Schlagwort-Archive: date

Palindrome Day 20200202

The year 2020 is definitely a very special one for all those who have a sense of symmetry – and this disposition was given to us by the evolution. Depending on the date format used, there are several palindrome days this year, i.e. dates that are symmetrical (or palindromic).

When written in the international ISO 8601 format YYYYMMDD, 2020-02-02 is the first palindromic date since 2011-11-02. In between there are 3014 days (more than 8 years). Of course, this is also a symmetrical date when written in the American format MMDDYYYY, i.e. 02/02/2020.

Moreover, that date is also palindromic in the long German date format DDMMYYYY, this is 02.02.2020. This format is also used in many other countries. It is the first such date since 21.02.2012 (2903 days ago). Please note: the symmetry is evaluated neglecting the delimiter symbol.

What’s next?

In February there are two additional palindromic dates in the short American format MMDDYY. These are 02/11/20 and 02/22/20. Depending on the used format we will experience further palindromic dates in the next year. In ISO YYYYMMDD format this will be 2021-12-02 which is also palindromic in the American format (12/02/2021). In the German DDMMYYYY format there will be two such dates in the near future, one in 2021: 12.02.2021 (same date as indicated for the ISO format), and another one in 2022: 22.02.2022 (which is not palindromic in the ISO format).

People who use the short German date format DDMMYY will encounter another symmetry this year on 02.11.20 (2020-11-02 = November 2nd, 2020). The previous symmetrical date in this format was 21.11.12 (2012-11-21) which is almost 8 years ago (2903 days). The closest future symmetrical dates in this format will be 12.11.21 and 22.11.22. A little bit later on 12/11/21 and 12/22/21 we see further symmetrical dates in the short American format MMDDYY.

Is it going on like this?

Why, no. After this accumulation of palindromic dates we will experience a long lasting „dry spell“ which will only end on 2030-03-02 (ISO format), 03/02/2030 (American format), 03/11/30 (short American format), 03.02.2030 (long German format), and 03.11.30 (short German format), respectively. See the tables below.

By the way

The very first palindromic date in ISO YYYYMMDD format after 1000-01-01 (Jan 01 1000) was 1001-10-01 (Oct 01 1001).

2020-02-02 is the 47th palindromic date in the YYYYMMDD format after the reference date 1000-01-01. In total, 372579 days have passed since then. The 331st and very last such date before the year 10000 is 9290-09-29 (Sep 29 9290). This will be the 3028132nd day after 1000-01-01 and therefore is still 2655553 days away (after 2020-02-02).

It is a little bit different in the DDMMYYYY format. The following applies here: 02.02.2020 is the 67th palindromic date after the reference date 01.01.1000. The last possible symmetrical date before the year numbers become five digits long one is 29.09.9092 which is the 335th such date in the list. It’s just the 2955814th day after 01.01.1000.

Hint: Because of the Gregorian Calendar Reform of 1582, the numbers of days after 1001-01-01 are fictitious, strictly spoken. They are valid only then, if we adopt the reform for dates before 1582, subsequently. To get the real number of days after ‘Jan 1 1000’ for years after 1582 subtract 5 from each term representing a date after 1582. This applies to all palindromic dates after the 43rd in YYYYMMDD format, and after the 61st in DDMMYYYY format. The value 5 comes from the 10 skipped “Gregorian” dates between 1582-10-04 (Oct 4 1582) and 1582-10-15 (Oct 15 1582) minus the 5 additional Julian leap days in the years 1000, 1100, 1300, 1400 and 1500 which are not Gregorian leap years.

Useless knowledge?

Do not ask about the benefits of these considerations and let me quote Bertolt Brecht: „Thinking is one of the greatest pleasures of the human race“. Jean-Baptiste le Rond d’Alembert (you should know him; possibly you remember the convergence criterion for infinite series that was named after him) says it even more clearly: „Mathematics is a kind of toy that nature has thrown at us for comfort and entertainment in the darkness“. – In Praise of Idleness.

Tables

Altogether, there are 331 palindromic dates in the YYYYMMDD format and 335 such dates in the DDMMYYYY format (between the years 1000 and 9999). The following two tables show excerpts from the complete lists of dates for both formats. In both cases the symmetry is evaluated neglecting the delimiter symbol.


Excerpt of palindromic dates in the YYYYMMDD format.

# Date # of days after 1000-01-01
1 10011001 638
2 10100101 3652
3 10111101 4321
4 10200201 7335
44 20011002 365882
45 20100102 368896
46 20111102 369565
47 20200202 372579
48 20211202 373248
49 20300302 376260
50 20400402 379944
51 20500502 383626
52 20600602 387310
326 92400429 3009717
327 92500529 3013399
328 92600629 3017083
329 92700729 3020765
330 92800829 3024449
331 92900929 3028132

Excerpt of palindromic dates in the DDMMYYYY format.

# Date # of days after 01.01.1000
1 10011001 374
2 20011002 749
3 30011003 1124
4 01011010 3652
65 11022011 369301
66 21022012 369676
67 02022020 372579
68 12022021 372955
69 22022022 373330
70 03022030 376233
71 13022031 376608
72 23022032 376983
73 04022040 379886
330 08099080 2951410
331 18099081 2951785
332 28099082 2952160
333 09099090 2955063
334 19099091 2955438
335 29099092 2955814

Finally, here are the complete lists of symmetrical dates in the DDMMYY and in the MMDDYY format: The symmetry is valid with and without the delimiter symbol.


All palindromic dates in the DDMMYY format.

# Date # of days after 01.01.00
1 101101 619
2 201102 994
3 301103 1369
4 011110 3897
5 111111 4272
6 211112 4648
7 021120 7551
8 121121 7926
9 221122 8301
10 031130 11204
11 131131 11579
12 231132 11955
13 041140 14858
14 141141 15233
15 241142 15608
16 051150 18511
17 151151 18886
18 251152 19262
19 061160 22165
20 161161 22540
21 261162 22915
22 071170 25818
23 171171 26193
24 271172 26569
25 081180 29472
26 181181 29847
27 281182 30222
28 091190 33125
29 191191 33500
30 291192 33876

All palindromic dates in the MMDDYY format.

# Date # of days after 01/01/00
1 101101 589
2 102201 600
3 011110 3603
4 012210 3614
5 111111 4272
6 112211 4283
7 021120 7255
8 022220 7297
9 121121 7955
10 122221 7966
11 031130 10967
12 032230 10978
13 041140 14651
14 042240 14662
15 051150 18333
16 052250 18344
17 061160 22017
18 062260 22028
19 071170 25699
20 072270 25710
21 081180 29383
22 082280 29394
23 091190 33066
24 092290 33077