Right Triangle Square Pyramid.By Aiya-Oba

[Aiya-Oba]

Four pairs of right triangles, form a square pyramid, whose four faces
are right triangles.-Aiya-Oba (Poet/Philosopher).

Thus,
4(a + b + c) = {(2a/c + 2) x c} + {(2b/c + 2) x c} + 2(a + b).

Where a, b, and c, are any of the Pythagorean Triplets.

Such that: a = 3, b = 4, and c = 5;

= 4(3 + 4 + 5) = {(2x3/5 + 2) x 5} + {(2x4/5 + 2) x 5} + 2(3 + 4),

= 4 x 12 = (3.2 x 5) + (3.6 x 5) + 2(3 + 4)

= 48 = ( 16 + 18 ) + 14

= 48 = 34 + 14

= 48 = 48

Q E D.

[translogi]

{(2a/c + 2) x c} + {(2b/c + 2) x c} + 2(a + b). <==>
(2a +2c) +(2b+2c) +(2a+2b) <==>
4a +4b +4c <==>
4(a+b+c)

What it has to do with pyramids I don't understand.
(maybe only that c is not zero)

You can not really make a pyramid from 4 triangles with sides 3,4, and
5, there is not a single apex.

[Aiya-Oba]

> 5, there is not a single apex.- Hide quoted text -
>
> - Show quoted text -

Thanks Tanslogi, for your observations concerning Right Triangle
Square Pyramid.

Please, let me admit that I intended to write:

Two pairs of right triangles, form a square pyramid, whose four faces
are right triangles.

Other than that, when the geometry of the two pairs of right trangles
are properly constructed,
a pyramid is formed, where the hypotenuce sides (4c),which are now the
sides of a pair of isosceles triangles, become its square base and
the single apex (vertex) of the resultant pyramid, is the common point
at which the four individual right angles meet.-Aiya-Oba.

[translogi]

> at which the four individual right angles meet.-Aiya-Oba.- Hide quoted text -

>
> - Show quoted text -

Still don't understand it.
the sum of all angles in the apex must be less than 4 x a square
angle. (if it are four square angles the "pyramid" is flat.

also for a "regular pyramid " the triangles must be isosceles.
(what is not the case with an "Pythagorean Triangle")

So i still don't understand it

[Aiya-Oba]

On Aug 3, 10:05�am, translogi <wilem...@googlemail.com> wrote:

> On Aug 1, 11:33�pm,Aiya-Oba<aaiya...@rcc.mass.edu> wrote:
>
>
>
>
>
> > On Aug 1, 4:50 pm, translogi <wilem...@googlemail.com> wrote:
>

> So i still don't understand it- Hide quoted text -

>
> - Show quoted text -

Hi Translogi:
Thanks for your continued interest.
Right Triangle Square Pyramid is a new discovery.

Two pairs of right triangles invariably form a square pyramid of four
faces, with uneven height, formed by the unequal sides of the original
pairs of right triangles. Hence 2(4 + 3).

The sum of the four right angles that meet at the apex of the pyramid
(which is directly above the center of its square base), is 4 x 90 =
360 degree.
-Aiya-Oba

[translogi]

>                           -Aiya-Oba- Hide quoted text -

>
> - Show quoted text -

no they do not form a pyramid they form a Rhombus
see http://en.wikipedia.org/wiki/Rhombus

[Aiya-Oba]

> seehttp://en.wikipedia.org/wiki/Rhombus- Hide quoted text -

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Hi Translogi:
Yes, it can be seen as rhombus, when one's point of view is any of the
non-right angles, and
at the same time, it is a Right Triangle Square Pyramid, when one's
point of view is any of the (hypotenuse) sides.

It's both Rhombus and Right Triangle Square Pyramid, if one is able
to sense the unfamiliar, in the familiar mode of the geometry. -Aiya-
Oba