How many digits into pi do you need to go to find your birthday?

March 17, 2017
By

(This article was first published on R – Decision Science News, and kindly contributed to R-bloggers)

FIND YOUR BIRTHDAY IN PI, IN THREE DIFFERENT FORMATS

It was Pi Day (March 14, like 3/14, like 3.14, get it?) recently and Time Magazine did a fun interactive app in which you can find your birthday inside the digits of pi.

However:
1) They only used one format of birthday, in which July 4th would be 704. But there are other ways to write July 4. Like 0704 or 74. And those must be investigated, right?
2) Our friend Dave Pennock said he wanted to see the locations of every possible birthday inside pi.

So here they are. Enjoy! And R code below if you are interested. Plot and other stuff use Hadley Wickham’s Tidyverse tools.

And what the heck, have a spreadsheet of fun (i.e., spreadsheet with all the birthdays and locations in it).

Birthday location Shorter form location Shortest form loc
01-01 2563 1-01 853 1-1 95
01-02 6599 1-02 164 1-2 149
01-03 25991 1-03 3487 1-3 111
01-04 1219 1-04 270 1-4 2
01-05 3982 1-05 50 1-5 4
01-06 1011 1-06 1012 1-6 41
01-07 23236 1-07 1488 1-7 96
01-08 16216 1-08 2535 1-8 425
01-09 4555 1-09 207 1-9 38
01-10 3253 1-10 175 1-10 175
01-11 19627 1-11 154 1-11 154
01-12 4449 1-12 710 1-12 710
01-13 362 1-13 363 1-13 363
01-14 4678 1-14 2725 1-14 2725
01-15 27576 1-15 922 1-15 922
01-16 5776 1-16 396 1-16 396
01-17 6290 1-17 95 1-17 95
01-18 7721 1-18 446 1-18 446
01-19 494 1-19 495 1-19 495
01-20 43172 1-20 244 1-20 244
01-21 6305 1-21 711 1-21 711
01-22 660 1-22 484 1-22 484
01-23 27847 1-23 1925 1-23 1925
01-24 8619 1-24 1081 1-24 1081
01-25 15458 1-25 1351 1-25 1351
01-26 4372 1-26 2014 1-26 2014
01-27 9693 1-27 298 1-27 298
01-28 1199 1-28 149 1-28 149
01-29 2341 1-29 500 1-29 500
01-30 5748 1-30 745 1-30 745
01-31 5742 1-31 1097 1-31 1097
02-01 9803 2-01 245 2-1 94
02-02 7287 2-02 1514 2-2 136
02-03 3831 2-03 1051 2-3 17
02-04 28185 2-04 375 2-4 293
02-05 12631 2-05 1327 2-5 90
02-06 9809 2-06 885 2-6 7
02-07 14839 2-07 2374 2-7 29
02-08 6141 2-08 77 2-8 34
02-09 24361 2-09 54 2-9 187
02-10 9918 2-10 1318 2-10 1318
02-11 4353 2-11 94 2-11 94
02-12 30474 2-12 712 2-12 712
02-13 524 2-13 281 2-13 281
02-14 10340 2-14 103 2-14 103
02-15 24666 2-15 3099 2-15 3099
02-16 4384 2-16 992 2-16 992
02-17 546 2-17 547 2-17 547
02-18 2866 2-18 424 2-18 424
02-19 716 2-19 717 2-19 717
02-20 15715 2-20 1911 2-20 1911
02-21 17954 2-21 1737 2-21 1737
02-22 1889 2-22 1736 2-22 1736
02-23 25113 2-23 136 2-23 136
02-24 12782 2-24 536 2-24 536
02-25 3019 2-25 1071 2-25 1071
02-26 6742 2-26 965 2-26 965
02-27 18581 2-27 485 2-27 485
02-28 4768 2-28 2528 2-28 2528
02-29 6707 2-29 186 2-29 186
03-01 1045 3-01 493 3-1 1
03-02 1439 3-02 818 3-2 16
03-03 15339 3-03 195 3-3 25
03-04 4460 3-04 4461 3-4 87
03-05 29985 3-05 366 3-5 10
03-06 3102 3-06 116 3-6 286
03-07 3813 3-07 65 3-7 47
03-08 35207 3-08 520 3-8 18
03-09 5584 3-09 421 3-9 44
03-10 7692 3-10 442 3-10 442
03-11 11254 3-11 846 3-11 846
03-12 11647 3-12 2632 3-12 2632
03-13 858 3-13 859 3-13 859
03-14 3496 3-14 1 3-14 1
03-15 8285 3-15 314 3-15 314
03-16 13008 3-16 238 3-16 238
03-17 4778 3-17 138 3-17 138
03-18 7291 3-18 797 3-18 797
03-19 4530 3-19 1166 3-19 1166
03-20 3767 3-20 600 3-20 600
03-21 18810 3-21 960 3-21 960
03-22 12744 3-22 3434 3-22 3434
03-23 8948 3-23 16 3-23 16
03-24 16475 3-24 2495 3-24 2495
03-25 12524 3-25 3147 3-25 3147
03-26 7634 3-26 275 3-26 275
03-27 9208 3-27 28 3-27 28
03-28 24341 3-28 112 3-28 112
03-29 16096 3-29 3333 3-29 3333
03-30 2568 3-30 365 3-30 365
03-31 13852 3-31 1128 3-31 1128
04-01 19625 4-01 1198 4-1 3
04-02 17679 4-02 1368 4-2 93
04-03 4776 4-03 724 4-3 24
04-04 1272 4-04 1273 4-4 60
04-05 10748 4-05 596 4-5 61
04-06 39577 4-06 71 4-6 20
04-07 4258 4-07 2008 4-7 120
04-08 5602 4-08 146 4-8 88
04-09 33757 4-09 340 4-9 58
04-10 11495 4-10 163 4-10 163
04-11 9655 4-11 2497 4-11 2497
04-12 20103 4-12 297 4-12 297
04-13 6460 4-13 1076 4-13 1076
04-14 3756 4-14 385 4-14 385
04-15 7735 4-15 3 4-15 3
04-16 10206 4-16 1709 4-16 1709
04-17 15509 4-17 1419 4-17 1419
04-18 7847 4-18 728 4-18 728
04-19 4790 4-19 37 4-19 37
04-20 3286 4-20 702 4-20 702
04-21 16028 4-21 93 4-21 93
04-22 4796 4-22 1840 4-22 1840
04-23 8220 4-23 2995 4-23 2995
04-24 1878 4-24 1110 4-24 1110
04-25 5716 4-25 822 4-25 822
04-26 1392 4-26 1393 4-26 1393
04-27 36946 4-27 630 4-27 630
04-28 910 4-28 203 4-28 203
04-29 4514 4-29 1230 4-29 1230
04-30 4619 4-30 519 4-30 519
05-01 21816 5-01 1344 5-1 49
05-02 25156 5-02 32 5-2 173
05-03 19743 5-03 838 5-3 9
05-04 9475 5-04 1921 5-4 192
05-05 36575 5-05 132 5-5 131
05-06 2094 5-06 1116 5-6 211
05-07 683 5-07 684 5-7 405
05-08 14658 5-08 1122 5-8 11
05-09 17171 5-09 1147 5-9 5
05-10 10274 5-10 49 5-10 49
05-11 444 5-11 395 5-11 395
05-12 2294 5-12 1843 5-12 1843
05-13 597 5-13 110 5-13 110
05-14 42236 5-14 2118 5-14 2118
05-15 10458 5-15 1100 5-15 1100
05-16 5367 5-16 3516 5-16 3516
05-17 24365 5-17 2109 5-17 2109
05-18 751 5-18 471 5-18 471
05-19 17096 5-19 390 5-19 390
05-20 20247 5-20 326 5-20 326
05-21 19553 5-21 173 5-21 173
05-22 2041 5-22 535 5-22 535
05-23 4317 5-23 579 5-23 579
05-24 15635 5-24 1615 5-24 1615
05-25 3233 5-25 1006 5-25 1006
05-26 3984 5-26 613 5-26 613
05-27 7300 5-27 241 5-27 241
05-28 18917 5-28 867 5-28 867
05-29 6373 5-29 1059 5-29 1059
05-30 367 5-30 368 5-30 368
05-31 26607 5-31 2871 5-31 2871
06-01 2400 6-01 1218 6-1 220
06-02 14854 6-02 291 6-2 21
06-03 9019 6-03 264 6-3 313
06-04 1172 6-04 1173 6-4 23
06-05 5681 6-05 750 6-5 8
06-06 13163 6-06 311 6-6 118
06-07 10861 6-07 287 6-7 99
06-08 13912 6-08 618 6-8 606
06-09 3376 6-09 128 6-9 42
06-10 13704 6-10 269 6-10 269
06-11 7448 6-11 427 6-11 427
06-12 11585 6-12 220 6-12 220
06-13 7490 6-13 971 6-13 971
06-14 2887 6-14 1612 6-14 1612
06-15 25066 6-15 1030 6-15 1030
06-16 6017 6-16 1206 6-16 1206
06-17 886 6-17 887 6-17 887
06-18 14424 6-18 1444 6-18 1444
06-19 6351 6-19 843 6-19 843
06-20 14967 6-20 76 6-20 76
06-21 2819 6-21 2820 6-21 2820
06-22 30206 6-22 185 6-22 185
06-23 51529 6-23 456 6-23 456
06-24 5491 6-24 510 6-24 510
06-25 5971 6-25 1569 6-25 1569
06-26 16707 6-26 21 6-26 21
06-27 5424 6-27 462 6-27 462
06-28 72 6-28 73 6-28 73
06-29 11928 6-29 571 6-29 571
06-30 10902 6-30 1900 6-30 1900
07-01 10640 7-01 167 7-1 40
07-02 544 7-02 545 7-2 140
07-03 10108 7-03 408 7-3 300
07-04 9882 7-04 2670 7-4 57
07-05 9233 7-05 561 7-5 48
07-06 5134 7-06 97 7-6 570
07-07 3815 7-07 755 7-7 560
07-08 8111 7-08 3061 7-8 67
07-09 3641 7-09 121 7-9 14
07-10 3169 7-10 681 7-10 681
07-11 4250 7-11 1185 7-11 1185
07-12 7695 7-12 243 7-12 243
07-13 36438 7-13 627 7-13 627
07-14 9546 7-14 610 7-14 610
07-15 5668 7-15 344 7-15 344
07-16 10242 7-16 40 7-16 40
07-17 15743 7-17 568 7-17 568
07-18 2988 7-18 2776 7-18 2776
07-19 8664 7-19 541 7-19 541
07-20 44221 7-20 1009 7-20 1009
07-21 756 7-21 650 7-21 650
07-22 2375 7-22 2140 7-22 2140
07-23 3300 7-23 1632 7-23 1632
07-24 8811 7-24 302 7-24 302
07-25 16244 7-25 140 7-25 140
07-26 288 7-26 289 7-26 289
07-27 12328 7-27 406 7-27 406
07-28 4879 7-28 1584 7-28 1584
07-29 4078 7-29 771 7-29 771
07-30 6892 7-30 898 7-30 898
07-31 2808 7-31 785 7-31 785
08-01 9508 8-01 3418 8-1 68
08-02 18639 8-02 1993 8-2 53
08-03 8283 8-03 85 8-3 27
08-04 1284 8-04 775 8-4 19
08-05 2292 8-05 957 8-5 172
08-06 9289 8-06 968 8-6 75
08-07 15787 8-07 451 8-7 306
08-08 4545 8-08 106 8-8 35
08-09 3009 8-09 1003 8-9 12
08-10 3207 8-10 206 8-10 206
08-11 10884 8-11 153 8-11 153
08-12 147 8-12 148 8-12 148
08-13 10981 8-13 734 8-13 734
08-14 4274 8-14 882 8-14 882
08-15 25257 8-15 324 8-15 324
08-16 1601 8-16 68 8-16 68
08-17 4857 8-17 319 8-17 319
08-18 30399 8-18 490 8-18 490
08-19 12786 8-19 198 8-19 198
08-20 4787 8-20 53 8-20 53
08-21 12923 8-21 102 8-21 102
08-22 5149 8-22 135 8-22 135
08-23 11957 8-23 114 8-23 114
08-24 10358 8-24 1196 8-24 1196
08-25 828 8-25 89 8-25 89
08-26 4294 8-26 2059 8-26 2059
08-27 619 8-27 620 8-27 620
08-28 24614 8-28 2381 8-28 2381
08-29 1123 8-29 335 8-29 335
08-30 816 8-30 492 8-30 492
08-31 25355 8-31 237 8-31 237
09-01 658 9-01 659 9-1 250
09-02 2074 9-02 715 9-2 6
09-03 6335 9-03 357 9-3 15
09-04 8107 9-04 909 9-4 59
09-05 23683 9-05 3191 9-5 31
09-06 8297 9-06 1294 9-6 181
09-07 2986 9-07 543 9-7 13
09-08 7828 9-08 815 9-8 81
09-09 12077 9-09 248 9-9 45
09-10 17009 9-10 2874 9-10 2874
09-11 6125 9-11 1534 9-11 1534
09-12 29379 9-12 483 9-12 483
09-13 17515 9-13 1096 9-13 1096
09-14 249 9-14 250 9-14 250
09-15 3413 9-15 1315 9-15 1315
09-16 5930 9-16 3370 9-16 3370
09-17 341 9-17 342 9-17 342
09-18 4731 9-18 2220 9-18 2220
09-19 2127 9-19 417 9-19 417
09-20 328 9-20 329 9-20 329
09-21 422 9-21 423 9-21 423
09-22 7963 9-22 687 9-22 687
09-23 23216 9-23 63 9-23 63
09-24 5122 9-24 1430 9-24 1430
09-25 4008 9-25 337 9-25 337
09-26 5380 9-26 6 9-26 6
09-27 1177 9-27 977 9-27 977
09-28 5768 9-28 2192 9-28 2192
09-29 7785 9-29 1854 9-29 1854
09-30 1494 9-30 194 9-30 194
10-01 15762 10-01 15762 10-1 853
10-02 6740 10-02 6740 10-2 164
10-03 12292 10-03 12292 10-3 3487
10-04 3849 10-04 3849 10-4 270
10-05 2881 10-05 2881 10-5 50
10-06 3481 10-06 3481 10-6 1012
10-07 4076 10-07 4076 10-7 1488
10-08 8281 10-08 8281 10-8 2535
10-09 1817 10-09 1817 10-9 207
10-10 853 10-10 853 10-10 853
10-11 3846 10-11 3846 10-11 3846
10-12 8618 10-12 8618 10-12 8618
10-13 8271 10-13 8271 10-13 8271
10-14 2781 10-14 2781 10-14 2781
10-15 2564 10-15 2564 10-15 2564
10-16 9987 10-16 9987 10-16 9987
10-17 8041 10-17 8041 10-17 8041
10-18 1224 10-18 1224 10-18 1224
10-19 15483 10-19 15483 10-19 15483
10-20 9808 10-20 9808 10-20 9808
10-21 2750 10-21 2750 10-21 2750
10-22 6400 10-22 6400 10-22 6400
10-23 6771 10-23 6771 10-23 6771
10-24 12736 10-24 12736 10-24 12736
10-25 12926 10-25 12926 10-25 12926
10-26 14679 10-26 14679 10-26 14679
10-27 164 10-27 164 10-27 164
10-28 3242 10-28 3242 10-28 3242
10-29 8197 10-29 8197 10-29 8197
10-30 20819 10-30 20819 10-30 20819
10-31 3495 10-31 3495 10-31 3495
11-01 2780 11-01 2780 11-1 154
11-02 12721 11-02 12721 11-2 710
11-03 3494 11-03 3494 11-3 363
11-04 23842 11-04 23842 11-4 2725
11-05 175 11-05 175 11-5 922
11-06 13461 11-06 13461 11-6 396
11-07 21819 11-07 21819 11-7 95
11-08 7450 11-08 7450 11-8 446
11-09 3254 11-09 3254 11-9 495
11-10 22898 11-10 22898 11-10 22898
11-11 12701 11-11 12701 11-11 12701
11-12 12702 11-12 12702 11-12 12702
11-13 3504 11-13 3504 11-13 3504
11-14 23209 11-14 23209 11-14 23209
11-15 27054 11-15 27054 11-15 27054
11-16 3993 11-16 3993 11-16 3993
11-17 154 11-17 154 11-17 154
11-18 14376 11-18 14376 11-18 14376
11-19 984 11-19 984 11-19 984
11-20 3823 11-20 3823 11-20 3823
11-21 710 11-21 710 11-21 710
11-22 12018 11-22 12018 11-22 12018
11-23 6548 11-23 6548 11-23 6548
11-24 25705 11-24 25705 11-24 25705
11-25 1350 11-25 1350 11-25 1350
11-26 12703 11-26 12703 11-26 12703
11-27 4252 11-27 4252 11-27 4252
11-28 14719 11-28 14719 11-28 14719
11-29 4450 11-29 4450 11-29 4450
11-30 9107 11-30 9107 11-30 9107
12-01 244 12-01 244 12-1 711
12-02 19942 12-02 19942 12-2 484
12-03 60873 12-03 60873 12-3 1925
12-04 11885 12-04 11885 12-4 1081
12-05 3329 12-05 3329 12-5 1351
12-06 3259 12-06 3259 12-6 2014
12-07 7511 12-07 7511 12-7 298
12-08 3714 12-08 3714 12-8 149
12-09 4729 12-09 4729 12-9 500
12-10 3456 12-10 3456 12-10 3456
12-11 50289 12-11 50289 12-11 50289
12-12 711 12-12 711 12-12 711
12-13 47502 12-13 47502 12-13 47502
12-14 4560 12-14 4560 12-14 4560
12-15 11942 12-15 11942 12-15 11942
12-16 6986 12-16 6986 12-16 6986
12-17 11078 12-17 11078 12-17 11078
12-18 9167 12-18 9167 12-18 9167
12-19 1426 12-19 1426 12-19 1426
12-20 36498 12-20 36498 12-20 36498
12-21 8732 12-21 8732 12-21 8732
12-22 17882 12-22 17882 12-22 17882
12-23 9550 12-23 9550 12-23 9550
12-24 661 12-24 661 12-24 661
12-25 9417 12-25 9417 12-25 9417
12-26 964 12-26 964 12-26 964
12-27 484 12-27 484 12-27 484
12-28 5183 12-28 5183 12-28 5183
12-29 30418 12-29 30418 12-29 30418
12-30 7146 12-30 7146 12-30 7146
12-31 9451 12-31 9451 12-31 9451

R CODE

library(ggplot2)
library(readr)
library(stringr)
library(tidyr)
pistring = read_file("pi.txt")
#choose 2016 b/c it's a leap year
dayvec = seq(as.Date('2016-01-01'), as.Date('2016-12-31'), by = 1)
dayvec = str_sub(dayvec, start = 6, end = 10)
shorterdayvec = sub("0(.-.)", "\\1", dayvec)
shortestdayvec = sub("(.-)0(.)$", "\\1\\2", shorterdayvec)
df = data.frame(
birthday = dayvec,
loc = str_locate(pistring, gsub("-", "", dayvec))[, 1],
shorter_bday = shorterdayvec,
shorter_loc = str_locate(pistring, gsub("-", "", shorterdayvec))[, 1],
shortest_bday = shortestdayvec,
shortest_loc = str_locate(pistring, gsub("-", "", shortestdayvec))[, 1]
)
write.csv(df, file = "birthdays_in_pi.csv", row.names = FALSE)
long_df = df %>% gather(key, location, loc, shorter_loc, shortest_loc)
p = ggplot(long_df, aes(x = location, fill = key))
p = p + geom_density(alpha = .3)
p = p + coord_cartesian(xlim = c(0, 40000))
p = p + theme(legend.position = "bottom")
p
ggsave(
plot = p,
file = "birthdays_in_pi.pdf",
height = 4,
width = 4
)

The post How many digits into pi do you need to go to find your birthday? appeared first on Decision Science News.

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