Problem of the Week #36: Monday September 11th, 2023 As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems. Please register for an account if you would like to join the discussion below or share your own problems.
Consider drawing squares using the lattice points in a grid as vertices, as shown below:
a). What is the area of the square drawn in the example?
b). How many squares are there in the grid above that have the same area as the example?
c). How many rows and columns of lattice points are needed to contain a square of area 13?
d). How many lattice points are there inside a square of area 13?
e). How many different areas can squares have in the grid above?
f). How many squares of any sizes can be drawn in the grid above?
g). How many different areas can squares have in an nxn grid, where n is a natural number?
h). How many squares of any sizes can be drawn in an nxn grid, where n is a natural number?
i). Share your own problem inspired by this one.
j). Give one of these questions to a friend/colleague/student/family member to start a mathematical discussion.