USING A PAIR OF COMPASSES :
if you start with a golden rectangle (see golden rectangle) shown yellow below
Place the point of your compasses on one corner and open them so they span the shorter
side of the rectangle and draw a circle centred on that corner.
Next, keeping your compasses as wide as the shorter side, draw another circle centred on
the corner at the other end of the longer side of the rectangle.
If you join the centres to the point where the circles cross (outside the rectangle) it
should look something like this . . .
if you start with a golden rectangle (see golden rectangle) shown yellow below
Place the point of your compasses on one corner and open them so they span the shorter
side of the rectangle and draw a circle centred on that corner.
Next, keeping your compasses as wide as the shorter side, draw another circle centred on
the corner at the other end of the longer side of the rectangle.
If you join the centres to the point where the circles cross (outside the rectangle) it
should look something like this . . .
Now take your compasses and open them to span the longer side of the golden rectangle.
Place the point of your compasses at the point where the lines you've just drawn meet (the place
where the circles cross also) and draw a larger circle.
Now draw straight lines which join the centres of the smaller circles to the points where the large
circle crosses the smaller circles (the points within the rectangle) and finally join these points
together with a straight line.
If you've done that, you've drawn a pentagon.
Place the point of your compasses at the point where the lines you've just drawn meet (the place
where the circles cross also) and draw a larger circle.
Now draw straight lines which join the centres of the smaller circles to the points where the large
circle crosses the smaller circles (the points within the rectangle) and finally join these points
together with a straight line.
If you've done that, you've drawn a pentagon.
WITHOUT COMPASSES:
you can take a square of stiff card and cut it in two to make two 2 x 1 rectangles.
Now cut one rectangle in half corner to corner giving you two right angled triangles.
Draw a nice long straight line on a piece of paper.
Mark a starting point on the line and place the hypotenuse (the longest side) of one of your
triangles on the line so that you can mark a distance along the line from your starting point equal to
the length of the hypotenuse.
From this new mark measure and mark the length of the shortest side.
You have now marked a length equal to the longest side plus the shortest side along the line.
Now take your two triangles and place the right angled corners at either end of the line so that
the most acute (pointiest) corners meet. Join the ends of your line to this meeting point.
Now fold your paper so that the ends of the length you marked earlier (equal to the long plus short
sides) meet this should give you a fold passing through the point where the triangles met and the
centre of the length . . .
Now you place the rectangle of card (remember that ?) so that one longer side sits along the fold
on the unmarked side of the first line and one shorter side sits along that (first) line, and take
one of your triangles and place it so that the right angled corner is touching the long side of
rectangle away from the fold and the most pointy corner is touching the end of the long plus short
length on the same side of the fold.
Draw a straight line from that end of the length to the point where the right angle touches the
rectangle.
Do it again on the other side of the fold.
Join the ends of those lines together with another straight line.
And that (if you've managed to follow it) should make a pentagon . . .
you can take a square of stiff card and cut it in two to make two 2 x 1 rectangles.
Now cut one rectangle in half corner to corner giving you two right angled triangles.
Draw a nice long straight line on a piece of paper.
Mark a starting point on the line and place the hypotenuse (the longest side) of one of your
triangles on the line so that you can mark a distance along the line from your starting point equal to
the length of the hypotenuse.
From this new mark measure and mark the length of the shortest side.
You have now marked a length equal to the longest side plus the shortest side along the line.
Now take your two triangles and place the right angled corners at either end of the line so that
the most acute (pointiest) corners meet. Join the ends of your line to this meeting point.
Now fold your paper so that the ends of the length you marked earlier (equal to the long plus short
sides) meet this should give you a fold passing through the point where the triangles met and the
centre of the length . . .
Now you place the rectangle of card (remember that ?) so that one longer side sits along the fold
on the unmarked side of the first line and one shorter side sits along that (first) line, and take
one of your triangles and place it so that the right angled corner is touching the long side of
rectangle away from the fold and the most pointy corner is touching the end of the long plus short
length on the same side of the fold.
Draw a straight line from that end of the length to the point where the right angle touches the
rectangle.
Do it again on the other side of the fold.
Join the ends of those lines together with another straight line.
And that (if you've managed to follow it) should make a pentagon . . .