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Origin (mathematics)

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In physical problems, the choice of origin is often arbitrary, meaning any choice of origin will ultimately give the same answer. This allows one to pick an origin point that makes the mathematics as simple as possible, often by taking advantage of some kind of
86:โ€”that is, the positions of their projections along each axis, either in the positive or negative direction. The coordinates of the origin are always all zero, for example (0,0) in two dimensions and (0,0,0) in three. 82:
of the system intersect. The origin divides each of these axes into two halves, a positive and a negative semiaxis. Points can then be located with reference to the origin by giving their numerical
98:, the origin may also be called the pole. It does not itself have well-defined polar coordinates, because the polar coordinates of a point include the angle made by the positive 299: 274: 247: 220: 192: 17: 146: 321: 75: 102:-axis and the ray from the origin to the point, and this ray is not well-defined for the origin itself. 269:, Pure and Applied Undergraduate Texts, vol. 21, American Mathematical Society, p. 134, 95: 264: 237: 182: 157: 8: 63: 106: 295: 270: 243: 216: 188: 51: 79: 47: 58:, used as a fixed point of reference for the geometry of the surrounding space. 208: 125: 121: 315: 151: 113: 140: 83: 39: 30: 109:, the origin may be chosen freely as any convenient point of reference. 215:, Springer series in Soviet mathematics, Springer-Verlag, p. 73, 117: 294:, Chapman & Hall Pure and Applied Mathematics, CRC Press, 160:, a function depending only on the distance from the origin 128: 187:, Delmar drafting series, Thompson Learning, p. 120, 313: 154:, a topological space with a distinguished point 124:intersect each other. In other words, it is the 89: 34:The origin of a Cartesian coordinate system 207: 289: 176: 174: 69: 29: 14: 314: 235: 180: 143:, an analogous point of a vector space 171: 27:Point of reference in Euclidean space 78:, the origin is the point where the 262: 116:can be referred as the point where 24: 25: 333: 147:Distance from a point to a plane 54:, usually denoted by the letter 283: 256: 229: 201: 184:Engineering Drawing and Design 13: 1: 236:Tanton, James Stuart (2005), 164: 7: 239:Encyclopedia of Mathematics 213:Learning higher mathematics 134: 76:Cartesian coordinate system 10: 338: 292:Classical Complex Analysis 181:Madsen, David A. (2001), 290:Gonzalez, Mario (1991), 90:Other coordinate systems 242:, Infobase Publishing, 96:polar coordinate system 322:Elementary mathematics 35: 263:Lee, John M. (2013), 158:Radial basis function 70:Cartesian coordinates 33: 266:Axiomatic Geometry 209:Pontrjagin, Lev S. 112:The origin of the 107:Euclidean geometry 64:geometric symmetry 36: 18:Origin (geometry) 16:(Redirected from 329: 306: 304: 287: 281: 279: 260: 254: 252: 233: 227: 225: 205: 199: 197: 178: 21: 337: 336: 332: 331: 330: 328: 327: 326: 312: 311: 310: 309: 302: 288: 284: 277: 261: 257: 250: 234: 230: 223: 206: 202: 195: 179: 172: 167: 137: 92: 72: 48:Euclidean space 28: 23: 22: 15: 12: 11: 5: 335: 325: 324: 308: 307: 300: 282: 275: 255: 248: 228: 221: 200: 193: 169: 168: 166: 163: 162: 161: 155: 149: 144: 136: 133: 126:complex number 122:imaginary axis 91: 88: 71: 68: 26: 9: 6: 4: 3: 2: 334: 323: 320: 319: 317: 303: 301:9780824784157 297: 293: 286: 278: 276:9780821884782 272: 268: 267: 259: 251: 249:9780816051243 245: 241: 240: 232: 224: 222:9783540123514 218: 214: 210: 204: 196: 194:9780766816343 190: 186: 185: 177: 175: 170: 159: 156: 153: 152:Pointed space 150: 148: 145: 142: 139: 138: 132: 130: 127: 123: 119: 115: 114:complex plane 110: 108: 103: 101: 97: 87: 85: 81: 77: 67: 65: 59: 57: 53: 50:is a special 49: 45: 41: 32: 19: 291: 285: 265: 258: 238: 231: 212: 203: 183: 111: 104: 99: 93: 73: 60: 55: 43: 37: 141:Null vector 84:coordinates 40:mathematics 165:References 118:real axis 316:Category 211:(1984), 135:See also 298:  273:  246:  219:  191:  44:origin 42:, the 94:In a 74:In a 52:point 46:of a 296:ISBN 271:ISBN 244:ISBN 217:ISBN 189:ISBN 129:zero 120:and 80:axes 105:In 38:In 318:: 173:^ 131:. 66:. 305:. 280:. 253:. 226:. 198:. 100:x 56:O 20:)

Index

Origin (geometry)

mathematics
Euclidean space
point
geometric symmetry
Cartesian coordinate system
axes
coordinates
polar coordinate system
Euclidean geometry
complex plane
real axis
imaginary axis
complex number
zero
Null vector
Distance from a point to a plane
Pointed space
Radial basis function


Engineering Drawing and Design
ISBN
9780766816343
Pontrjagin, Lev S.
ISBN
9783540123514
Encyclopedia of Mathematics
ISBN

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