weird problem

[marcel]

I have 4 pieces that fit together in different ways. The size of triangles remains the same but I have a hole in the second. Am I crazy?

[Prodigy]

impressive...

[marcel]

He He! A cigar for the person who solves the problem!

[Steve]

It's to do with the red and green triangles and how the shapes tessilate, it's "tetris" syndrome, the lengths of the BOTTOM lengths of the shape in image 1 equals the same length as the length of the shape in image 2 wit the hole in the bottom

It's to do with tessilation and surface area of the red and green triangles

[marcel]

It is not a problem of length. not a problem of triangle too. but you are near the solution.

[Steve]

Aaaah, never said length though, surface area, how much space it fills, both triangles have the same surface area, they are just packed differently, it's how they all tessilate together

The red and green triangles are fractals, so when the red triangle forms the Hypotenuse/base angle it creates half of the triangle already without needing any other shapes, it fillls the portion of the big shape perfectly

the green triangle is an identical object, same angles, which means the hypotenuse is the same angle, just scaled smaller, so it still fills a portion of the large triangle perfectly, just less of it. In both of those images, the hypotenuse is the same length because you are adding the lengths of the red and green's hypotenuses together, which will creat the same base and height measurements

so when you swap the two triangles around, the hypotenuse will be the same length, its just the pieces that make up the rest of the triangle will make a different formation, the way the shapes are made up is no longer effecient enough, thus creating that hole

[marcel]

Not a problem of fractal too. If both big triangle have the same dimension and angle, there is no reason to have a hole in one of them because they must to have the same area. The solution is more simple

[clintonman]

The triangles don't have the same slope. Very tricky.

[Benji]

Yes, I see it now. If you look very closely, the main edge of each combined triangle has a "kink" where the two minor triangles meet.

Well spotted clintonman, this had me stumped.

[3dvisuals dude]

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