Superlesson
Project 5-2
Foundations of Algebra and Geometry
Chapter 5, Spatial Relations
Geometric designs appear in the works of artists as diverse as Native American weavers and window designers of the Middle Ages.
Part A, Triangles, Parallelograms, and Trapezoids
1. Using the Internet, answer the following questions.
a. Look at the Navajo "Gallup Throw Rug". The design is made from three identical (or nearly identical) geometrical patterns. Draw a careful sketch of the middle of the three patterns.
b. Draw a horizontal line of symmetry through the middle of the pattern. Then identify each polygon in the figure using "T" for triangle, "TZ" for trapezoid, and "P" for parallelogram.
c. At the bottom of the pattern is a dark triangle with a base of about 2 in. and a height of about 1 in. On its top vertex balances a dark polygon. Find the area of the triangle. Then estimate the area of the polygon. Explain how you made your estimate.
d. Use triangles, parallelograms, and trapezoids to create a simple symmetrical pattern. Use at least two of each type of polygon in your pattern. Draw the line or lines of symmetry.
Part C, Making Connections
2. The Cathedral at Chartres, France, was built during the 12th Century. The cathedral's stained glass windows are masterpieces of medieval art. Study the Window at the main entrance to the cathedral.
a. The figure in the center circle of the window is life-size. Estimate the radius of the entire window.
b. Based on your estimate, what is the circumference of the window? What is the area? Use 3.14 for π.
c. Around the outside of the window are 12 approximate semi-circles (blue in the figure). Each contains a circle (red). Estimate the diameter of each semi-circle. Explain how you made your estimate.
d. Estimate the diameter of each red circle.
e. Compare the diameter of each red circle with the diameter of the entire window.
