planet.nl.
Astrolabe
The astrolabe is a mechanical instrument to solve problems related to the position of sun and stars, in the past, at the moment and in the future. For example, you can determine when the sun rises on your birthday, or at what time the sun goes down. The astrolabe tells you how high the sun is in the sky at 11:00 on December 30. You can also determine what time it is when the star Betelgeuse in the constellation Orion is just above the horizon. With Islamic astrolabes you can determine the times of prayer. You can even find the direction of prayer towards Mecca.
Nowadays you can find the answers to these kinds of questions on the internet or with a handy app on your phone, but when there were no computers, the astrolabe gave a definite answer, at least if you had a good one that matched your location.
The astrolabe is an old instrument. In Greek times, mathematical knowledge was available before the beginning of the era. The first descriptions date from the sixth century after the era. In the Arabic language area it is written about in the tenth century, for example by Abu Rayhan Muhammad ibn Ahmad al-Biruni. In museums there are copies from that same time. Four centuries later the first astrolabes appear in Western Europe.
Today, the astrolabe is a historical instrument and a great tool for understanding the mathematics behind the stereographic projection and spherical triangle measurement.
In 2019, my pupils at HWC drew an astrolabe in six lessons. In 2022, participants drew part of an astrolabe during a workshop at Fatih Sultan Mehmet Vakif University in Istanbul. In 2023 and 2024, highschoolers, students and math lovers learned about stereographic projection and drew part of an astrolabe during a five day workshop at Nesin Math Village in Sirince.
Below is an animation of an astrolabe with which you see step by step how the stereographic projection works and how all those different lines are geometrically constructed.
- 3D printed astrolabe
On request, a 3D-printed astrolabe is available. Rhino/Grasshopper is my development tool. Thanks to its parametric design capabilities, I can produce astrolabes for any latitude, in any size, and as much detail as I want. Documentation is available in English and Turkish.
- Workshop Nesin Math Village 2024
Another week in Ali Nesin Math Village: Everyone can draw an astrolabe (and understand star positions and sundials)
- Documentary TRT Belgesel
My contribution to the TRT Belgesel documemtary on navigation
- Workshop Nesin Math Village 2023
Participants drew an astrolabe on paper. Step by step, they learned about the mathematical background of this sophisticated ancient instrument. The program stretched over five consecutive days (four hours in the morning, four hours in the afternoon). Participants received hands-on training in geometry, trigonometry, spherical trigonometry, stereographic projection and many hands-on activities. All received a handy astrolabe on laminated paper for the real thing, and a 3D printed astrolabe as a souvenir.
- Workshop Fatih Sultan Mehmet 2022
In 2022, participants drew part of an astrolabe during a workshop at Fatih Sultan Mehmet Vakif University in Istanbul.
- Animation GeoGebra
It includes a stepwise explanation how all lines, circles and curves can be drawn. The animation can be configured for every time zone and latitude.
- Workshop Hermann Wesselink College 2019
My students learned how to draw the lines and curves of an astrolabe using stereographic projection.
3D printed astrolabe
On request, a 3D-printed astrolabe is available. Rhino/Grasshopper is my development tool. Thanks to its parametric design capabilities, I can produce astrolabes for any latitude, in any size, and as much detail as I want. Documentation is available in English and Turkish.
|
|
|
|
Documentary Kronovizör 5. Bölüm (Navigasyon) TRT Belgesel
TRT Belgesel did an interview with me about astrolabes and navigation.
YouTube: Kronovizör 5. Bölüm (Navigasyon) TRT Belgesel
Everyone Can Draw An Astrolabe
In 2022, participants drew part of an astrolabe during a workshop at Fatih Sultan Mehmet Vakif University in Istanbul.
|
|
|
|
Misconceptions
An astrolabe does not show the position or orbit of the planets. An astrolabe shows the orbit and position of the sun and of the stars. Therefore, the instrument is of little value to an astrologer who wants to draw a horoscope.
According to David King, the astrolabe is not intended for navigation and certainly not for navigation on a ship at sea. The mariner's astrolabe is an incomparably different instrument that has only its name in common.
An astrolabe is not intended for calculating latitude. On the contrary, each astrolabe is designed for a specific latitude.
An astrolabe is not intended to determine the direction to Mecca, although this can be done with a great deal of ingenuity and skill.
Some astrolabes have lines indicating prayer times. However, it is more easy to use a sundial in order to determine prayer times related to the length of the shadow.
Links to animation in Geogebra
Below are two images of the animation with Geogebra. It includes a stepwise explanation how all lines, circles and curves can be drawn. The animation can be configured for every time zone and latitude.
Start animation
Student workshop
My students learned how to draw the lines and curves of an astrolabe using stereographic projection.
|
|
|
Nesin's Maths Village 2024
Participants drew an astrolabe on paper. Step by step, they learned about the mathematical background of this sophisticated ancient instrument. The program stretched over five consecutive days (four hours in the morning, four hours in the afternoon). Participants received hands-on training in geometry, trigonometry, spherical trigonometry, stereographic projection and many hands-on activities. All received a handy astrolabe on laminated paper for the real thing, and a 3D printed astrolabe as a souvenir.
|
|
Nesin's Maths Village 2023
Participants drew an astrolabe on paper. Step by step, they learned about the mathematical background of this sophisticated ancient instrument. The program stretched over five consecutive days (four hours in the morning, four hours in the afternoon). Participants received hands-on training in geometry, trigonometry, spherical trigonometry, stereographic projection and many hands-on activities. All received a handy astrolabe on laminated paper for the real thing, and a 3D printed astrolabe as a souvenir.
|
|
|
|
Links to other websites
- full screen animation
- James E. Morrison: old website
- James E. Morrison: The Astrolabe
- David King: Islamic Astrolabes
- Hendrik Hollander: Algemene informatie over het astrolabium
- Hendrik Hollander: Instructions for use of the astrolabe
Literature
- Van der Blij, Platte en Bolle Meetkunde
- Jenkins: The Sun's position in the sky
- Martin: Young Trigonometers Compleat Guide
- Martin: Young Trigonometers Compleat Guide
- Mitchell: The Astrolabe in Theory and Practice
- Morrison: the Astrolabe
- North: the Astrolabe
- Smart, Textbook on Spherical Astronomy
- Smart, Textbook on Spherical Astronomy
- Thomson, Jordanus de Nemore and the Mathematics of Astrolabes: De plana spera.
- Thomson, Pseudo-Masha'allah, On the Astrolabe: A Critical Edition of the Latin Text with English Translation
- Todhunter, Spherical Trigonometry: For the use of colleges and schools
- Nesin Math Village
Another week in Ali Nesin Math Village: Everyone can draw an astrolabe (and understand star positions and sundials)
- Astrolabe
She says her friends can do.
- Astrolabe
A short holiday is enough to start a production facility in my office: low-cost, good-quality, unique design, astrolabes for Dutch pupils. I am proud of the innovative mounting (thank you neighbour).
- Alidade
New feature on my astrolabe. I made an alidade to measure altitude of the sun or a star
- Astrolabe
My 3D printed astrolabe doesn't have text (quite a limitation of 3D printing). Here is the documentation. Printing of one astrolabe takes twelve hours.
- Astrolabe
I admire Murphy for his reliability. His law is a true friend who never lets you down and never disappoints you.
- Astolabe
Almost ready, always afraid of mistakes. Next weeks, I want to do a lot of exercises to beat Murphy!
- Astolabe
3D printing of an astrolabe is my latest challenge. Almost done.
- Astrolabe Workshop FSM
Everyone can draw an astrolabe. It takes time, focus, accuracy, and hard work.
- Astrolabe Workshop FSM
After weeks of preparations, we were ready to do our workshop Everyone Can Draw An Astrolabe. (to be continued tomorrow)
- Sara Choudrey
Thank you for sending a postcard!
Dutch
Turkish