Wikipedia:Reference desk/Archives/Mathematics/2012 November 10

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November 10

Conway puzzle

In conway puzzle, the diagram is wrong. This was pointed out 2 years ago, but nothing has happened. Does anyone here have the ability (and inclination) to redraw it? -- SGBailey (talk) 07:36, 10 November 2012 (UTC)

I think the diagram is actually correct, and that it is being misperceived. Looie496 (talk) 15:50, 10 November 2012 (UTC)

A slightly different angle would make it more obvious. the middle block touches the other two blocks at the corners. If you can describe it better then try editing the article to give a short description under the diagram. Dmcq (talk) 15:59, 10 November 2012 (UTC)

I suggest adding a normal projection onto the two vertical planes, to make it's location obvious. StuRat (talk) 20:52, 12 November 2012 (UTC)

The nearest block occupies positions (1,1,1), (2,1,1) and (3,1,1). The vertical block occupies (4,2,2), (4,2,3) and (4,2,4). The farthest block occupies (5,3,5), (5,4,5) and (5,5,5). The vertical block looks like it starts at (5,3,1) but it's an illusion - it starts at (4,2,2), because it is higher it looks from this perspective as if it's farther. -- Meni Rosenfeld (talk) 19:14, 13 November 2012 (UTC)

Euler axis/angle to Tait–Bryan angles (yaw, pitch, roll) conversion

I have a rotation vector for a camera where the length represents the angle and the direction the axis about which I rotate. While this is an elegant way to store rotation it is not very user friendly. One typically wants to know the yaw (pan), pitch (tilt) and roll of the camera. The article on rotation formalisms in three dimensions gives a bunch of conversion formulae for some cases, but not this one. I preferably do not want to go via expressing the rotation as a matrix (combining the first two conversions given), that seems cumbersome if both representations use just 3 values. 41.164.7.242 (talk) 13:20, 10 November 2012 (UTC) Eon

Axis-angle representation and Rodrigues' rotation formula may well help you here as they describe your way of representing a rotation, and conversion to a rotation matrix. I think using matrices will help you, essentially these are a way of storing three linear combinations of three values.--Salix (talk): 08:03, 11 November 2012 (UTC)

Thanks, so I'll go (Euler axis/angle) -> (rotation matrix) -> (yaw, pitch, roll). I don't care for the matrix though. 105.236.57.198 (talk) 14:06, 11 November 2012 (UTC) Eon