Amsterdam: mathematical cityscape

Looking at a city

 A planned Math field trip for an MYP 4 class in Amsterdam morphs into something a little different but no less fun, as Donovan Carroll reports, and suggests we could all become scavengers!


Shapes, angles, numbers

Amsterdam. Historical City, and for me everywhere there are shapes, angles, numbers, volumes, elevations, mathematical relationships, the very history of number and engineering.  Heights to be estimated. Coordinates to be plotted. I suppose this is true of any city, but Amsterdam is a more than usually interesting place for a Mathematician to live, especially one with a historical or architectural turn of mind.

Rene Descartes lived here briefly during the summer of 1634 (there’s even a plaque). The church nearby  – Westerkerk – had just been built in 1630; however, the beautiful tower, the Westertoren, wasn’t completed until 1637.  When Descartes looked out of his window, he wouldn’t have seen the same completed tower that we do today.

Seeing what’s there

I love it. And there’s nothing I love more than to help other people see what’s there and learn how to appreciate it. In my teaching, I specialize in relating mathematics to the real world and finding ways to get students to learn mathematics outside of the classroom. The funny thing is, that when they look at buildings, students often see things that I have not noticed myself, as I found out on a recent mathematical “scavenger hunt”.

Field trip plans

I had just finished a unit on coordinate geometry with an MYP 4 class of 22 students (ages 14-15). There was plenty of potential for fieldwork. The students had been studying distance formula, gradients, etc. with the Cartesian coordinate system that was named after Descartes.  In addition to this, we had also covered collinear points, perpendicular bisectors, classifications of triangles, etc.  I planned to follow this up with an assessment piece based on field trip to the Westermarkt area of the city, where Descartes had lived.

Westermarkt is also where you’ll find three large pink granite triangles that form an even larger triangle.  This is the Homomonument, dedicated in 1987 to the memory of those who died in the Holocaust because of their sexual orientation.

It is an amazing piece of urban monumental sculpture and full of mathematical potential: one task for the students would be to classify the triangles by sides and by angles and explain how they know that they are correct using only a measuring tape.

All change!

A week before the trip, I asked the other math teachers at school if they’d like to bring their classes as well and they all accepted.  The other students in the same grade had not been covering the same topics.  So what had started out to be a small class trip ended up becoming 66 students plus 7 teacher chaperones for an entire grade trip.  Because of the addition of so many students with a variety of abilities and math backgrounds, I opted for a mathematical scavenger hunt instead of the other questions I had planned based on the unit we had been covering – but this was still going to be fun!

The logic of the hunt

When we got to Westermarkt, the kids were absorbed – and as usual, they noticed all sorts of different thing – the weird objects in the decorations on the outside of the church – babies, skulls, pelicans, musical instruments, an hourglass.


Still – some of these features had been incorporated into the hunt, which also used the street numbers beside the doors of the shops along the ground level of the church.

The answers to one question would lead the students to the street number for the next question, and so on, as you can see in the question sheet. Just click the picture to the left.  


Get scavenging!

It was a great outing. Amsterdam is an architecturally rich city – but with imagination, this way of observing an environment – mathematically – can really be done anywhere.

What the kids learn on trips like this will stay with them for life – the habit of noticing and interpreting their surroundings. I encourage you to take it up!


Donovan Carroll is a freelance Math Teacher, blogger, vlogger and tour guide, specialising in mathematical walking tours.

He lives (of course!) in Amsterdam.

For more about his work see:



Feature Image: Pixabay








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