New Year Puzzle: In a magic square, the sum of numbers on each row, each column, and each diagonal is the same. Fill in the numbers in the following squares to make them become magic squares.
Today let us look at the following two tricky questions:
Question 1: Among these two numbers 4444 x 55555 and 5555 x 44444, which one is smaller? which one is larger?
Question 2: How about 5000 x 5000 and 4999 x 5001, which one is smaller? which one is larger?
Using compass and straightedge, we can construct the midpoint of a line segment, and we can easily divide a line segment into, say three equal parts. The question is, is it possible to do these constructions with just the compass.
The answer is "yes"! Indeed, it is possible to construct the midpoint of a line segment, and it is possible divide a line segment into a number of equal parts by using the compass alone. How amazing is that?! Today, we will look at these constructions!
Normally in geometric construction problems, we use straightedge and compass. Today, we will look at an unusual type of construction problems where we are only allowed to use compass.