## Dürer Classroom Activity

### Objectives: NCTM Standards: Number and Operations and Connections]

1. Students will learn the definition of a magic square.
2. Students will learn the historical background of magic squares.
3. Students will experience the artistic aspects of magic squares.

### Materials:

Method 1: If Internet display capabilities are available or students have access to the Web at individual computer stations, the activity can be structured by viewing Melancholia, the magic square found in Melancholia, and information on Albrecht Dürer [Albrecht Dürer - engraver and More about Albrecht Dürer] interactively and then continuing with the activity.

Method 2: Prepare overhead transparencies and/or handouts before presenting the activity, including:

1. Dürer Magic Square
2. Background Information on Albrecht Dürer
3. 4x4 grid
4. Dürer Magic Square with lines
5. Melancholia - the engraving optional
6. The magic square found in Melancholia. optional

For both Methods 1 and 2:

1. Blank paper
2. Blank overhead transparency and pens
3. Rulers

### Procedure:

Display the Dürer Magic Square.

History Questions:

1. In what year did Albrecht Dürer create the engraving, Melancholia?
2. After reading about Albrecht Dürer's background, why do you think he included a magic square in his engraving?
3. If you were to make a magic square with this year's date [1996], what size grid would you need to fill?

Number Questions:

1. What is magic about the arrangement of the numbers in the 4x4 cell square?
2. What is the first number that Dürer used?
3. What is the last number?
4. How many numbers are there?
5. Is any number repeated?
6. What is the sum of the numbers in the1st row? 2nd row? 3rd row? 4th row?
7. What is the sum of the numbers in the1st column? 2nd column? 3rd column? 4th column?
8. What is the sum of the numbers on one diagonal? the other diagonal?

With the teacher modeling on the overhead projector, have the students construct a 4x4 grid. Use the engraving and write in the grid the numerals used by Dürer. [The numerals should be positioned in the center of each cell of the grid.]

Draw a dot in the center of each numeral for reference. Using a ruler, connect the dots starting at 1, going to 2, 3, ....to 16. [Refer to Dürer Magic Square with lines.]

Symmetry Questions:

1. What patterns do you see?
2. What are the symmetrical relationships?
3. Is the line design you have created, an example of
rotation symmetry?
translation symmetry?
reflection symmetry?
glide reflection symmetry?

[Note: To discover the symmetry involved, create a transparency (just trace the original) of the lines and use it to test for rotation, translation (slide), and reflection (flip).]