Investigations
2 

Investigate
the number of diagonals of a polygon.
Change the
number of sides of the polygon and then draw the diagonals.


Investigate the number of lines joining dots round a circle.
Change the
number of dots and then draw the diagonals.
Polygon,
Mystic Rose and the famous Handshakes problem and work on triangular numbers
all go hand in hand!


The mean crunching
machine likes working out the mean of two numbers. Input two numbers and
the machine will generate a sequence of numbers in which the next term is
the mean of the previous two terms.
For example: 2, 5, 3.5, 4.25, 3.875, 4.0625 .......
The sequence
will converge to a particular value which the machine will spit out.
Can you predict what the final number will be for any pair of starting numbers?
The graph will help you. 

The number crunching machine divides and adds over and over again.
For example, start with 37 and divide by 5 and add 1. The sequence of
numbers will converge to a final number which the machine will spit out.
Try
other starting numbers, does it matter what number you start with?
Divide by 4 instead of dividing by 5, what difference does that make?
Input
any number and predict what will come out.
A little knowledge of the equivalence of decimals and fractions is needed.
