The document provides instructions for creating several geometric shapes and patterns using a compass and straightedge. It describes how to make a vesica piscis, equilateral triangle, golden rectangle, regular pentagon, regular hexagon, and 30-degree diagonal grid by following steps such as drawing lines of specific lengths and angles and constructing arcs and intersections between lines and circles. The overall purpose is to demonstrate techniques for drafting geometric forms.

1. Creating Geometric Shapes
Starting with a Vesica Piscis

2. • 1. Draw a 1 7/8” line
centered in the first
rectangle (draw 15/16” on
either side of the center).
• 2. Mark a point at 5/16”
on either side of the center
of the line.
• 3. Place your compass
point on each point on the
line and draw a circle of
5/8” radius (open the
compass to the end of the
line). Label the drawing.
• Creating a Vesica Piscis

3. • Creating an
Equilateral Triangle
• 1. Draw a 24’-0” line at
1/16”=1’-0” scale centered
left to right in the rectangle,
15/16” up from the bottom
of the rectangle.
• 2. Place your compass point
on each end of the line,
opened to the length of the
line, and draw arcs that
intersect above the line.
• 3. Draw lines from the arc
intersections to each end of
the base line with a 60˚
triangle. Label the drawing,
indicate the scale.

4. • Creating a
Golden Rectangle
• 1. Draw a 10’-0” square at
1/8”=1’-0” scale, centered
vertically on the rectangle
and 7/8” in from the left side.
• 2. Divide the square in half,
place your compass point on
the midpoint of the bottom
line of the square and open it
to the top right corner of the
square.
• 3. Draw an arc down to the
base line of the square and
extend the rectangle to it.
• 4. Draw a vertical line up to
the height of square and
close the (golden) rectangle.

5. • Creating a
Golden Rectangle
• 5. Draw a light diagonal from
the lower left to the upper
right corner of the rectangle.
• 6. Where it crosses the right
side of the original square,
draw a horizontal line to the
end of the rectangle, creating
a second square.
• 7. Draw a second light
diagonal from the lower right
to the upper left of the new,
smaller, rectangle (this
diagonal should be
perpendicular to the original
diagonal).

6. • Creating a
Golden Rectangle
• 8. Where the second
diagonal crosses the second
square, draw a vertical line to
the edge of the rectangle,
creating a third square and
rectangle.
• 9. A fourth and fifth (and six
and seventh…) set of squares
and rectangles can be created
by the intersections of the
diagonals and rectangles.
• 10. A golden spiral can be
created by drawing arcs of
circles within the sequence of
squares.
• Label the Golden Rectangle
and the scale.

7. • Creating a Regular
Pentagon from a circle
inscribed within a square
• 1. Lightly draw a 6’-0” square,
centered in the rectangle, at
¼”=1’-0” scale, and lightly
inscribe a circle within that
square with your compass.
• 2. Lightly draw a diagonal
from the lower left corner of
the square to the midpoint of
the top of the square.
• 3. Place the point of your
compass at the midpoint of
the top of the square and
open it to where the diagonal
crosses the diameter of the
circle.
• 4. Draw an arc that intersects
the circle in two places.

8. • Creating a Regular
Pentagon from a circle
inscribed within a square
• 5. Place the point of your
compass on the intersections
of the arc with the circle and
draw arcs intersecting the
circle at the bottom of the
square.
• 6. Connect the points where
the arcs intersect the circle
with chords (lines) that will
form a regular pentagon.
• 7. You can connect each of
the vertices to each other to
construct a pentagram
(composed of golden
triangles).
• 8. Label the Regular
Pentagon and the scale.

9. • Creating a Regular Hexagon
• 1. Draw a regular hexagon, 8”
per side, at 1 ½”=1’-0” scale,
centered in the rectangle.
• 2. From your center, draw
three 16” (at scale) lines, all
centered: one 30˚ line
sloping right, one 30˚ line
sloping left, and the third line
vertical.
• 3. Connect the ends of these
lines with your 30˚ triangle
with heavier lines.
• 4. By heavying every other
line from the perimeter to
the center, an isometric of a
cube is created.

10. • 1. Draw a 12 inch “x”, at
3”=1’-0” scale, centered on
the rectangle, with a 30˚
triangle.
• 2. Draw a box around the “x”.
• 3. Measure off 1” (at scale)
increments along the two
diagonals.
• 4. Draw the 1” grid with your
30˚ triangle (or adjustable
triangle set at 30˚) along both
diagonals.
• 5. Accentuate the diamond
(rhombus) by heavying up the
lines that connect the centers
of the box.
• Drafting a 30˚ Diagonal Grid