Triangle Puzzle
- Thread starter ukbug
- Start date
A
andrew
Guest
I think, and this is only a guess, that the area of the second triangle is different to that of the first because the angles change, hence the extra square!. Please tell me someone!! ....am I right????? ???
my head hurts >
I know, i know!!! Erm basically both hypotenuse of the two triangles within the triangle arent at the same gradient (angle as each other). When theyre changed around it allows the yellow shaped to move out slightly.
Its kinda hard what im trying to explain, but if you look at the first traingle shape made, the hypotenuse of the whole shape bends in slightly, taking up the area of the square which becomes available when the shapes are moved to the position of the second triangle (if you look at the hypotenuse of the second triangle made by the shapes it bends out slightly, allowing for the extra square to be available).
Kinda hard to explain, but i hope you all get the drift of what im saying.
;D ;D ;D ;D ;D
Its kinda hard what im trying to explain, but if you look at the first traingle shape made, the hypotenuse of the whole shape bends in slightly, taking up the area of the square which becomes available when the shapes are moved to the position of the second triangle (if you look at the hypotenuse of the second triangle made by the shapes it bends out slightly, allowing for the extra square to be available).
Kinda hard to explain, but i hope you all get the drift of what im saying.
;D ;D ;D ;D ;D
Whats a hypotenuse when its at home ?
The answer is that both triangles are not the same size.
We can see the straight line along the bottom and the straight line up the right side are the same..
Its the angled line from top right to bottom left thats different.. On one it bends out slightly.. on the other it bends in slightly.. the slight bend is hard to spot unl;ess your told and affords enough free space on both to make up a whole square..
As they curve in or out then its most noticable half way down the line..Find a square half way down and you will see theres a slight difference in how much room a square takes up along the lines.. like I say.. enough to make up a whole square if ya add them together
The answer is that both triangles are not the same size.
We can see the straight line along the bottom and the straight line up the right side are the same..
Its the angled line from top right to bottom left thats different.. On one it bends out slightly.. on the other it bends in slightly.. the slight bend is hard to spot unl;ess your told and affords enough free space on both to make up a whole square..
As they curve in or out then its most noticable half way down the line..Find a square half way down and you will see theres a slight difference in how much room a square takes up along the lines.. like I say.. enough to make up a whole square if ya add them together
So what Harry is saying is that neither shape is a triangle, but a tetrahedron. The hypoteneuse (long bit) on one is concave and on the other is convex.Can all be proved by trig, which is where the Fibonacci guy comes in. The sequencing of the shapes along with our instant assumptions fools the eye. 
Went to Rhyddings too, who was your old maths teacher?