Tag Archives: arithmetic

Multiplying points in the plane

It is easy to add points in the plane “coordinatewise”, that is, by writing (x,y)+(z,w)=(x+z,y+w). This even has a very nice geometric interpretation: completing the parallelogram with first three corners (0,0), (x,y), and (z,w). But it isn’t easy to multiply points because the simple rule (x,y)*(z,w)=(xz,yw) doesn’t allow division. In this activity we looked for something better. Continue reading Multiplying points in the plane

Patterns in the Fibonacci numbers

This special discussion was led by Zach Teitler and concerned patterns in the famous Fibonacci sequence of numbers. This sequence begins with 1,1 and then each successive number is obtained by taking the sum of the previous two. Here are the next few in the list:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169

Which Fibonacci numbers are even? Which ones are odd? Which Fibonacci numbers are divisible by 3? In this discussion we answered these questions and many more. Continue reading Patterns in the Fibonacci numbers