.Thanks, I didn't think thoroughly before posting this silly question, sorry.Petek said:
Lattice points on a circle are the points where the coordinates are both integers on a Cartesian plane with the center of the circle being at the origin.
The number of lattice points on a circle depends on the radius of the circle. If the radius is an integer, there will be 4 times the radius number of lattice points. If the radius is a fraction, there will be 4 times the numerator of the fraction of lattice points.
The equation for finding lattice points on a circle is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius.
Lattice points on a circle can be used in various scientific research, such as in crystallography, where they represent the positions of atoms in a crystal lattice. They can also be used in computer graphics and simulations to generate circular patterns.
Yes, lattice points on a circle have real-life applications in fields such as optics, where they represent the positions of diffraction grating lines, and in signal processing, where they are used to generate circular patterns for antenna arrays. They can also be used in navigation systems to calculate the distance and direction from a certain point on a circle.