A243309 - OEIS

A243309

Decimal expansion of DeVicci's tesseract constant.

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

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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.

From Amiram Eldar, May 29 2021: (Start)

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

Table of n, a(n) for n=1..103.

Hallard T. Croft, Kenneth Falconer and Richard K. Guy, Unsolved Problems in Geometry, Springer-Verlag New York, 1991, Section B4, p. 53.

Richard K. Guy and Richard J. Nowakowski, Monthly Unsolved Problems, 1969-1997, The American Mathematical Monthly, Vol. 104, No. 10 (1997), pp. 967-973.

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.

Kay R. Pechenick DeVicci Shultz, Largest m-Cube in an n-Cube: Partial Solution, Notes written in 1996 and assembled in 2013 with a preface by Greg Huber, KITP preprint NSF-ITP-13-142.

Eric Weisstein's World of Mathematics, Prince Rupert's Cube.

Wikipedia, Prince Rupert's cube.

Index entries for algebraic numbers, degree 8

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

(PARI) polrootsreal(4*x^8-28*x^6-7*x^4+16*x^2+16)[3] \\ Charles R Greathouse IV, Apr 07 2016

(PARI) sqrt(polrootsreal(Pol([4, -28, -7, 16, 16]))[1]) \\ Charles R Greathouse IV, Apr 07 2016