Netherlands

029

The Escher Museum, The Hague, Netherlands

52° 5′ 0″ N, 4° 18′ 52″ E

The Escher Museum

The Escher Museum in The Hague truly lets you enter the world of M. C. Escher through its large collection of his artwork and a clever optical illusion.

The museum contains almost all of Escher’s prints, including his famous, never-ending waterfall, hands that appear to draw themselves on the page, and Ascending and Descending, where monks climb an infinite staircase. Escher’s prints of transformation—where tiled fishes turn into birds and other animals metamorphosize into shapes, tilings, or even towns—are on display at the museum, as are rarely seen works such as his lithographs of the Amalfi coast.

For an additional fee, visitors can be photographed in a room that warps the viewer’s perspective is such a way that one visitor appears tiny and the other huge. Because of the way the warped walls are painted, the mind is fooled into misjudging the two heights.

One of Escher’s best-known prints depicts ants crawling around a Möbius strip (a surface with only one side). Much of Escher’s work relies on unusual shapes (like the Möbius strip), impossible shapes (see sidebar), and optical illusions. The museum has a special exhibition on how optical illusions work.

Escher’s work often has underlying mathematical meaning. His Circle Limit IV lithograph depicts devils and angels tessellated inside a circle. As the tiles approach the edge of the circle, they become smaller and smaller, depicting a mathematical limit and infinity in a finite amount of space.

The museum explains the meanings of Escher’s work and the process used to create it. Information is available in English throughout the museum, and tours in English are available if booked in advance.

Practical Information

Full details in English are available on the Escher Museum’s website at http://www.escherinhetpaleis.nl/.

Impossible Shapes

Escher’s art is filled with impossible shapes—monks climbing a never-ending staircase, water flowing uphill to create a waterfall that powers the flow itself, and buildings with staircases in every direction.

Three of the basic impossible shapes used in Escher’s work are the Necker Cube, the Penrose Triangle, and Penrose Stairs.

The Necker Cube (Figure 29-1) is a simple wire frame cube with nothing to reveal the depth of the image and which therefore can be seen from two different perspectives. In Escher’s Belvedere, a drawing of a Necker Cube rests on the ground, and a boy is seen holding an Impossible Cube.

Figure 29-1. A Necker Cube

The Impossible Cube (Figure 29-2) appears to be solid, but closer examination shows that it cannot possibly be constructed from straight edges in our world.

Figure 29-2. An Impossible Cube

In the 1950s, the British mathematician Roger Penrose created the Penrose Triangle (Figure 29-3), an apparently rigid triangle with impossible edges and angles. The shape subsequently appeared in Escher’s Waterfall, where a pair of Penrose Triangles form a gutter up which water flows.

Figure 29-3. Penrose Triangle

Penrose, together with his father, also created Penrose Stairs (Figure 29-4), which are featured in Escher’s Ascending and Descending. Penrose Stairs continue in an infinite loop, with no top and no bottom.

Figure 29-4. Penrose Stairs