Creating Geometric Shapes

Starting with a Vesica Piscis

• 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

• 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.

• 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.

• 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).

• 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.

• 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.

• 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.

• 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.

• 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