Question about Ark's "Troubling Triangle" from the Dot Connector Magazine

[Cosmos]

on page 90 of the DCM number 12 is the Troubling Triangle from Ark.

since I saw it I was fascinated by this Triangle.
I'm sorry if the questions I'm asking are silly but I'm curious.

I've made a model of this triangle that is four times bigger then it is shown in the Magazine out of paper.
I made one triangle in wich the pieces are cut and one triangle that is intact.

now when I overlay the cut out pieces on the fixed triangle in the configuration that no "hole" is seen, the outer edges of the cut out pieces fit pretty good with the outer edges of the intact triangle.

but when I change the configuration of the cut out pieces into the position where the "hole" appears it seems like the outer edges of the cut out triangle overlap the intact triangle a bit.

after that I made the same model out of plexiglas and made the intact triangle like that (fixed with glue):

the configuration without the hole (notice the free spaces):

the configuration with the hole (notice the free spaces are now a bit less):

now the questions:
is there actually more free space with the last example or is it the exact same free space as in the second photo just rearranged so that the impression of more free space is created?

is there actually more free space ?
is that proof that there is more to this triangle then we can perceive (other dimensions?)
is the overlaping in the paper model (and the more space in the Plexiglas model) coused by the inaccuracy of my cut ?

is this Troubling Triangle actually what it appears to be (something impossible in 3D terms)?

 

[combsbt]

Why don't you measure the length and width of the free spaces in the two configurations? If you multiply them for both cases and get the same number, problem solved!

 

[Cosmos]

Why don't you measure the length and width of the free spaces in the two configurations? If you multiply them for both cases and get the same number, problem solved!

it is actually not that easy to measure all the free spaces and come to a accurate number when you look at it (Plexiglas) OSIT

 

[combsbt]

Just from counting pixels in your photos, it appears the slope of your bigger triangle is approximately 2/5, and the slope of the smaller triangle is about 3/8. Thus when they are put together the resulting figure is not actually a triangle. You can see that the hypotenuse of the supposed resulting triangle is not straight.

 

[Search]

Between the last 2 photos, the first one has more free space than the second one. Because, the second rectangle is bigger than first one.
Also you can measure it. Measure the length and width of the rectangles. Then length multiply by width (length and width of the 1st rectangle)(you'll get the area of the first rectangle) and do the same with the second rectangle. Then compare the area of the first rectangle with the area of second one, whose area will be bigger, that picture will have less free space.

Edit: area=surface area

 

[Search]

Sorry Pashalis, I a little missunderstood.
Let me take a look once again.

 

[Cosmos]

for those of you who have not seen it in the DCM here it is:

text next to the triangles:

The first triangle below is made up of four shapes. In the second triangle the exact same shapes are used, but simply rearranged. But there’s a problem: where does this hole come from? If you can figure it out, maybe you will have discovered the answer to “free energy”!

Edit: description from Ark

 

[Cosmos]

I think I have found the answer now.

I think part of the solution is found in the text from Ark next to the Troubling Triangle.
the other part is found by observing both the text and the Triangles and your own thinking.

 

[Search]

I just don't understand what you're asking about because of my English.

Thanks Pashalis. Can you please write what is wrote on the picture , I can't see it clearly.

 

[Cosmos]

I just don't understand what you're asking about because of my English.

Thanks Pashalis. Can you please write what is wrote on the picture , I can't see it clearly.

I have edited the text to my penultimate post

 

[Search]

I just don't understand what you're asking about because of my English.

Thanks Pashalis. Can you please write what is wrote on the picture , I can't see it clearly.

I have edited the text to my penultimate post

I see. Thanks.
Very interesting task. I just take my squared notebook and draw the same there. I don't get it.
I don't know how I would go to sleep without the solution.

 

[truth seeker]

Interesting indeed! I'm not great with math, but I do like puzzles.

is that proof that there is more to this triangle then we can perceive

The above would be my guess as it relates to the examples in Dot - that the space exists or not depending upon configuration but in terms of perception, it's always there/available whether visible or not if that makes sense. There's probably a more scientific/mathematical explanation however. :/ For what it's worth.

 

[Search]

The above would be my guess as it relates to the examples in Dot - that the space exists or not depending upon configuration but in terms of perception, it's always there/available whether visible or not if that makes sense. There's probably a more scientific/mathematical explanation however. :/ For what it's worth.

Maybe it is so. But what is the mathematical solution of it?
I have pain in my forehead. It feels like I because of my limited thinking.

 

[Deleted member 4320]

solution :)

_http://zapodaj.net/08f42d7ef576.jpg.html

 

[Mike]

I posted about this a little while back.

http://cassiopaea.org/forum/index.php/topic,25253.msg300611.html#msg300611

The red and green triangles slopes are not the same, so the top photo with the four figures combined is not a triangle.