The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A088896 Length of longest integral ladder that can be moved horizontally around the right angled corner where two hallway corridors of integral widths meet. 1
 125, 1000, 2197, 3375, 4913, 8000, 15625, 17576, 24389, 27000, 39304, 42875, 50653, 59319, 64000, 68921, 91125, 125000, 132651, 140608, 148877, 166375, 195112, 216000, 226981, 274625, 314432, 343000, 389017, 405224, 421875, 474552, 512000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The set of values for the integral-widths corridors and longest ladder are merely the cubes of Pythagorean triples, viz. (A046083, A046084, A009000). The corridors' widths may be parametrically expressed as d*(sin x)^3 and d*(cos x)^3, for a longest ladder length d making an angle x with one of the corridors. A given ladder, however, is maximum-corner-bending for a family of infinite pairs of perpendicular corridor widths and that the envelope of the maximum bending positions is that of a sliding rod against the outer wall, which is a branch of an astroid or four-cusped hypocycloid. REFERENCES E. Mendelson, 3000 Solved Problems in Calculus, Chapter 16 Problem 16.56 pp. 131, Mc Graw-Hill 1988. M. Spiegel, Theory and Problems of Advanced Calculus, Chapter 4 Problem 40 pp. 75, Mc Graw-Hill 1974. LINKS Table of n, a(n) for n=1..33. C. Azeredo, The Ladder Problem L. Husch and M. Szapiel, The Longest Ladder M. Kantor, Knox College, Puzzle of the Week J. J. O'Connor and E. R. Robertson, Astroid T. Sillke, longest ladder D. Sjerve, Solution to problem No.3 W. H. Steeb, Solved Problem Eric Weisstein's World of Mathematics, Astroid FORMULA a(n)=d^3, where d=A009003(n). CROSSREFS Sequence in context: A204611 A296037 A355885 * A016851 A204795 A352161 Adjacent sequences: A088893 A088894 A088895 * A088897 A088898 A088899 KEYWORD nonn AUTHOR Lekraj Beedassy, Nov 28 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 29 21:40 EDT 2023. Contains 363042 sequences. (Running on oeis4.)