Eikonal Blog

2010.03.09

Transcendental numbers: pi

Filed under: mathematics — Tags: , — sandokan65 @ 14:23

Source: http://www.wolframalpha.com/

\pi = 3.141, 592, 653, 589, 793, 238, 462, 643, 383, 279, 502, 884, 197, 169, 399, 375, 105, 820, 974, 944, 592, 307, 816, 406, 286, 208, 998, 628, 034, 825, 342, 117, 067, 982, 148, 086, 513, 282, 306, 647, 093, 844, 609, 550, 582, 231, 725, 359, 408, 128, 481, 117, 450, 284, 102, 701, 938, 521, 105, 559, 644, 622, 948, 954, 930, 381, 964, 428, 810, 975, 665, 933, 446, 128, 475, 648, 233, 786, 783, 165, 271, 201, 909, 145, 648, 566, 923, 460, 348, 610, 454, 326, 648, 213, 393, 607, 260, 249, 141, 273, 724, 587, 006, 606, 315, 588, 174, 881, 520, 920, 962, 829, 254, 091, 715, 364, 367, 892, 590, 360, 011, 330, 530, 548, 820, 466, 521, 384, 146, 951, 941, 511, 609, 433, 057, 270, 365, 759, 591, 953, 092, 186, 117, 381, 932, 611, 793, 105, 118, 548, 074, 462, 379, 962, 749, 567, 351, 885, 752, 724, 891, 227, 938, 183, 011, 949, 129, 833, 673, 362, 440, 656, 643, 086, 021, 394, 946, 395, 224, 737, 190, 702, 179, 860, 943, 702, 770, 539, 217, 176, 293, 176, 752, 384, 674, 818, 467, 669, 405, 132, 000, 568, 127, 145, 263, 560, 827, 785, 771, 342, 757, 789, 609, 173, 637, 178, 721, 468, 440, 901, 224, 953, 430, 146, 549, 585, 371, 050, 792, 279, 689, 258, 923, 542, 019, 956, 112, 129, 021, 960, 864, 034, 418, 159, 813, 629, 774, 771, 309, 960, 518, 707, 211, 349, 999, 998, 372, 978, 049, 951, 059, 731, 732, 816, 096, 318, 595, 024, 459, 455, 346, 908, 302, 642, 522, 308, 253, 344, 685, 035, 261, 931, 188, 171, 010, 003, 137, 838, 752, 886, 587, 533, 208, 381, 420, 617, 177, 669, 147, 303, 598, 253, 490, 428, 755, 468, 731, 159, 562, 863, 882, 353, 787, 593, 751, 957, 781, 857, 780, 532, 171, 226, 806, 613, 001, 927, 876, 611, 195, 909, 216, 420, 198, 938, 095, 257, 201, 065, 485, 863, 278, 865, 936, 153, 381, 827, 968, 230, 301, 952, 035, 301, 852, 968, 995, 773, 622, 599, 413, 891, 249, 721, 775, 283, 479, 131, 515, 574, 857, 242, 454, 150, 695, 950, 829, 533, 116, 861, 727, 855, 889, 075, 098, 381, 754, 637, 464, 939, 319, 255, 060, 400, 927, 701, 671, 139, 009, 848, 824, 012, 858, 361, 603, 563, 707, 660, 104, 710, 181, 942, 955, 596, 198, 946, 767, 837, 449, 448, 255, 379, 774, 726, 847, 104, 047, 534, 646, 208, 046, 684, 259, 069, 491, 293, 313, 677, 028, 989, 152, 104, 752, 162, 056, 966, 024, 058, 038, 150, 193, 511, 253, 382, 430, 035, 587, 640, 247, 496, 473, 263, 914, 199, 272, 604, 269, 922, 796, 782, 354, 781, 636, 009, 341, 721, 641, 219, 924, 586, 315, 030, 286, 182, 974, 555, 706, 749, 838, 505, 494, 588, 586, 926, 995, 690, 927, 210, 797, 509, 302, 955, 321, 165, 344, 987, 202, 755, 960, 236, 480, 665, 499, 119, 881, 834, 797, 753, 566, 369, 807, 426, 542, 527, 862, 551, 818, 417, 574, 672, 890, 977, 772, 793, 800, 081, 647, 060, 016, 145, 249, 192, 173, 217, 214, 772, 350, 141, 441, 973, 568, 548, 161, 361, 157, 352, 552, 133, 475, 741, 849, 468, 438, 523, 323, 907, 394, 143, 334, 547, 762, 416, 862, 518, 983, 569, 485, 562, 099, 219, 222, 184, 272, 550, 254, 256, 887, 671, 790, 494, 601, 653, 466, 804, 988, 627, 232, 791, 786, 085, 784, 383, 827, 967, 976, 681, 454, 100, 953, 883, 786, 360, 950, 680, 064, 225, 125, 205, 117, 392, 984, 896, 084, 128, 488, 626, 945, 604, 241, 965, 285, 022, 210, 661, 186, 306, 744, 278, 622, 039, 194, 945, 047, 123, 713, 786, 960, 956, 364, 371, 917, 287, 467, 764, 657, 573, 962, 413, 890, 865, 832, 645, 995, 813, 390, 478, 027, 590, 099, 465, 764, 078, 951, 269, 468, 398, 352, 595, 709, 825, 822, 620, 522, 489, 407, 726, 719, 478, 268, 482, 601, 476, 990, 902, 640, 136, 394, 437, 455, 305, 068, 203, 496, 252, 451, 749, 399, 651, 431, 429, 809, 190, 659, 250, 937, 221, 696, 461, 515, 709, 858, 387, 410, 597, 885, 959, 772, 975, 498, 930, 161, 753, 928, 468, 138, 268, 683, 868, 942, 774, 155, 991, 855, 925, 245, 953, 959, 431, 049, 972, 524, 680, 845, 987, 273, 644, 695, 848, 653, 836, 736, 222, 626, 099, 124, 608, 051, 243, 884, 390, 451, 244, 136, 549, 762, 780, 797, 715, 691, 435, 997, 700, 129, 616, 089, 441, 694, 868, 555, 848, 406, 353, 422, 072, 225, 828, 488, 648, 158, 456, 028, 506, 016, 842, 739, 452, 267, 467, 678, 895, 252, 138, 522, 549, 954, 666, 727, 823, 986, 456, 596, 116, 354, 886, 230, 577, 456, 498, 035, 593, 634, 568, 174, 324, 112, 515, 076, 069, 479, 451, 096, 596, 094, 025, 228, 879, 710, 893, 145, 669, 136, 867, 228, 748, 940, 560, 101, 503, 308, 617, 928, 680, 920, 874, 760, 917, 824, 938, 589, 009, 714, 909, 675, 985, 261, 365, 549, 781, 893, 129, 784, 821, 682, 998, 948, 722, 658, 804, 857, 564, 014, 270, 477, 555, 132, 379, 641, 451, 523, 746, 234, 364, 542, 858, 444, 795, 265, 867, 821, 051, 141, 354, 735, 739, 523, 113, 427, 166, 102, 135, 969, 536, 231, 442, 952, 484, 937, 187, 110, 145, 765, 403, 590, 279, 934, 403, 742, 007, 310, 578, 539, 062, 198, 387, 447, 808, 478, 489, 683, 321, 445, 713, 868, 751, 943, 506, 430, 218, 453, 191, 048, 481, 005, 370, 614, 680, 674, 919, 278, 191, 197, 939, 952, 061, 419, 663, 428, 754, 440, 643, 745, 123, 718, 192, 179, 998, 391, 015, 919, 561, 814, 675, 142, 691, 239, 748, 940, 907, 186, 494, 231, 961, 567, 945, 208, 095, 146, 550, 225, 231, 603, 881, 930, 142, 093, 762, 137, 855, 956, 638, 937, 787, 083, 039, 069, 792, 077, 346, 722, 182, 562, 599, 661, 501, 421, 503, 068, 038, 447, 734, 549, 202, 605, 414, 665, 925, 201, 497, 442, 850, 732, 518, 666, 002, 132, 434, 088, 190, 710, 486, 331, 734, 649, 651, 453, 905, 796, 268, 561, 005, 508, 106, 658, 796, 998, 163, 574, 736, 384, 052, 571, 459, 102, 897, 064, 140, 110, 971, 206, 280, 439, 039, 759, 515, 677, 157, 700, 420, 337, 869, 936, 007, 230, 558, 763, 176, 359, 421, 873, 125, 147, 120, 532, 928, 191, 826, 186, 125, 867, 321, 579, 198, 414, 848, 829, 164, 470, 609, 575, 270, 695, 722, 091, 756, 711, 672, 291, 098, 169, 091, 528, 017, 350, 671, 274, 858, 322, 287, 183, 520, 935, 396, 572, 512, 108, 357, 915, 136, 988, 209, 144, 421, 006, 751, 033, 467, 110, 314, 126, 711, 136, 990, 865, 851, 639, 831, 501, 970, 165, 151, 168, 517, 143, 765, 761, 835, 155, 650, 884, 909, 989, 859, 982, 387, 345, 528, 331, 635, 507, 647, 918, 535, 893, 226, 185, 489, 632, 132, 933, 089, 857, 064, 204, 675, 259, 070, 915, 481, 416, 549, 859, 461, 637, 180, 270, 981, 994, 309, 924, 488, 957, 571, 282, 890, 592, 323, 326, 097, 29...

Transcedental numbers: e

Filed under: mathematics — Tags: , — sandokan65 @ 14:21

Source: http://www.wolframalpha.com/

e = 2.718, 281, 828, 459, 045, 235, 360, 287, 471, 352, 662, 497, 757, 247, 093, 699, 959, 574, 966, 967, 627, 724, 076, 630, 353, 547, 594, 571, 382, 178, 525, 166, 427, 427, 466, 391, 932, 003, 059, 921, 817, 413, 596, 629, 043, 572, 900, 334, 295, 260, 595, 630, 738, 132, 328, 627, 943, 490, 763, 233, 829, 880, 753, 195, 251, 019, 011, 573, 834, 187, 930, 702, 154, 089, 149, 934, 884, 167, 509, 244, 761, 460, 668, 082, 264, 800, 168, 477, 411, 853, 742, 345, 442, 437, 107, 539, 077, 744, 992, 069, 551, 702, 761, 838, 606, 261, 331, 384, 583, 000, 752, 044, 933, 826, 560, 297, 606, 737, 113, 200, 709, 328, 709, 127, 443, 747, 047, 230, 696, 977, 209, 310, 141, 692, 836, 819, 025, 515, 108, 657, 463, 772, 111, 252, 389, 784, 425, 056, 953, 696, 770, 785, 449, 969, 967, 946, 864, 454, 905, 987, 931, 636, 889, 230, 098, 793, 127, 736, 178, 215, 424, 999, 229, 576, 351, 482, 208, 269, 895, 193, 668, 033, 182, 528, 869, 398, 496, 465, 105, 820, 939, 239, 829, 488, 793, 320, 362, 509, 443, 117, 301, 238, 197, 068, 416, 140, 397, 019, 837, 679, 320, 683, 282, 376, 464, 804, 295, 311, 802, 328, 782, 509, 819, 455, 815, 301, 756, 717, 361, 332, 069, 811, 250, 996, 181, 881, 593, 041, 690, 351, 598, 888, 519, 345, 807, 273, 866, 738, 589, 422, 879, 228, 499, 892, 086, 805, 825, 749, 279, 610, 484, 198, 444, 363, 463, 244, 968, 487, 560, 233, 624, 827, 041, 978, 623, 209, 002, 160, 990, 235, 304, 369, 941, 849, 146, 314, 093, 431, 738, 143, 640, 546, 253, 152, 096, 183, 690, 888, 707, 016, 768, 396, 424, 378, 140, 592, 714, 563, 549, 061, 303, 107, 208, 510, 383, 750, 510, 115, 747, 704, 171, 898, 610, 687, 396, 965, 521, 267, 154, 688, 957, 035, 035, 402, 123, 407, 849, 819, 334, 321, 068, 170, 121, 005, 627, 880, 235, 193, 033, 224, 745, 015, 853, 904, 730, 419, 957, 777, 093, 503, 660, 416, 997, 329, 725, 088, 687, 696, 640, 355, 570, 716, 226, 844, 716, 256, 079, 882, 651, 787, 134, 195, 124, 665, 201, 030, 592, 123, 667, 719, 432, 527, 867, 539, 855, 894, 489, 697, 096, 409, 754, 591, 856, 956, 380, 236, 370, 162, 112, 047, 742, 722, 836, 489, 613, 422, 516, 445, 078, 182, 442, 352, 948, 636, 372, 141, 740, 238, 893, 441, 247, 963, 574, 370, 263, 755, 294, 448, 337, 998, 016, 125, 492, 278, 509, 257, 782, 562, 092, 622, 648, 326, 277, 933, 386, 566, 481, 627, 725, 164, 019, 105, 900, 491, 644, 998, 289, 315, 056, 604, 725, 802, 778, 631, 864, 155, 195, 653, 244, 258, 698, 294, 695, 930, 801, 915, 298, 721, 172, 556, 347, 546, 396, 447, 910, 145, 904, 090, 586, 298, 496, 791, 287, 406, 870, 504, 895, 858, 671, 747, 985, 466, 775, 757, 320, 568, 128, 845, 920, 541, 334, 053, 922, 000, 113, 786, 300, 945, 560, 688, 166, 740, 016, 984, 205, 580, 403, 363, 795, 376, 452, 030, 402, 432, 256, 613, 527, 836, 951, 177, 883, 863, 874, 439, 662, 532, 249, 850, 654, 995, 886, 234, 281, 899, 707, 733, 276, 171, 783, 928, 034, 946, 501, 434, 558, 897, 071, 942, 586, 398, 772, 754, 710, 962, 953, 741, 521, 115, 136, 835, 062, 752, 602, 326, 484, 728, 703, 920, 764, 310, 059, 584, 116, 612, 054, 529, 703, 023, 647, 254, 929, 666, 938, 115, 137, 322, 753, 645, 098, 889, 031, 360, 205, 724, 817, 658, 511, 806, 303, 644, 281, 231, 496, 550, 704, 751, 025, 446, 501, 172, 721, 155, 519, 486, 685, 080, 036, 853, 228, 183, 152, 196, 003, 735, 625, 279, 449, 515, 828, 418, 829, 478, 761, 085, 263, 981, 395, 599, 006, 737, 648, 292, 244, 375, 287, 184, 624, 578, 036, 192, 981, 971, 399, 147, 564, 488, 262, 603, 903, 381, 441, 823, 262, 515, 097, 482, 798, 777, 996, 437, 308, 997, 038, 886, 778, 227, 138, 360, 577, 297, 882, 412, 561, 190, 717, 663, 946, 507, 063, 304, 527, 954, 661, 855, 096, 666, 185, 664, 709, 711, 344, 474, 016, 070, 462, 621, 568, 071, 748, 187, 784, 437, 143, 698, 821, 855, 967, 095, 910, 259, 686, 200, 235, 371, 858, 874, 856, 965, 220, 005, 031, 173, 439, 207, 321, 139, 080, 329, 363, 447, 972, 735, 595, 527, 734, 907, 178, 379, 342, 163, 701, 205, 005, 451, 326, 383, 544, 000, 186, 323, 991, 490, 705, 479, 778, 056, 697, 853, 358, 048, 966, 906, 295, 119, 432, 473, 099, 587, 655, 236, 812, 859, 041, 383, 241, 160, 722, 602, 998, 330, 535, 370, 876, 138, 939, 639, 177, 957, 454, 016, 137, 223, 618, 789, 365, 260, 538, 155, 841, 587, 186, 925, 538, 606, 164, 779, 834, 025, 435, 128, 439, 612, 946, 035, 291, 332, 594, 279, 490, 433, 729, 908, 573, 158, 029, 095, 863, 138, 268, 329, 147, 711, 639, 633, 709, 240, 031, 689, 458, 636, 060, 645, 845, 925, 126, 994, 655, 724, 839, 186, 564, 209, 752, 685, 082, 307, 544, 254, 599, 376, 917, 041, 977, 780, 085, 362, 730, 941, 710, 163, 434, 907, 696, 423, 722, 294, 352, 366, 125, 572, 508, 814, 779, 223, 151, 974, 778, 060, 569, 672, 538, 017, 180, 776, 360, 346, 245, 927, 877, 846, 585, 065, 605, 078, 084, 421, 152, 969, 752, 189, 087, 401, 966, 090, 665, 180, 351, 650, 179, 250, 461, 950, 136, 658, 543, 663, 271, 254, 963, 990, 854, 914, 420, 001, 457, 476, 081, 930, 221, 206, 602, 433, 009, 641, 270, 489, 439, 039, 717, 719, 518, 069, 908, 699, 860, 663, 658, 323, 227, 870, 937, 650, 226, 014, 929, 101, 151, 717, 763, 594, 460, 202, 324, 930, 028, 040, 186, 772, 391, 028, 809, 786, 660, 565, 118, 326, 004, 368, 850, 881, 715, 723, 866, 984, 224, 220, 102, 495, 055, 188, 169, 480, 322, 100, 251, 542, 649, 463, 981, 287, 367, 765, 892, 768, 816, 359, 831, 247, 788, 652, 014, 117, 411, 091, 360, 116, 499, 507, 662, 907, 794, 364, 600, 585, 194, 199, 856, 016, 264, 790, 761, 532, 103, 872, 755, 712, 699, 251, 827, 568, 798, 930, 276, 176, 114, 616, 254, 935, 649, 590, 379, 804, 583, 818, 232, 336, 861, 201, 624, 373, 656, 984, 670, 378, 585, 330, 527, 583, 333, 793, 990, 752, 166, 069, 238, 053, 369, 887, 956, 513, 728, 559, 388, 349, 989, 470, 741, 618, 155, 012, 539, 706, 464, 817, 194, 670, 834, 819, 721, 448, 889, 879, 067, 650, 379, 590, 366, 967, 249, 499, 254, 527, 903, 372, 963, 616, 265, 897, 603, 949, 857, 674, 139, 735, 944, 102, 374, 432, 970, 935, 547, 798, 262, 961, 459, 144, 293, 645, 142, 861, 715, 858, 733, 974, 679, 189, 757, 121, 195, 618, 738, 578, 364, 475, 844, 842, 355, 558, 105, 002, 561, 149, 239, 151, 889, 309, 946, 342, 841, 393, 608, 038, 309, 166, 281, 881, 150, 371, 528, 496, 705, 974, 162, 562, 823, 609, 21...

Computational tools online

Filed under: mathematics — Tags: , , , , — sandokan65 @ 13:22

Tebe Interesno

Filed under: art and fun — Tags: , — sandokan65 @ 11:55

This site (http://www.flylyf.com/inspiration-tebe-interesno/) has a selection of images from some Ukrainian graphical artist (nicknamed “Tebe Interesno”). His home page is at http://tebe-interesno.livejournal.com/.

2010.03.03

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A Field Guide to Critical Thinking

Filed under: critical thinking — Tags: — sandokan65 @ 12:37

The Skeptical Inquirer has an archive version of their article from 1990: “A Field Guide to Critical Thinking” by James Lett (Volume 14.4, Fall 1990) – http://www.csicop.org/si/show/field_guide_to_critical_thinking/.

The following extract is taken from the Clipmarks site (http://clipmarks.com/clipmark/79A7D35D-875A-4739-8577-240C2A300117/):

A Field Guide to Critical Thinking

The six rules of evidential reasoning are my own distillation and simplification of the scientific method. To make it easier for students to remember these half-dozen guidelines, I’ve coined an acronym for them: Ignoring the vowels, the letters in the word “FiLCHeRS” stand for the rules of Falsifiability, Logic, Comprehensiveness, Honesty, Replicability, and Sufficiency. Apply these six rules to the evidence offered for any claim, I tell my students, and no one will ever be able to sneak up on you and steal your belief. You’ll be filch-proof.

  • 1) Falsifiability:
    It must be possible to conceive of evidence that would prove the claim false.
  • 2) Logic:
    Any argument offered as evidence in support of any claim must be sound.
  • 3) Comprehensiveness:
    The evidence offered in support of any claim must be exhaustive — that is all of the available evidence must be considered.
  • 4) Honesty:
    The evidence offered in support of any claim must be evaluated without self-deception.
  • 5) Replicability:
    If the evidence for any claim is based upon an experimental result, or if the evidence offered in support of any claim could logically be explained as coincidental, then it is necessary for the evidence to be repeated in subsequent experiments or trials.
  • 6) Sufficiency:
    The evidence offered in support of any claim must be adequate to establish the truth of that claim, with these stipulations:

    • 1. the burden of proof for any claim rests on the claimant,
    • 2. extraordinary claims demand extraordinary evidence, and
    • 3. evidence based upon authority and/or testimony is always inadequate for any paranormal claim

2010.03.01

IT Magazines

Filed under: it — Tags: , — sandokan65 @ 14:01

Note: see also https://eikonal.wordpress.com/2010/02/01/infosec-online/.

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