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Difference between revisions of "Lattice point"
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A '''lattice point''' is a [[point]] in a [[Cartesian coordinate system]] such that both its <math>x</math>- and <math>y</math>-coordinates are [[integer]]s. A lattice point is a point at the [[intersection]] of two or more grid lines in a regularly spaced array of points, which is a '''point lattice'''. In a [[plane]], point lattices can be constructed having unit cells in the shape of a [[square]], [[rectangle]], [[hexagon]], and other shapes. If not specified, a point lattice is usually a point in a square array.
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A '''lattice point''' is a [[point]] in a [[Cartesian coordinate system]] such that both its <math>x</math>- and <math>y</math>-coordinates are [[integer]]s. A lattice point is a point at the [[intersection]] of two or more grid lines in a regularly spaced array of points, which is a ''' point lattice'''. In a [[plane]], point lattices can be constructed having unit cells in the shape of a [[square]], [[rectangle]], [[hexagon]], and other shapes. If not specified, a point lattice is usually a point in a square array. Lattice points are complicated, so don't get stressed if you don't get it right away! Here's an example to help you to understand it better:
  
 
==Example==
 
==Example==
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A point lattice is constructed by plotting all of the points <math>(a,b)</math> such that <math>a,b \in \Z^{+}</math>. How many points in the point lattice lie on the line <math>y = -3x + 8</math>?
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A point lattice is constructed by plotting all of the points <math>(a,b)</math> such that <math>a</math> and <math>b</math> are positive integers. How many points in the point lattice lie on the line <math>y = -3x + 8</math>?
  
 
==Solution==
 
==Solution==
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[[Category:Geometry]]
 
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[[Category:Definition]]
 
[[Category:Definition]]
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[https://artofproblemsolving.com/wiki/index.php/TOTO_SLOT_:_SITUS_TOTO_SLOT_MAXWIN_TERBAIK_DAN_TERPERCAYA TOTO SLOT]

Revision as of 15:58, 19 February 2024

This article is a stub. Help us out by expanding it.

A lattice point is a point in a Cartesian coordinate system such that both its $x$- and $y$-coordinates are integers. A lattice point is a point at the intersection of two or more grid lines in a regularly spaced array of points, which is a point lattice. In a plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, and other shapes. If not specified, a point lattice is usually a point in a square array. Lattice points are complicated, so don't get stressed if you don't get it right away! Here's an example to help you to understand it better:

Example

A point lattice is constructed by plotting all of the points $(a,b)$ such that $a$ and $b$ are positive integers. How many points in the point lattice lie on the line $y = -3x + 8$?

Solution

Notice that $y > 0 \implies -3x + 8 > 0 \implies x \leq 2$. So, $(1,5)$ and $(2,2)$ are the only such points, giving us $\boxed{2}$ points.

~advanture

See Also

TOTO SLOT

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