The most familiar form of the pentagon is the regular pentagon. Its sides are of equal length and each of its interior angles is 108 degrees. Artists like Albrecht Dürer, along with numerous mathematicians, have proposed methods of constructing pentagons. Using graph paper simplifies the process, making it easy for anyone to master the shape.

Place the point of the compass on the corner of one of the squares near the centre of the graph paper.

Move the pencil away from the point to a distance of 8cm.

Draw a circle and mark the centre with a "1."

Follow the line on the graph paper up from "1" to the top of the circle. Mark that point with an "A."

Draw a line connecting "1" and "A."

Follow the horizontal line that leads right from "1" to the edge of the circle. Mark that point with a "B."

Mark a point with a "C" halfway across the line between "1" and "B."

Place the point of the compass on "C." Move the arm so the tip of the pencil touches "A." Draw a circle.

Follow the horizontal line left until it intersects with the new circle. Mark that point with a "D."

Place the point of the compass on "A." Move the arm so the tip of the pencil touches "D." Draw a circle.

Mark the points where the new circle meets the very first circle with an "E" and an "F."

Place the point of the compass on "E." Move the arm so the tip of the pencil touches "A." Draw a circle.

Mark the point where that circle touches the original circle with a "G."

Place the point of the compass on "F." Move the arm so the tip of the pencil touches "A." Draw a circle.

Mark the point where that circle meets the original circle with an "H."

Draw a heavy line between "A" and "F" using the ruler to keep it straight. Then draw a heavy line between "F" and "H," "H" and "G," "G" and "E," and "E" and "A."

### Things you need

- Graph paper
- Compass
- Pencil
- Ruler

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