Saturday, March 14, 2015

How to draw a Pentagon

I was researching the easiest way to draw a pentagon with one side known. I think this method based on Euclid Elements book 6 proposition 30 is the easiest to remember. Which is how to cut a line into a long part and a short part medially. It's basically the problem of dividing a line segment into two unequal parts, such that the whole is to the long part as the long is to the short. That doesn't make a lot of sense until you draw the pentagon using the  golden ratio  of 1.61803398875.

Golden Ratio Formula

Basically all we need to remember is the number  1.618

With one side of the pentagon known, 292mm in this example. The long part of the whole is equal to 1.618 x 292 = 472.456.

Step 1:
Draw a line equal to the known side length. Then draw a perpendicular bisector.

Step 2:
Draw two arcs from center point A & B using radius 472.456.

 Step 3:
Draw two lines intersecting the perpendicular bisector where the arcs intersect.

Step 4:
Draw two arcs from center point A & C using radius 292.

Step 5:
Draw the lines that form the pentagon.

Step 6:
Draw perpendicular bisectors on each side of the pentagon for the profile rafter runs.

Step 7:
Draw the hip rafter run lines, radius lines of the pentagon.

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