What is a Lattice Point in Geometry?

[mateomy]

What exactly is a lattice point (in relation to geometry)? I seriously doubt my simple minded explanation suffices...

A lattice point is the meeting of the y and x integers on the Cartesian plane. And if that's in essence correct, is the way to find the number of lattice points found by simply finding the area of the shape?


Forgive my feeble mind.

 

[enricfemi]

Do you mean this:

http://mathworld.wolfram.com/PointLattice.html

 

[chaoseverlasting]

If you're finding out area, x and y don't need to be integers. Lattice points are something else altogether.

If you take a mesh you can see that there are horizontal and vertical wires which form the mesh. The points of intersection of these horizontal and vertical lines are called lattice points.

If you can now imagine a wire frame cube, each of the corners of the cube (where three lines meet) is a lattice point.

I think the x*y formula you're referring to has a different meaning in this sense.

If you have x horizontal lines and y vertical lines, then their points of intersection will be x*y in number.

This is because each horizontal line will have y points of intersection as it goes through all the vertical lines and there are x such lines. In this case, as you cannot have 1.5 lines, x and y must be integers.