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von Zak
06.01.2019 13:03
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

x3mEn
Hi! How are the searches going? In the project statistics, the progress so far seems to be unresultative... My own brutal force application still brought nothing too. May be this can be useful to you:
new.png
new.png (154.29 KiB) 1015 mal betrachtet
von Zak
13.12.2018 15:16
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

x3mEn
e10.JPG
e10.JPG (68.31 KiB) 1552 mal betrachtet
von Zak
08.12.2018 07:28
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

One of the face diagonals is divisible by 4, and I had every right to write: (defg)^2=16n^2. Is it clear?
Let's transform both last equations to the reduced form and try to determine the integer roots:
e3.JPG
e3.JPG (66.32 KiB) 1593 mal betrachtet
Are you still in doubt?
von Zak
07.12.2018 22:44
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

x3mEn
Is it clear:
e1.JPG
e1.JPG (48.58 KiB) 1402 mal betrachtet
e2.JPG
e2.JPG (80.56 KiB) 1402 mal betrachtet
?
Do you agree?
von Zak
04.12.2018 21:12
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

x3mEn
Hi! Let me invite you to this discussion:
http://mathhelpplanet.com/viewtopic.php?f=57&t=62956
I think there is not roots among the divisors of the free member of two last equations.
von Zak
30.10.2018 19:08
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

x3mEn
Are you looking for complex values of the face diagonal? It is obvious that if integer values are needed, not complex values, when x^2<4e^4f^4. Insert this condition and try the same one more time, please.
von Zak
28.10.2018 14:53
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

x3mEn
The discriminant cannot be zero, I made a mistake above, there will always be two roots.
Maybe you will be interested to solve the last expression in integers, it will be the geometric mean, then both roots will be integers, if I don't mistake:
g.JPG
g.JPG (18.64 KiB) 2289 mal betrachtet
von Zak
27.10.2018 18:30
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

x3mEn
Try:
m7.JPG
m7.JPG (12.17 KiB) 2338 mal betrachtet
von Zak
27.10.2018 13:01
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

I think it is possible only in case D=0, d1=d2:
m6.JPG
m6.JPG (20.67 KiB) 2353 mal betrachtet
von Zak
26.10.2018 19:32
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

x3mEn
Is it fair?
m5.JPG
m5.JPG (32.23 KiB) 2373 mal betrachtet
Or may be two perfect bricks exists? How to explain it?
von Zak
26.10.2018 06:23
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

If you will find integer d,e,f,x and calculate a,b,c,g based on d,e,f , they (I mean a,b,c,g ) will not necessarily be integer, some of them or even entire all can turn to irrational. Despite the fact that x^2=16a^2*b^2*c^2*g^2 will be TRUE. Because a product of irrational numbers could be an integ...
von Zak
25.10.2018 21:00
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 254
Zugriffe: 113219

Re: [sub-project] Perfect cuboid

Even if x=sqr(16a^2b^2c^2(a^2+b^2+c^2))?
Try to get integer x=4abc*sqr(a^2+b^2+c^2) by using real(including irrational, of course) values.
I can't. May be you can do it?

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