Happy Pi day everyone!!
03-18-2019, 05:40 PM
Post: #27
 Thomas Klemm Senior Member Posts: 1,607 Joined: Dec 2013
RE: Happy Pi day everyone!!
(03-18-2019 08:07 AM)EdS2 Wrote:  Thanks! That led to Kevin Brown's Rounding Up To PI - MathPages.

Here are other links that I found interesting:

The Combinatorics of Mancala-Type Games:
Ayo, Tchoukaillon, and 1/π

Duane M. Broline, Daniel E. Loeb

My Favorite Integer Sequences
by N. J. A. Sloane
Chapter 12 Tchoukaillon solitaire (or Mancala, or Kalahari)

Quote:The sequence can be obtained by a sieving process: write 1, 2, . . . in a
column. To get the second column, cross off 1 and every second number. To
get the third column, cross off the first and every third number. Then cross off
the first and every fourth number, and so on (see Fig. 13). The top number in
column n is t(n).

1     1
2     2     2
3     3
4     4     4     4
5     5
6     6     6     6     6
7     7
8     8     8
9     9
10    10    10    10    10    10
11    11
12    12    12    12    12    12    12
13    13
14    14    14
15    15
16    16    16    16
17    17
18    18    18    18    18    18    18    18
19    19
20    20    20

Fig. 13. A sieve to generate the sequence t(1),t(2), . . . = 1, 2, 4, 6, 10, 12, 18, . . ..
At stage n, the first number and every nth are crossed off.

Cheers
Thomas
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 Messages In This Thread Happy Pi day everyone!! - Namir - 03-14-2019, 12:25 PM RE: Happy Pi day everyone!! - ttw - 03-14-2019, 12:34 PM RE: Happy Pi day everyone!! - Valentin Albillo - 03-14-2019, 03:53 PM RE: Happy Pi day everyone!! - Dieter - 03-14-2019, 08:09 PM RE: Happy Pi day everyone!! - Eddie W. Shore - 03-14-2019, 01:30 PM RE: Happy Pi day everyone!! - Gerson W. Barbosa - 03-14-2019, 08:58 PM RE: Happy Pi day everyone!! - Gerson W. Barbosa - 03-17-2019, 01:48 AM RE: Happy Pi day everyone!! - Thomas Klemm - 03-14-2019, 10:12 PM RE: Happy Pi day everyone!! - DA74254 - 03-14-2019, 10:34 PM RE: Happy Pi day everyone!! - Valentin Albillo - 03-15-2019, 12:45 AM RE: Happy Pi day everyone!! - mpark - 03-15-2019, 05:11 PM RE: Happy Pi day everyone!! - EdS2 - 03-16-2019, 07:50 AM RE: Happy Pi day everyone!! - Carsen - 03-15-2019, 04:31 AM RE: Happy Pi day everyone!! - Valentin Albillo - 03-15-2019, 05:07 AM RE: Happy Pi day everyone!! - Ángel Martin - 03-15-2019, 06:35 AM RE: Happy Pi day everyone!! - Carsen - 03-16-2019, 06:27 AM RE: Happy Pi day everyone!! - Thomas Okken - 03-17-2019, 12:38 AM RE: Happy Pi day everyone!! - Geoff Quickfall - 03-15-2019, 07:09 AM RE: Happy Pi day everyone!! - Csaba Tizedes - 03-15-2019, 08:35 AM RE: Happy Pi day everyone!! - Thomas Klemm - 03-16-2019, 03:18 PM RE: Happy Pi day everyone!! - EdS2 - 03-18-2019, 08:07 AM RE: Happy Pi day everyone!! - ttw - 03-16-2019, 04:23 PM RE: Happy Pi day everyone!! - Thomas Klemm - 03-16-2019, 05:11 PM RE: Happy Pi day everyone!! - Valentin Albillo - 03-16-2019, 10:43 PM RE: Happy Pi day everyone!! - Thomas Klemm - 03-16-2019, 06:14 PM RE: Happy Pi day everyone!! - ttw - 03-17-2019, 12:56 AM RE: Happy Pi day everyone!! - Thomas Klemm - 03-18-2019 05:40 PM

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