 135: 131: 126: 116: 115:unit interval 104: 98: 94: 88: 78: 60: 56: 48: 44: 40: 33: 28: 22: 21:Square (unit) 330: 287: 278: 252: 242: 203: 176: 152: 137: 133: 127: 96: 92: 84: 54: 42: 36: 228:Unit sphere 218:Unit circle 43:unit square 39:mathematics 351:1 (number) 345:Categories 234:References 53:. Often, 32:real plane 332:MathWorld 223:Unit cube 286:(1991), 212:See also 206:rational 141:, where 302:  267:  173:, and 103:square 75:(1, 1) 73:, and 71:(0, 1) 67:(1, 0) 47:square 117:from 85:In a 63:(0, 0 45:is a 300:ISBN 265:ISBN 175:1 + 109:and 41:, a 292:doi 257:doi 121:to 65:), 55:the 37:In 347:: 329:. 298:, 263:, 180:. 169:, 165:, 136:× 125:. 95:, 77:. 69:, 335:. 294:: 259:: 192:: 177:i 171:i 167:1 163:0 143:I 138:I 134:I 123:1 119:0 111:y 107:x 99:) 97:y 93:x 91:( 51:1 23:.

Index

Square (unit)

real plane
mathematics
square
Cartesian plane
Cartesian coordinate system
square
unit interval
Cartesian product
complex plane
complex numbers
(more unsolved problems in mathematics)
rational
Unit circle
Unit cube
Unit sphere
"IFSs and the Interactive Design of Tiling Structures"
doi
10.1007/978-1-4612-3034-2
ISBN
978-1-4612-7770-5
Guy, Richard K.
doi
10.1007/978-1-4899-3585-4
ISBN
978-1-4899-3587-8
Weisstein, Eric W.
"Unit square"
MathWorld

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.