Discussion:
MathPuzzle 204: The fourth dimension
Peter Hendriks
2007-11-22 15:02:39 UTC
MathPuzzle 204: The fourth dimension

Good afternoon from sunny Ruuro,

Today's puzzle is about the fourth dimension. Unfortunately, I was not able
to find the right words. It is your challenge to nevertheless find an answer
to the question. This should not be too difficult as soon as you understand
what the puzzle is all about.

Puzzle 198, with the bridges, has been closed. Your solutions have been
(still) more than welcome.

Have fun with the new puzzle !
Best regards,
Peter

Jutta Gut
2007-11-25 19:33:10 UTC
Post by Peter Hendriks
Today's puzzle is about the fourth dimension. Unfortunately, I was not
able to find the right words. It is your challenge to nevertheless find an
answer to the question. This should not be too difficult as soon as you
understand what the puzzle is all about.
Meiner Meinung nach ist das Puzzle mit diesen Angaben nicht lösbar (ich
komme z.T. auf negative Längen für die Stäbe).

mfg
Jutta
Chip Eastham
2007-11-25 20:50:46 UTC
Post by Jutta Gut
Post by Peter Hendriks
Today's puzzle is about the fourth dimension. Unfortunately, I was not
able to find the right words. It is your challenge to nevertheless find an
answer to the question. This should not be too difficult as soon as you
understand what the puzzle is all about.
Meiner Meinung nach ist das Puzzle mit diesen Angaben nicht lösbar (ich
komme z.T. auf negative Längen für die Stäbe).
mfg
Jutta
Rough translation: In my opinion the puzzle with these data is not
solvable
(in part because of negative lengths for the sticks).

Hi, Jutta:

I got the same result and sent Peter a comment to that effect.

regards, chip
Ralf Goertz
2007-11-26 09:09:48 UTC
Post by Jutta Gut
Post by Peter Hendriks
Today's puzzle is about the fourth dimension. Unfortunately, I was not
able to find the right words. It is your challenge to nevertheless
find an answer to the question. This should not be too difficult as
soon as you understand what the puzzle is all about.
Meiner Meinung nach ist das Puzzle mit diesen Angaben nicht lösbar
(ich komme z.T. auf negative Längen für die Stäbe).
Ich auch. Ich habe mupad befragt, und einer der drei Werte war immer
negativ. Was mich allerdings etwas stutzig macht, ist, dass ich nur vier
Lösungen bekomme. Da das Gleichungssystem

a +b +c =3
a^2+b^2+c^2=9
a^3+b^3+c^3=24

symmetrisch in a,b,c ist, sollte mit einer Lösung auch jede Permutation
eine Lösung sein, es also wenigstens sechs Lösungen geben.

float(solve({a+b+c-3,a^2+b^2+c^2-9,a^3+b^3+c^3-24},MaxDegree=3))
{[a = -0.5320888862, b = 0.6527036447, c = 2.879385242],
[a = -0.5320888862, b = 2.879385242, c = 0.6527036447],
[a = 0.6527036447, b = -0.5320888862, c = 2.879385242],
[a = 2.879385242, b = -0.5320888862, c = 0.6527036447]}

Warum werden die Lagebeziehungen in den verschiedenen Dimensionen
unterschiedlich (und kursiv) beschrieben: /after/, /next/ /to/, /on/
/top/ /of/ /each/ /other/? "Nebeneinander" hätte doch für jede Dimension
gepasst. Auf jedenfall klingt es für mich so, als wenn die Gebilde immer
disjunkt sein sollen, also zum Beispiel kein Quadrat in einem anderen
enthalten.

Ralf