今日は私の誕生日、ISC(Inverse Symbolic Calculator)でこの日が何の数式か調べてみる。

GoogleとTwitterは誕生日になるとそれぞれロウソクと風船がトップページになる。

ほぼ毎年やってますが、ISC(Inverse Symbolic Calculator)で今日が何の数式か見てみよう。

http://wayback.cecm.sfu.ca/projects/ISC/ISCmain.html

まず2.0200614は

Your input of 2.0200614 was probably generated by one
the following functions or found in one of the given tables.
Answers are given from shortest to longest description

Sum(1/(b**n*P(n)),n=1..infinity), P(n) : 2nd and 3rd degree polynomials.
2020061433073306 = sum(1/(5^n*(4*n^3-22*n^2+59*n-40)),n=1..inf)

次は0.6142020は

Your input of .6142020 was probably generated by one
the following functions or found in one of the given tables.
Answers are given from shortest to longest description

Sum(1/(b**n+P(n)),n=1..infinity), P(n) : 2nd and 3rd degree polynomials.
6142020691893405 = sum(1/(5^n+(3/2*n^3-n^2+7/2*n+18)),n=1..inf)

おお、結構似た数式になった。カシオの高精度計算サイトkeisan.casio.jpで実際に計算してみよう。

1 , 0.2 ,                                0.037037037037037037
2 , 0.201818181818181818 , 0.0542784163473818646
3 , 0.201988394584139265 , 0.05968382175278727
4 , 0.202004394584139265 , 0.0610406738559080299
5 , 0.202005955559749021 , 0.0613416067478731217
6 , 0.202006121362857829 , 0.0614042948120656994
7 , 0.202006140553262627 , 0.0614170121190487726
8 , 0.202006142941322328 , 0.061419567213267872
9 , 0.202006143256399252 , 0.0614200789350222384
10 , 0.20200614329997372 , 0.0614201813197886956
11 , 0.202006143306234802 , 0.0614202017989783882
12 , 0.202006143307163179 , 0.0614202058949363114
13 , 0.202006143307304493 , 0.0614202067141341706
14 , 0.202006143307326485 , 0.0614202068779740636
15 , 0.202006143307329973 , 0.0614202069107420583
16 , 0.202006143307330536 , 0.061420206917295658
17 , 0.202006143307330627 , 0.061420206918606378
18 , 0.202006143307330643 , 0.061420206918868522
19 , 0.202006143307330645 , 0.0614202069189209508
20 , 0.202006143307330646 , 0.0614202069189314366
21 , 0.202006143307330646 , 0.0614202069189335337
22 , 0.202006143307330646 , 0.0614202069189339532
23 , 0.202006143307330646 , 0.061420206918934037
24 , 0.202006143307330646 , 0.0614202069189340538
25 , 0.202006143307330646 , 0.0614202069189340572
26 , 0.202006143307330646 , 0.0614202069189340579
27 , 0.202006143307330646 , 0.061420206918934058
28 , 0.202006143307330646 , 0.061420206918934058
29 , 0.202006143307330646 , 0.061420206918934058
30 , 0.202006143307330646 , 0.061420206918934058

なるほど確かにこの式で計算できた。