## Monday, August 20, 2012

### A little puzzle

I set my cell phone display-up on a flat surface (a table) and I turn on Google Maps.  I rotate the phone so that it "points north" (that is, the phone is on its back, the display is facing up, the top edge of the display is facing north, the left and right edges are parallel to rotation of the earth).

On Google Maps there is a little arrow-shaped icon that represents the position and orientation of the phone.  Naturally, it points at the top of the map, which is at the top of the display, and therefore the little arrow points north as well.

If I now rotate my phone slightly clockwise, what does the arrow do?

a) move in the same direction as the phone (clockwise)
b) move in the opposite direction as the phone (counter-clockwise)
c) not rotate

and how fast?

a) twice the speed as the phone rotates
b) exactly the same speed as the phone
c) half the speed as the phone rotates
d) it doesn't rotate

1. My guess would be that it would turn clockwise twice as fast (as in, you turn the phone 10 degrees, the arrow would turn 10 degrees relative to the phone, for 20 degrees total).

What I'm getting is significant lag so it isn't clear what the answer is.

2. I thought that the pointer is relative to the map (and controlled via successive GPS measurements) and totally agnostic to the physical orientation of the phone. So my guess was that it doesn't move.

I tried it, though, and my guess is wrong -- it moves. So today I learned there's a compass in my phone.

3. The phone turns by a certain angle clockwise, and is now pointing towards, say 10deg north east. the map on the phone also rotates by the same (north is still top). the pointer should move by twice as much to keep the correct orientation w.r.t the map.
Wish i had a phone with that feature so i could check :D

4. It depends on the frame of reference, and there are at least three: the Earth, the phone, and the map. In the phone frame of reference, the arrow continues to point to the top of the phone.