This document summarizes a student project where they looked at paintings by three European artists - Paul Klee, Piet Mondrian, and M.C. Escher - to find mathematical elements. The students observed how these artists used geometric shapes, lines, patterns, and more. They then created their own artworks inspired by each artist's style, incorporating math problems and concepts related to shapes, areas, perimeters and patterns. The project helped students discover how math can be found in art and how they could apply math to create art.

1. Finding Math Elements in Paintings
In this progectwe looked at some paintings of three European artists:
Paul Klee, Piet Mondrian and M.C. Escher. We observed the artwork and
saw the math elements in them (geometrical elements, shapes, lines,
patterns). Then we created our own artwork inspired by these artists’
style.
Paul Klee – Castle and Sun
We studied the painting «Castle and Sun» by Paul Klee. We discovered
geometrical shapes in it (squares, rectangles and a circle). We also
looked at the relationσ bstween someshapes. For example, two
triangles make a square, or four smaller squares makeone bigger
square. Can you find them?

2. We filled a piece of paper (10Χ14cm) with geometric shapes (triangles,
squares, rectangles)
With these shapes we made our own castles.
All our castles had the same area. Can you estimate the area of the
following castle?

3. Finally we completed our artwork by playing with colours, shapes and
patterns

4. Piet Mondrian
We studied Piet Mondrian’s paintings and we saw that they were made
of squares and rectangles. We noticed that some characteristics are
repeated in many of his works:
a. He only used the three basic colours (yellow, blue and red) to
paint the shapes and he left a lot of white space.
b. The lines that created the shapes wereblack and met in right
angles
We found out that many artists tried to mimic Mondrian’s styleto make
various kinds of objects, furniture, clothes, buildings.

5. We tried to make designs like his starting from the shapeof a country or
a continent. We used squared paper, we drew veritcal and horisontal
black lines and created squares and rectangles. Finally we coloured the
shapes within the country with blue, red or yellow colour. This is how we
created artwork in the style of Piet Mondrian.

6. Can you guess which are the following two Mondrian style countries?
Then some of us prepared some math problems based on Mondrian’s
painting style:
Make a drawing in Mondrian’s style. You can use squared paper
for guidance. The squaresor rectanglescan be red, yellow, blue or
white with black lines. Leave enough white space.
When making your drawingfollow one or more of the following
instructions:
1. Make a drawing thatcontains three differentrectangleswith the
same perimetre.
2. Your drawing mustinclude a square and a rectangle with double
the area of the square.
3. Your drawing mustcontain two differentrectangles. One of them
should have an area that is three times bigger than the area of the
other one.
4. Your drawing mustinclude two squaresor rectangleswith the
same perimetre, butwith differentareas.
5. Make n drawing thatcontainstwo squaresor rectanglesthat have
the same areas, buthave differentperimetres.

7. When you are done you can then:
1. Describe your artworkand compare itwith Mondrian’spaintings.
2. Explain the mathematicalside of your work.
Mauritius Cornelius Escher
When looking at M.C. Escher’s artwrk wenoticed that they are made by
repeated shapes that made patterns and sometimes are rotated. The
shapes are closely fitted together without gaps or overlapping. The sides
of one shapehe drew were also sides of the ones next to it.
We tried to make drawings thatlooked like Escher’s. For start, wetook a
small squarepaper and drew two shapes from the square’s two corners.
We cut the two shapes and placed them on a different place on the
paper. We then looked at the new shape we created and tried to
imagine whatformit looked like. A bird? A fish? A monster?

8. Finally we took a bigger piece of paper and drew repeatetly and
coloured our new form, trying not to leave any gaps in between. This is
how we made artwork like Escher’s.

9. Conclusions
Through this projectwe discovered that if you look carefully there’s a lot
of Math in some artworks in hidden or obvious ways. Wecan use
artworks to talk about Math and then use Math to make our own
artworks.