This has irked me because those who don't know anything about touch screen technology don't seem to understand that 'taps' are actually small swipes. The sensors have a far higher resolution than your fingers ability to stay still, so the system rounds down small 'swipes' based on x time over y legnth into what the user meant as taps. It senses the touch down (start point) and the touch up (end point) which may or may not be a zero length swipe or even a small distance swipe.

At a a hardware level and strictly speaking, taps are swipes, Apple just abstracted tiny swipes away into a tap function.

It irks me that some people who don't know anything about the physics of touch screen technology and don't seem to understand that 'taps' are actually small changes of capacitance of an array of capacitors. [0]

At a a physics level, and strictly speaking, taps and swipes don't exist.

Patents are pragmatic and full of abstractions. You are not required to specify a patent at every level of abstraction all the way down to its mathematical or quantum properties.

(I have to read a number of mechanical patents each week as part of my job).

[0] http://en.wikipedia.org/wiki/Capacitive_sensing

This is very interesting, thanks for the perspective.

No. A line (or line segment, as was clearly meant) has a non-zero length by definition. If it had a zero length, it's not a line anymore. It is a point.

We only get to argue that once :) http://news.ycombinator.com/item?id=4085613

Even in math, a line goes through two distinct points. You can't define a line with just a single point. And a segment is a piece of a line with a measurable length.

So, in English or in Math, the answer is no.

This has been discussed here before, but no, in common English usage, a point is not a zero length line. Maybe in mathematics, but not in everyday English as the judge was using the terms.

Don't take my word for it, draw a dot on a piece of paper and ask ten non-geeky people, "Is this a line?" :-)

Actually, it's not true in mathematics either. A line is something which has one and only one dimension, and a point is something which has no dimension. A zero length line would not be a line, as it would have fewer than one dimension. So, there is no such thing as a zero length line.

Lines are infinitely extended. Maybe you meant a line segment. Line segments have a minimum of 2 points.

Line segments have a minimum of an infinite number of points.

I assume they meant two end points (which cannot be the same point) to which the line segment is bound.

That's one of the paradoxes of Euclidean geometry, where a line/line segment is made up of an infinite number of points, but those points have no length or width, and infinity times 0 is still 0, so technically a line should have no length. Clearly, it does not.

Infinity times zero isn't zero, it's undefined.