Whilst we have seen that we can create a pentagon from within the Golden Triangle, it is sometimes convenient to create a pentagon from scratch. Below we will cover how to create a Pentagon using only a Straightedge and Compass. It is my view that Geometry, at least in basic form, should be independent of numbers or any other units. It should focus on proportion and form and is, in effect, scale invariant.
STEP 1: Draw a vertical line.
STEP 2: Draw a circle on the vertical line.
STEP 3: Find the midpoint and draw a line from the centre of the circle to the right.
STEP 4: Find the midpoint of the horizontal line.
STEP 5: Draw a circle with radius equal to quarter the original circle so that its perimeter passes though the centre and is tangential to the outer circle.
STEP 6: Draw a line from the bottom so that it passes through the centre of the inner circle and touches the perimeter on the far side.
STEP 7: Use this length to draw an arc which is tangential to the inner circle at the point marked.
STEP 8: Using your compass, draw an arc with radius equal to the distance from the top of the original circle to where this new arc crosses the original circle.
These are the second and third points of your pentagon.
STEP 9: Taking your compass and placing it on the two points we just created, mark off arcs which are equidistant. If you have been careful in the construction you should be able to create a five petalled flower from these circles as seen in the image attached.
STEP 10: Finally, connect the points we have marked and create your regular pentagon. Marked in bold in the image attached.
