Foundations of Algebra and Geometry
Chapter 5, Spatial Relations
Artists and architects use mathematics both to design and to create their works.
Part B, Comparing Sizes
1. You can use the Web to look at artists' works and discover how they are able to represent relative size.
a. Study the painting The Annunciation by the Italian Renaissance painter Leonardo da Vinci. Find the horizon line, the vanishing point, and orthogonal lines. Then click on the buttons to see if you were right.
b. Study the painting Little Street by the Dutch painter Jan Vermeer. Explain how to find the vanishing point.
c. If the artist was across the street from the building, on what floor would you say he was? Explain your choice.
d. Study the drawing of Six cubes. Name ways that, along with perspective, an artist can use to create the illusion of three dimensions.
e. How has the artist made the Sculpture behind the collonade appear larger than it really is?
f. Copy the rectangles on a sheet of paper. Then complete the drawing in a way that shows that the rectangle on the left is an object in the background which is larger than the object represented by the rectangle on the right (in the foreground).
Part D, Making Connections
2. More than three thousand years ago, sculptors of the Olmec culture on Mexico's Gulf Coast carved some of the most massive heads that have ever been created. Learn more about the Olmec heads and the people who carved them.
a. One of the heads at the Olmec site of San Lorenzo is shown from four angles. It is 6 ft tall. Estimate the width and depth of the head to the nearest foot.
b. Assume that the stone from which the head was carved was a rectangular prism with the dimensions in a. Sketch the prism showing cubic units measuring 1 ft x 1 ft x 1 ft.
c. What was the volume of the prism?
d. Estimate the weight of the head, if each cubic foot of the material it is made from weighs 150 lb.