Spirals occur frequently in nature in flowers, seashells and even pineapples. Spiral is defined as a curve on a plane that turns endlessly outward or inward (or both). There are many types of spirals. Because of its repeated occurrence in geometry, the Golden Spiral is perhaps the most recognised. The Golden Spiral is derived from the Golden Rectangle, which is made up of the Golden Ratio, or phi. Ancient Greeks considered phi to be a number of perfection, often incorporating it into their architectural designs. The Fibonacci spiral is very similar to the Golden Spiral. A basic Fibonacci spiral uses a repeated pattern of Fibonacci numbers as coordinates and is simple to graph.
- Skill level:
- Moderately Easy
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Things you need
- Graph paper
Draw a horizontal line that is 13 squares long. Count up eight squares and draw another horizontal line 13 squares long, directly above the one you just drew. You should now have two parallel lines.
Draw vertical lines connecting the end points of the horizontal lines, forming a rectangle.
Count from the bottom left corner of the rectangle eight squares to the right. Draw a line from this point up to the top line of the rectangle, creating a large square that is eight squares long and eight squares high.
Count from the top right corner of the rectangle five squares to the left. Draw a line that is five squares in length down from this point, and then draw another line five squares to the right, forming a large square.
Count from the bottom right corner of the rectangle three squares to the left. Draw a line up from this point that is three squares in length, and then draw another line three squares to the right, forming a square.
Count from the bottom right corner of the original rectangle three squares to the left. Count up two squares. Draw a line from this point to the left that is two squares in length. This line should touch the line drawn for the 8 x 8 square.
Draw a line separating the two small squares located just above the 2 x 2 square and just below the 5 x 5 square. You should now have six squares measuring 8 x 8, 5 x 5, 3 x 3, 2 x 2, 1 x 1 and 1 x 1.
Draw a dot at the bottom left corner of the original rectangle. From this point, draw a continuous line to the top right corner of the 8 x 8 square, then to the bottom right corner of the 5 x 5 square, then to the bottom left corner of the 3 x 3 square, then to the top left corner of the 2 x 2 square, then to the top right corner of the closest 1 x 1 square, then to the bottom right corner of the remaining 1 x 1 square. Curve the line as you draw around the graph to create the appearance of a continuous spiral rather than separate lines joined together.
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