Have A Look At This Article, Please.

[Tilly2]

http://www.bbc.co.uk/news/magazine-29688355

The angle on the cube answer is really bugging me. I understand the isoceles triangle answer but if it's a cube made of squares, why isn't the angle two bisections ie, 90 degrees?

[sandyRoe]

60°

[sandyRoe]

If you joined the two unconnected end of the red lines would you have an equilateral triangle?

[Peter Pedant]

no it has to be 60' because.....

if you join the two ends of the red lines so that if forms a triangle
then a moments reflection will reveal that the sides are equal ( all three equal and that means equilateral triangle ) and so the angle is 60'

[sandyRoe]

each of the sides being the length of the diagonal

[Svejk]

I knew the hole in an metal ring got bigger, tilly. ;o)

[Svejk]

and before you tell me off, I didn't type AN above^.

[Peter Pedant]

The sides of the said triangle are all diagonals and are therefore root(2) times the unit length of the cube

and yes I had my Aha ! moment as described in the article

[sandyRoe]

2 What should the question be? Anybody any ideas?

[Tilly2]

I know it's 60 degrees . As I said, I do understand the answer.

But...is all the sides are squares, which they are, a diagonal line drawn from corner to corner would bisect thr right angle. Therefore, two bisections would add up to another right angle.

[Svejk]

I know what you mean, till. ;) but don't know why that doesn't apply.

[Peter Pedant]

I knew that Svejk - it made sense....

the hole in the doughnut q came up regularly in Phys A Level in the sixties.

If you heat a cartwheel rimmy thing to fit over a wooden cartwheel (!) well it was 50 y ago, then the radius expands linearly ( as well as the circumference, since they are linearly related )

[Tilly2]

Sandy, something like, 'If I asked ypur companion which road to take, what would he say?

Then take the other route.

[Peter Pedant]

The angle tills you describe goes up in the air ( makes a tent shape)
and the angle they want is between the two lines

[Svejk]

if you did the same with 2 flat(side by side) squares, you'd have a 90d angle and 2 45's.

[Tilly2]

Exactly, sweety.

The question asked would have to be, 'If I asked your companion if this was the right road ( pointing to one) what would he say?'

Then take the other road.

[Tilly2]

Time to make a move. Thanks for trying to help.

[Tilly2]

Equilateral triangle, I meant. Not isosceles.

Still don't get it. Time to blow the cobwebs out of my head.

[sandyRoe]

The fact that the red lines bisect right angles is irrelevant. You're really looking at an isosceles triangle 'buried' in the cube.

[Tilly2]

Sandy it's an equilateral triangle and the lines are on the surface. I realyy do understand 60° but still can't figure why it's not 90 °

[sandyRoe]

It is an equilateral triangle. (don't know where I got isosceles from) and the red lines aren't on the same plain.