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# harey

Member Since 24 Jul 2013
Offline Last Active Today, 03:20 PM

### In Topic: Relatively prime

28 April 2015 - 04:32 PM

100% loss

Spoiler for

### In Topic: Airplane with or without wind

23 March 2015 - 08:34 PM

by ignoring travel perpendicular to the direction of the wind, where it has no effect on the plane's speed

Even here, it increases the travel time.

A non-zero component of the plane's speed is used to compensate the wind.

### In Topic: Illuminating a Convex Solid At Higher Dimensions

29 January 2015 - 01:00 PM

This assumes that a point is (at least partially) illuminated if a straight line can be drawn uninterrupted between it and a light source.

### In Topic: Sides = Diagonal

29 January 2015 - 12:52 PM

Spoiler for I think quite a lot...

### In Topic: Illuminating a Convex Solid At Higher Dimensions

27 January 2015 - 08:54 AM

These thoughts suggest what I think is an interesting question:

for each N, find an example of a convex solid that can be illuminated with the fewest lights.

That's the start to the original question

What bothers me with points and lines:

We do not illuminate an object as such, we illuminate it's surfaces. (Already a problem with a sphere and alike: in this case, we may not consider the sphere has one surface, but infinity.) If a surface is illuminated, does it imply that it's edges and vertexes are illuminated, too? One answer would be that this question does not have a sense, but it seems a little week as argument.