114 Lattice points
Exercise
1.Consider the lattice triangleABCwithA=(0,0),B=(36,15)
andC=(16,30). Calculate the lengths of the sides of the triangle.
What is the area of the triangle? How many boundary and interior
points does it have?2.Repeat the same for the lattice triangleABCwithA=(0,0),B=
(24,45)andC=(48,55).3.Give an example of a lattice triangle whose side lengths are 13, 14,- What is the area? How many interior and boundary points does
the triangle have?
4.There is a list ofnstatements. Fork =1, 2, ...,n, thek-th
statement reads:The number of false statements in this list is greater thank.Determine the truth value of each of these statements.5.Solve the equation
⌊
x+1
2⌋⌊
x+2
3⌋⌊
x+3
4⌋
= 819.
6.Write 97 as a sum of 2 squares and find the lattice points on the
circle of radius 97.