You may also like

problem icon

GOT IT Now

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

problem icon

Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

problem icon

Reverse to Order

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

Pick's Theorem

Stage: 3 Challenge Level: Challenge Level:1

When the dots on square dotty paper are joined by straight lines the enclosed figures have dots on their perimeter ($p$) and often internal ($i$) ones as well.

Figures can be described in this way: $(p, i)$.
For example, the red square has a $(p,i)$ of $(4,0)$, the grey triangle $(3,1)$, the green triangle $(5,0)$ and the blue shape $(6,4)$:

This text is usually replaced by the Flash movie.

Each figure you produce will always enclose an area ($A$) of the square dotty paper.

The examples in the diagram have areas of $1$, $1 {1 \over 2}$, and $6$ sq units.

Do you agree?

Draw more figures; tabulate the information about their perimeter points ($p$), interior points ($i$) and their areas ($A$).

Can you find a relationship between all these three variables ($p$, $i$ and $A$)?

Click here for a poster of this problem.