My favorite

Yavuz Selim Mosque in Istanbul

From the center, I walk via the Şehzade and Fatih to Yavuz Selim, high on a hill. I love the serene tranquility of this mosque with its beautiful garden. At the feet of the terrace lies the old city and across the Golden Horn there are the skycrapers of Taksim and Levent, but in the garden, I am out of reach of the city noise of screeching sirens, motorbikes, and honking cars.

ArchNet: Sehzade

ArchNet: Fatih

ArchNet: Yavuz Selim



Metametrik is an online project about designing, architecture, tools, software. Sema Alaçam, Orkan Güzelci, and Kumsal Sen want to convey the issues that we feel lacking during formal education. In their blog, they paid attention to my muqarnas project in their blog in Turkish.


The blog is in Turkish. For those like me who do not master Turkish, a translation in English is available.



My name is Henk Hietbrink. My family name is unpronounceable, so call me Mr. Henk, as my students do. I am a teacher of mathematics in the Netherlands. My pupils are 15 to 20 years old and most of them are afraid of math because they forgot to do their homework on time. Math is difficult, I know, therefore, I tell stories about math and its applications and stories about the history of the people who invented mathematics. My message is that math helps to solve every day life's problems.

As a young boy, I have seen the western European Gothic and Roman cathedrals (start googling for Chartres Cathedral, Laon cathedral, Limburg an der Lahn cathedral and you may understand why). I was amazed by the height of the pillars, the geometrical patterns in the roof, the arrangements of the walls, the mosaic on the floor. At home, I investigated how to draw these patterns with compass and ruler. I also love history. Isn't it astonishing how they made these complex structures without electrical engines, heavy transporters, and computers?

One day in 2012, friends of mine invited me to join a summer school in Istanbul next to the Istanbul Museum of the History of Science and Technology in Islam (you should go there yourself). From 2016 on, the Bursa Science Center allowed me to perform workshops on sundials, with an ever-growing group of students and teachers volunteering. Since then, I have been twice a year in Istanbul, until Covid-19 disturbed my plans this year (like it did yours). I travelled through Istanbul and walked my way from Eyup to Sakarin Camii to Camlika and back to Ortakoy and Fatih (I admit that I sometimes took a bus) to visit the Istanbul mosques. I am excited by the beauty of the buildings, the complexity of muqarnas, the colourful paintings, the ease with which the dome appears to rest on the walls, the quiet and peaceful atmosphere inside, and the kind people outside who offer me cay and tell their stories (thanks to google translate, we can communicate).


As I told before, I am a teacher and I use stories to explain the applications of mathematics, for example, instruments to find reflection points in mirrors, sundials, muqarnas, astrolabes, perfect compasses and. You can read more about these subjects in the Prof. Dr. Fuat Sezgin Library in Gulhane Park. (find out what Mr. Fuat Sezgin achieved and you understand why I am grateful for his kindness to support my research).

In 2019, I held a talk and performed a workshop during The First International Prof. Dr. Fuat Sezgin History of Science in Islam Symposium in 2019 in Istanbul about an amazing instrument in the Museums of Science and Technology in Islam in Frankfurt and Istanbul. This instrument combines the scientific traditions of the Islamic world and Western Europe. According to the catalogue, it was designed by Leonardo da Vinci (1452-1519) to solve the famous problem of Alhazen (Ibn al-Haytham, 965-1039) on reflection in spherical mirrors. The instrument is a practical solution, by a brilliant inventor and painter, for a theoretical problem by a mathematician and scientist. A drawing and notes on the instrument are found in Leonardo da Vinci's manuscripts. It was Prof. Dr. Fuat Sezgin who again drew attention to the instrument and constructed a model for his museums. In 2015 I prepared a workshop on the instrument for the summer school of the Prof. Dr. Fuat Sezgin Research Foundation in Istanbul. Since then, the workshop has been given a number of times in the Netherlands and Turkey. For me, the challenge is to tell the story for a wide-ranging audience at different levels of education. I like to see how people start experimenting with cut-out sheets, assemble the instrument, attack the problem of reflection and accept that they found a very good approximation of the point where one sees the image of something in a spherical mirror. The next step is to find exact formula's with those who are not afraid of hardcore geometry and algebra. But there is also a story about the miraculous ways of human progress in science.


Since 2013, I do workshops on sundials. It is my aim to introduce the concepts of the movements of sun and earth in such a way that children and their parents understand the idea of hourlines. I handover cut out models of the horizon plane, the heavens, the sun arcs and finally a cutout sheet of a sundial. Learning materials like an inflatable earth balloon and cut-out worksheets are essential during a one-hour workshop. I believe in learning by doing. At a high-school level, trigonometry is introduced. I want that students understand what they are doing, and do not want to teach wizard tricks. So, students cut out their worksheets to investigate which angles and right-angled triangles result in the angles of azimuth and altitude. My message is that they can do the job with plain trigonometry. Only at the end of the one-day event, I tell them that there is something like spherical trigonometry with magical formulas.

Muqarnas are very attractive when teaching space geometry. I like to invite young people to build a muqarnas themselves. I hand over a lego-like construction plate, a design drawing, and a box with sixteen different types of muqarnas building blocks. Each box contains about a hundred 3D printed lego-like assembly blocks. This way, everybody can construct a two-level muqarnas. When they are ready and want to try more, I ask to design another muqarnas for the same construction plate. The next question is a mathematical one: How many different designs are possible for that construction plate? Another question is whether there exist more than these sixteen. There are many more interesting questions about the size, surface, or content of each building block. The fun thing is that there are puzzles for everybody, ranging from a starter question to real expert mode topics.

For those who don't like math (in the Netherlands, there are many), there is more to discover. Let's talk about art. For what reason are some muqarnas more beautiful than others? Or to put it bluntly, why are some ugly? My building locks are 4 cm height, small, light-weight plastic pieces printed by a 3D printer, but a stonemason has to carve and stack heavyweight blocks of half a meter height or more. What should he (or she) do to obtain stability? When a muqarnas has been ruined, how should the architect (he or she) do the restoration works? Let's talk about history. Who invented the muqarnas? Why are Turkish muqarnas so different from Iranian or from Moroccan? (if you know all the answers, appoint for a professorship).


Anyway, during each visit, I had a wonderful time, so much beauty, regularity, symmetry, innovations, discoveries, and surprises, so many kind people willing to help. After each visit, I had plenty of ideas for new workshops, new questions, new activities, and a lot of stories in the classroom. All I want is that people remember how mathematics is involved in the history of our society. Teacher talking and student listening is not enough to achieve a real understanding. In my opinion, students (adults, children, pupils) should practice and find out how things are connected. So, if you are curious like me, if you want to investigate muqarnas as I do, I would suggest: build a muqarnas from paper models, construct muqarnas from 3D printed building blocks, sketch designs yourself, do mathematics to count the number of possible combinations, develop software to visualize muqarnas on webpages, design building blocks of your own using 3D software, buy a 3D printer and let it run for weeks and weeks. The fascination for the marvellous creations of the past (up till yesterday) is driving me. I am waiting for the day to return to Istanbul and continue my research on muqarnas, coming home with new inspirations for new lesson plans and workshops.




GeoGebra Books

Visualizations have been made in a seperate GeoGebra book, including workshop materials.


Workshop materials