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## Math Activity: Perspective

### Math Enrichment Activity

Italian
Street Scene for Theatrical Set
engraving on paper
11 1/16 in x 16 7/16 in (28.1 cm x 41.75 cm);18 in x 22 in (45.72 cm x 55.88 cm)
Museum purchase for the Paul Leroy Grigaut Memorial Collection
Kanō School
Temple in the Mountains
hanging scroll, ink on paper
32 11/16 in x 5 3/16 in (83.03 cm x 13.18 cm)
Gift of Mr. and Mrs. Province M. Henry
Jacob Matham
Landscape with Shepherds Watching the Flight of Icarus and Daedalus
engraving on paper
17 1/2 x 14 3/16 in. (44.4 x 35.9 cm)
Museum Purchase
Urs Graf
Christ Before Pilate, from The Passion of Christ I
woodcut on thin, slightly textured beige paper
8 3/4 x 6 3/8 in. (22.2 x 16.1 cm);19 5/16 x 14 3/8 in. (49 x 36.5 cm)
Museum Purchase made possible by the Friends of the Museum of Art

This activity could take place in the museum or in the classroom. It is differentiated so educators can decide how best to adjust the level of instruction to fit students' abilities.

Objective: Students will become familiar with vocabulary (horizon line, orthogonal, atmospheric perspective, linear perspective, scale). They will make connections between linear perspective, graphing, and slope.

Elementary:

1. Begin by introducing vocabulary related to perspective. Ask students to situate the word "horizon." Perhaps they have heard it in relation to sunrise or sunsets, or when they look at the sky. Reinforce that horizon line is where the land meets the sky. Older students can discuss how it can be low or high, and typical composition in design is to aim for the rule of thirds - composing with either sky or land as 2/3 of overall composition.

2. Introduce the term orthogonal - diagonal lines that run towards the vanishing point (point of focus where objects seem to disappear).

3. Study images of atmospheric and linear perspective (such as Temple in the Mountains or Landscape with Shepherds) and explore how the artist uses techniques to make objects seem to be farther away (mist, faded color, and smaller scale).

4. Find an object in the foreground of an image, such as a tree. Measure it, either precisely or using estimation, and then measure a tree in the middle ground or background. Why are those trees smaller? Ask students to do the same with tangible objects. For example, measure the height of a classmate or a desk. Then place that person or object at the end of a hallway and measure perceived height. Discuss the nature of scale in relation to perspective.

Middle School:

1. Introduce the topic in a similar way, but incorporate terms such as vertical, horizontal, and parallel. Explain how orthogonal lines are truly parallel. They never intersect, although linear perspective makes it appear that they will. In reality, parallel lines have the same Y intercept and same slope.

Extension: Calculate where to place a movie projector in a room in order to achieve optimal focus.

High School:

1. Review terminology such as: horizon line, vanishing point, orthogonal, atmospheric perspective, linear perspective, vertical, parallel.

2. Study a drawing that features linear perspective, such as Christ Before Pilate. Does the perspective seem accurate? Sometimes artists did not correctly calculate the correct angle, especially early in the Renaissance, when artists were rediscovering dimensional drawing. Ask students to: 1) find the error if it exists 2) consider how the perspective would change if the orthogonal lines were not vertical or parallel.

3. Place image on a coordinate plane and determine the slope of line.

#### Part of 1 Learning Collection

Math + Art: A List of Possibilities
<p>Geometry, Mapping, Pattern, Perspective, Perspec...

Math Activity: Mapping
<p>Math Enrichment Activity</p>

Math Activity: Early Computing and Weaving
<p>Math Enrichment Activity</p>

Math Activity: 2D Geometry
<p>Math Enrichment Activity</p>

Math Activity: Golden Section
<p>Math Enrichment Activity</p>

Math Activity: Interpret and Compare Data
<p>Math Enrichment Activity</p>

Math Activity: Pattern
<p>Math Enrichment Activity</p>

Math Activity: Perspective
<p>Math Enrichment Activity</p>

Math Activity: Proportion
<p>Math Enrichment Activity</p>

Math Activity: Symmetry
<p>Math Enrichment Activity</p>

Math Activity: Trigonometry
<p>Math Enrichment Activity</p>

#### & Author Notes

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#### Last Updated

July 15, 2020 7:42 p.m.

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