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von x3mEn
12.02.2021 09:34
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Heronian Triangles with Square Sides
Antworten: 0
Zugriffe: 76

[sub-project] Heronian Triangles with Square Sides

Abstract If Perfect cuboid exists, the squares of 3 its face diagonals should construct a Heronian triangle. Proof: photo_2021-02-12_10-19-32.jpg Note: Heronian triangle is a triangle that has side lengths and area that are all integers. At the moment it is known about only two Heronian triangles w...
von x3mEn
30.10.2018 20:52
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

Zak,
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von x3mEn
29.10.2018 22:33
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

Zak,
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von x3mEn
27.10.2018 16:42
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

Zak,
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von x3mEn
25.10.2018 20:57
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

x3mEn I know about you had showed. But I told about other equation whith new integer variable x, which included sqr(16a^2b^2c^2g^2). The equation will be TRUE only in case when d,e,f will correspond perfect brick's face diagonals. By means of transformations and finding the roots of the equation, w...
von x3mEn
25.10.2018 15:14
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

Decision of equation in integers will be equal to full task, because if we will have d,e,f , then we can find all the rest. We can find g and then we can find a,b,c. You are not right. When you have a system of Diophantine X equations with Y variables, theoretically you can simplify it to an equati...
von x3mEn
25.10.2018 08:40
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

the fourh exponent is not too big? It's time to talk about how Math works. :) With the help of strict math logic of equivalent expressions you transfered from the given system of 4 Diophantine equations to consequent (and, btw, not necessary equivalent to input system) expression, which says: "If t...
von x3mEn
24.10.2018 21:41
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

Zak, you are muddling up 'necessary' and 'enough'. If undersquare expression is 2f^2e^2, yes, it's enough to aquire z as a full square of the sum or the difference of f^2 and e^2. But, is it necessary? No. There are a lot of other expressions binding f and e which are a full square too. The world is...
von x3mEn
23.10.2018 21:17
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

Some ideas regarding the last equation. As far as One edge, two face diagonals and the body diagonal must be odd, one edge and the remaining face diagonal must be divisible by 4, and the remaining edge must be divisible by 16. Two edges must have length divisible by 3 and at least one of those edges...
von x3mEn
23.10.2018 09:57
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

Zak, no problem, buу Wolfram|Alpha Pro to get the proof.
von x3mEn
21.10.2018 21:05
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

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Zak, before publish anything, please-please-please verify all your ideas on some trivial samples known as Edge and Face cuboids.
von x3mEn
17.10.2018 15:49
Forum: Fehler, Wünsche / Bugs, Wishes
Thema: [sub-project] Perfect cuboid
Antworten: 256
Zugriffe: 146491

Re: [sub-project] Perfect cuboid

Perfect Cuboid 3rd (loooooong) Batch has finished If a perfect cuboid exists, its body diagonal exceeds 2^53. During this batch we were investigating the range of body diagonal from 2^51 (2'251'799'813'685'248) to 2^53 (9'007'199'254'740'992). 17'408 face cuboids, 34'816 imaginary cuboids, 156'672 t...

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