Triangle

[Skeeter]

The below triangle is made up of some shapes.

But, if you move the shapes around to form the triangle below, then a square of space appears? Where does this square come from? Its the same shapes, and the same triangle is formed?

Again, dont post the answer straight away, let the 1 or 2 people who dont already know have a bash

 

[Skeeter]

They're not triangles.

 

[Skeeter]

A triangle has 3 sides. The top picture has 4.

seen as both pictures are made of the same shapes, the bottom one must too.

 

[Skeeter]

Yeah, the same triangle hasn't been formed.

Trigonometry at its best

Yeah, I figured this would keep those looking for geometric solutions to the earlier ones happy.

 

[Skeeter]

Clearly, the area of the bottom triangle is 1 unit squared bigger than the top. that's why the hole has appeared

Nope, because...

Neither of the two (complete/large) triangles are actually triangles.

The top triangle hypotenuse bows in slightly, whilst the bottom triangle hypotenuse bows out slightly.

This is because the red and dark green smaller triangles that compose the hypotenuse are both of different gradients (The red is 0.375 and the green is 0.4).

The difference causes the hypotenuse to bow in for on triangle, and out for the other, and the difference in that is equal to 1 square.

This is great to cut out and give to people, because its clearly the same pieces then. The areas are identical.

 

[Skeeter]

Of course, if anyone actually examined the red and dark green triangles to check they were the same in both pictures, they would have noticed straight away they weren't equal gradients.

I figured this out (after a long time) by realising that 5/2 is not equal to 8/3