A introduction to how patterns can be deceiving, and what is and is not a proof.

An AP rectangle is one whose area is numerically equal to its perimeter. If you are given the length of a side can you always find an AP rectangle with one side the given length?

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

The diagram shows a 5 by 5 geoboard with 25 pins set out in a square array. Squares are made by stretching rubber bands round specific pins. What is the total number of squares that can be made on a. . . .

Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at. . . .

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.