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The Mathematical Art of
 David A. Reimann
1944 (artwork)
1944 Digital Print 2013

During World War II, M.C. Escher began investigating ribbon patterns from simple blocks. One of Escher's ribbon designs was a hexagonal tile with bands connecting pairs of sides and two accented corners. This artwork uses Escher's hexagonal tile to create a pattern having cyclic symmetry of order 3. This work pays homage to Samuel Jessurun de Mesquita, Escher's art teacher. On January 31, 1944, de Mesquita was taken from his home in the Netherlands by the German Forces to Auschwitz; he died on February 11, 1944. The central hexagram represents de Mesquita. The black knot represents the Nazi strangle on Europe. The small yellow points represent other Jews, some protected by friends represented by orange bands.

Background and Inspiration

Escher's hexagonal stamp. Photo courtesy of Doris Schattschneider.

M.C. Escher explored patterns created from simple motifs carved from square stamps during the years 1938 to 1943. Escher referred to this as the Potato Game, which he played with his children, as the stamps could be easily carved from potatoes. He preserved in a notebook tessellations using several motifs from plain to yarn-like in appearance made using a square stamp. Escher’s son George commented …of course, the game can be extended to triangular and hexagonal grids. The book M.C. Escher : Visions of Symmetry by Doris Schattschneider contains a picture of a hexagonal stamp made by Escher (page 52). The pattern and a variant are shown in Figure 1. However, none of Escher's ribbon patterns using the hexagonal motif are known to exist. I was intruiged to see how such patterns might look. The above artwork gives a sense of what is possible with this simple stamp. I wrote a short paper on this topic and presented it at the annual Bridges conference in 2013. It contains a few other symetric patterns made using this hexagonal motif.

In 2010 I was on sabbatical and had the opportunity to travel to The Netherlands to do some research on M.C. Escher. I was especially interested in finding more information on the ribbon patterns he created in several notebooks. In addition to visiting the Escher Museum, the Escher archives at the Kunstmuseum Den Haag (then the Gemeentemuseum Den Haag), we saw several artworks Escher created for buildings in The Netherlands. We also visited the Anne Frank House in Amsterdam.

During this time I became aware of the tragic story of Samuel Jessurun de Mesquita, Escher's art teacher. The juxaposition of his death and the death of Anne Frank were the inspiration of this piece. How can one group of people so reject the dignity and worth of others? And yet, there were some who risked much all over Europe to help those they could.

Historical Background

Here is a rough time frame of key events during WWII.
12 June 1929
Anne Frank was born in Frankfurt.
September 1, 1939
Germany invades Poland, WWII begins.
10 May 1940
German invasion of the Netherlands.
January 1, 1941
Everyone required to carry ID card, a `J' was stamped on Jews.
22-23 Feb 1941
First deportations of Dutch Jews; 427 men (aged 18-35) sent to Mauthausen.
December 7, 1941
Japan bombs Pearl harbor.
December 11, 1941
Hitler declares war on USA.
November 1942
Resistance organisation started to help people go into hiding.
1943
34,000 Dutch Jews were murdered.
3 May 1942
Jews required to wear a six-pointed yellow Star of David.
June 12, 1942
Anne Frank recives a diary for birthday present.
July 1942
Frank family goes into hiding. Of course we are not allowed to look out of the window at all or go outside. Also we have to do everything softly in case they hear us below.
January 31, 1944
de Mesquita taken from his home in the Netherlands by the Nazi Forces.
February 11, 1944
de Mesquita dies at Auschwitz.
June 6, 1944
D-Day, America forces land in France.
4 August 1944
Frank family discovered by police.
30 April 1945
Hitler commits suicide.
February 1945
Margot and Anne Frank die in Bergen-Belsen.
One day, they just weren't there anymore. — Rachel van Amerongen
May 8-9, 1945
Germany surrenders, war in Europe ends.
August 14-15, 1945
Japan unconditionally surrenders, WWII ends.

An estimated six million Jews perished in WWII. Of those, 100,000-102,000 were Dutch Jews. More than 25,000 Jews were in hiding with 8,000-9,000 captured by the Nazis.

We do not consider the Jews to be members of the Dutch nation. … The Jews are the enemy with whom no armistice or peace can be made. … We will smite the Jews where we meet them and whoever goes along with them must take the consequences.
— Arthur Seyss-Inquart, 1941 (Nazi commander of the Netherlands)

There are a great number of organizations, such as The Free Netherlands, which forge identity cards, supply money to people underground, find hiding places for people, and work for young men in hiding, and it is amazing how much noble, unselfish work these people are doing risking their own lives to help and save others. Our helpers are a good example. They have pulled us through up till now and we hope they will bring us safely to dry land. Otherwise, they will have to share the same fate as the many others who are being searched for. … That is something we must never forget; although others may show heroism in the war against the Germans, our helpers share heroism in their cheerfulness and affection.
— Anne Frank, Diary, January 28, 1944

I still have the greatest difficulty with the Krauts. … I was not involved with the Resistance, but I had many Jewish friends who were killed. My old teacher, de Mesquita. He did not want to go into hiding. They were Portuguese Jews and the Krauts had always stated they belonged to the elite. One night they were all taken away. His son, Jaap, a clever boy, had worked day and night… He had often gone to see the Krauts in order to talk with them about his ancestors. They were not noble, but almost. … One bad day they were all gone. In 1944, during the famine winter, I wanted to bring them something, apples… I walked to their house. The windows on the first floor were broken. The neighbors said: 'You hadn’t heard? The De Mesquitas have been taken away.' This (a drawing) lay on the floor with the impressions of the cleats from the Krauts' boots. It was lying under the staircase. And in his studio everything was a mess, everything on the floor. I took home two hundred prints… Later they were exhibited in the Stedelijk Museum. Wertheim, from 'Kunstbezit', was with in Westerbork. Wertheim survived, the De Mesquita's were taken away. No matter what you do, you cannot forget such things. I cannot… Taken away in the middle of the night. And he could have been saved. I tried so hard to convince him. No he was protected, he said. Why should he hide? Afterwards I blamed myself. But they did not wish to. Jaap in his talks with the Krauts had produced all sorts of genealogical registers. They were half noble. The Krauts found that impressive. They almost never left their home. Really terrible, you know, such sweet people, carried away like cattle to be butchered.
— M.C. Escher, 1968

On January 27, 2020, at the 75th anniversary of the liberation of Auschwitz by the Soviets, the Prime Minister of the Netherelands, Mark Rutte, formally apologized saying Now, while the last survivors are still with us, I apologise on behalf of the government for the conduct of the Dutch authorities at that time. I do so in the knowledge that there are no words that can capture the enormity and the horror of the Holocaust. It is our duty, as the post-war generations, to continue to commemorate. To honour the names of the dead. To continue to render account. To stand strong together in the here and now.

I hope this artwork can, in some small way, help us remember the many innocent people lost in those tragic days of the second world war, and the brave souls who risked much to help those oppressed. And say Never Again.

Exhibition History

Publication History

  • Bridges Enschede Conference Art Exhibition Catalog, p. 141, Edited by Robert Fathauer and Nathan Selikoff, ISBN: 978-1-938664-07-6, Tessellations Publishing, 2013.

References