|
|
A243309
|
|
Decimal expansion of DeVicci's tesseract constant.
|
|
1
|
|
|
1, 0, 0, 7, 4, 3, 4, 7, 5, 6, 8, 8, 4, 2, 7, 9, 3, 7, 6, 0, 9, 8, 2, 5, 3, 5, 9, 5, 2, 3, 1, 0, 9, 9, 1, 4, 1, 9, 2, 5, 6, 9, 0, 1, 1, 4, 1, 1, 3, 6, 6, 9, 7, 7, 0, 2, 3, 4, 9, 6, 3, 7, 9, 8, 5, 7, 1, 1, 5, 2, 3, 1, 3, 2, 8, 0, 2, 8, 6, 7, 7, 7, 9, 6, 2, 5, 2, 0, 5, 5, 1, 4, 7, 4, 6, 3, 5, 9, 2, 3, 9, 4, 2
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
This "tesseract" constant is the edge length of the largest 3-dimensional cube that can be inscribed within a unit 4-dimensional cube.
Named by Finch (2003) after Kay R. Pechenick DeVicci Shultz.
The problem was apparently first posed by Gardner (1966). According to Gardner (2001), he had received the correct answers to the problem from Eugen I. Bosch (1966), G. de Josselin de Jong (1971), Hermann Baer (1974) and Kay R. Pechenick (1983). (End)
|
|
REFERENCES
|
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.14 DeVicci's tesseract constant, p. 524.
Martin Gardner, Is It Possible to Visualize a Four-Dimensional Figure?, Mathematical Games, Sci. Amer., Vol. 215, No. 5, (Nov. 1966), pp. 138-143.
Martin Gardner, Mathematical Carnival: A New Round-Up of Tantalizers and Puzzles from Scientific American, New York: Vintage Books, 1977, Chapter 4, "Hypercubes", pp. 41-54.
Martin Gardner, The Colossal Book of Mathematics, New York, London: W. W. Norton & Co., 2001, Chapter 13, "Hypercubes", pp. 162-174.
|
|
LINKS
|
Greg Huber, Kay Pechenick Shultz and John E. Wetzel, The n-cube is Rupert, The American Mathematical Monthly, Vol. 125, No. 6 (2018), pp. 505-512.
|
|
FORMULA
|
Positive root of the polynomial 4*x^8 - 28*x^6 - 7*x^4 + 16*x^2 + 16.
|
|
EXAMPLE
|
1.00743475688427937609825359523109914192569...
|
|
MATHEMATICA
|
Root[4*x^8 - 28*x^6 - 7*x^4 + 16*x^2 + 16, x, 3] // RealDigits[#, 10, 103]& // First
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|