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Nir Dahan Inner circle Munich, Germany 1390 Posts |
I tried to post this last night but it failed for some reason.
I am also sure that most of you know this already but maybe not in a limerick form... here goes: On two sides of a cube they are drawn two diagonals as depicted and shown they meet in a corner but can you discover the angle they form - that's unknown Nir Click here to view attached image. |
honus Veteran user 354 Posts |
Nobody's done this? Okay, I'll have a go.
Since the two lines drawn are diagonals of the cube, they are equal in length. Connect the two corners they are drawn to; this forms a triangle, with the third side also equal to a diagonal of the cube. Since this makes an equilateral triangle, and equilateral triangles are equiangular, the given angle must be 60 degrees. |
Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
Confused here (about usual)
Each diagonal splits its corner at forty five degrees. An angle is a plane feature. The two planes are adjacent on the cube. But the two angles are not in the same plane and so can't be added. If however we CUT the cube along the diagonal lines on the adjacent planes, the leftover polygon does appear to have an equilateral triangular face.
...to all the coins I've dropped here
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TomasB Inner circle Sweden 1144 Posts |
Jonathan, the two drawn diagonals are in the same plane. That plane is not parallell to any of the sides of the cube. Any two non-parallell lines that have a point in common define the plane they are in.
/Tomas |
Nir Dahan Inner circle Munich, Germany 1390 Posts |
The diagonals meet, as one sees
connect their other ends if you please the triangle that came has all sides the same so the angle is 60 degrees |
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