

A124250


Finite set of numbers found inscribed on faces of a 17th or 18th century Mughal gold box in the shape of an icosahedron, from the treasury of Tipu Sultan.


1



11, 20, 21, 31, 41, 51, 61, 71, 81, 91, 101, 201, 202, 301, 401, 501, 601, 701, 801, 901
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OFFSET

1,1


COMMENTS

The significance of these numbers is not known. One possible explanation has been proposed by Paul Bien, see below. The box is of interest because of its rarity and great value.


REFERENCES

Paul Bien, paper presented at the 10th Conference on Fibonacci Numbers and their Applications (2002) but which did not appear in the Proceedings. It appeared in an earlier format in The Eighth Midwest History of Mathematics Comference, October 2000.
Harry Waldman, MAA is offered opportunity to buy a unique gold logo, FOCUS (Math. Assoc. Amer.), Vol. 26 (No. 9, 2006), p. 13. [The icosahedron is the logo of the Math. Assoc. America.]


LINKS

Table of n, a(n) for n=1..20.
Rohit Gupta, The icosahedron of Tipoo Sultan (2014)
Brian Hayes, Math baubles
National Galleries of Scotland, Icosahedron
Saratoga Fine Art, Picture


EXAMPLE

The numbered faces are as follows:
......./ \../ \
....../202\/601\
......
......\901/\701/
.......\ /801\/

\ 11/\91/\ 71/\ 51/\ 31/\
.\ /20\/ 81\/61\/ 41\ /21\
..
..\101/\201/\301/\401/\501/
...\/...\/...\/...\/...\/
The hinge is on the edge common to the faces 71 and 801 with the top section as shown here being on the lid. Paul Bien relates the sums of numbers in the top, round the middle bottom and the total to give approximations (to 3 decimal places) to Pi, Pi squared, Pi cubed, Phi (golden mean), Phi squared, Phi cubed, root 2, root 3 and root 6 [Comments from Ron Knott, Dec 16 2006]


CROSSREFS

Sequence in context: A102815 A105957 A105958 * A124251 A279431 A230541
Adjacent sequences: A124247 A124248 A124249 * A124251 A124252 A124253


KEYWORD

nonn,fini,full,unkn


AUTHOR

N. J. A. Sloane, based on email from T. D. Noe, Dec 15 2006


STATUS

approved



