Tag Archives: Sextant

Al-Bîrûnî’s birthday

Abû al-Rayhân Muhammad ibn Ahmad al-Bîrûnî was born near Kath in the region of Khwârazm (now Kara-Kalpakskaya) in September 4, 973, and was died in Gbazna(?) after 1050. He lived in Kath and in Jurjanîyya and we know that he began his studies under Abû Nasr Mansûr (970-1036). He became a good mathematician and astronomer very fast and he measured the latitude of Kath observing the maximum altitude of the Sun when he was only 17 y.o. He also wrote some astronomical and mathematical works before 995 as we can check in his  Cartography (a book about map projections).

About 995, al-Bîrûnî left the civil war in Khwârazm and moved to Rayy (now near Tehran) where he lived in poverty. We know that he worked with al-Khujandî who had a large sextant with which he had determined the obliquity of the ecliptic.

Through the observational data registered by him we know that he spent some days in Rayy and that he was back in his birthplace in 1004. That year he became protected by the rulers of the region and he got enough money to build an instrument at Jurjanîyya to observe solar meridian transits. He made observations with it in 1016 and one year later he and Abû Nasr Mansûr were made prisoners by Mahmûd, the new ruler of Khwârazm. Al-Bîrûnî continued working as astronomer but he had a lot of problems with victorious Mahmûd. However, between 1018 and 1020 he made observations from Ghazna supported by Mahmûd and this work allowed him to determinate the latitude of the place.

Al-Bîrûnî travelled to India together with Mahmûd’s military expedition and he spent at least five years working on his India, in which he computed latitudes of cities and explained calendars, geography, literature…

After Mahmud’s death, the next rulers allow al-Bîrûnî to be free to travel and work in his interests and he became the most prolific Arabic mathematician in the World. He produced 146 works with more than 13.000 pages!

Russian stamp (1973)

So, al-Bîrûnî’s doodle published two years ago in the Arabic countries is a very good example of a great scientific contribution!

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Playing with Maths in the Hewelianum Centre

Photography by Carlos Dorce

Photography by Carlos Dorce

The “puzzle” exhibition isn’t the only place in the Hewelanium Centre where you can discover mathematical facts. For example, in the exhibition about the History of the Centre there are cannons in a defensive fortress with which you can learn a lot about parabolic shots…

Photography by Carlos Dorce

Photography by Carlos Dorce

…or how many cannonballs you have in a pyramid… Is Kepler’s theorem right? Do you think about a better way of stacking cannonballs?

There also is space for optical illusions, technology,… and a very modern Archimedes screw:

Photography by Carlos Dorce

Photography by Carlos Dorce

You can also play with the Galilean experiments about movement and see how a piece of wood climbs a path down:

Photography by Carlos Dorce

Photography by Carlos Dorce

In a hidden corner of the museum, a sextant tells you goodbye:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Hewelianum Centre in Gdansk (map)

The National Technical Museum in Prague

Photography by Carlos Dorce

Photography by Carlos Dorce

This is one of the Top 10 Museums in Prague! The museum was founded in 1908 and has been in its current location since 1941. It’s a very big building and the collection exhibited is so big although the exhibition about transports is its main attraction:

Photography by Carlos Dorce

Photography by Carlos Dorce

But for me, the exhibition about Astronomy has been the interesting part of the museum and I have been able to visit it on my own meanwhile my children were playing in another room with some technical toys. The astronomical rooms are very dark so it has been very difficult to take good pictures although I’ve tried to do my best. The collections has sundials, armilar spheres, quadrants, astrolabes,… and a lot of other astronomical instruments:

Photography by Carlos Dorce

Photography by Carlos Dorce

For example, the polyhedrical sundials are so beautiful like this constructed on a cube by German David Beringer around 1750:

Photography by Carlos Dorce

Photography by Carlos Dorce

Or… what about this other constructed by Mathias Karl Krausler in 1691?

Photography by Carlos Dorce

Photography by Carlos Dorce

The oldest exhibited astrolabe is this unsigned one from around 1450:

Photography by Carlos Dorce

Photography by Carlos Dorce

And there also is an unsigned torquetum from the late 16th century:

Photography by Carlos Dorce

Photography by Carlos Dorce

One of the instruments which have surprised me has been Joost Bürgi’s sextant for measuring the angles of celestial bodies (I knew that Bürgi, one of the inventor of logarithms, had constructed a lot of clocks and astronomical instruments but I didn’t expect to find one here!). Kepler used it to measure two consecutive oppositions of the planet Mars in 1602 and 1604.

There also is Habermel’s sextant, built by Erasmus Habermel (1538 – 15th of November of 1606 in Prag) who was  mechanic at the court of Emperor Rudolph II:

Photography by Carlos Dorce

Photography by Carlos Dorce

The prevailing opinion for a long time was that the instrument belonged to Brahe and so it was called the “Tychonian sextant”.

Habermel was specialised in small devices and portable sundials and one example is this sundial in the form of a book (c.1600)…

Photography by Carlos Dorce

Photography by Carlos Dorce

… and another is this equinoctial sundial (1585):

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, look at this armilar sphere from the second half of the 16th century! It’s a piece of art!

Photography by Carlos Dorce

LocationNational Technical Museum in Prague (map)

Brahe and Kepler together near Saint Vitus

Photography by Carlos Dorce

Photography by Carlos Dorce

Almost nobody knows that near St. Vitus Cathedral there is this wonderful sculpture representing these two great astronomers together looking at the sky. Everybody visit the cathedral, the castle and Loreto and if they walked a little bit more they’d arrive to a high school called Johannes Kepler where they’d find these two statues by Josef Vajce in 1983.

Photography by Carlos Dorce

Photography by Carlos Dorce

By the way, it seems that it’s forbidden to climb on the pedestal because two policemen had come to me and… nothing important. But it’s forbidden.

Photography by Carlos Dorce

Photography by Cristina Martínez

Location: Gimnasium Jana Keplera (map)

A very known bank in Bristol

Photography by Carlos Dorce

Photography by Carlos Dorce

This building was erected in 1857 by The West of England and South Wales District Bank. The architects W. B. Gingell and T. R. Lysaght, based its High Renaissance style in Jacopo Sansovino’s Library of St. Mark, Venice. It has been occupied by Lloyds Bank Limited since 1892 and the exterior remains substantially in its original form. The facade is full of allegories and we can see a lot of mathematical objects:

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: The West of England and South Wales District Bank (map)

Tycho Brahe Museum in Ven

Main entrance of the museum dedicated to Tycho Brahe Photography by Carlos Dorce

Main entrance of the museum dedicated to Tycho Brahe
Photography by Carlos Dorce

Ven is a small island in the Öresund strait.  Its population is less than 400 inhabitants and it is situated in Landskrona Municipality in Sweden although the island was Danish in Brahe’s times. It is a very quiet place and the landscape is very beautiful but I have visited it today for another important reason (a very mathematical reason!): astronomer Tycho Brahe (1546-1601) built two observatories here between 1576 and 1596, Uraniborg and Stjerneborg. This is my second post about Brahe and I am very happy because I have had the opportunity of learning things about Brahe’s life that I didn’t know before (link to Brahe’s bithplace). Brahe was an aristocratic person who was so interested for the Astronomy. I’ve been in Uraniborg with one of my colleagues (Laura Gómez) and the staff of the museum has opened it only for us and a guide has very kind for having shown us all the details of the museum. Nowadays, the museum is inside a church and Uraniborg castle and Stjeneborg are in the gardens:

The museum is inside this church Photography by Carlos Dorce

The museum is inside this church
Photography by Carlos Dorce

The day has been very cold and windy but this hasn’t been a problem for us. The first panel of the museum has welcomed us with a short ad about Brahe:

Tycho Brahe lived in the second half of the sixteenth century, during he era known as the Renaissance  He was born into one of the most powerful families of the Danish kingdom, and he received the thorough education of a young nobleman at different German universities.

His lefelong passion was astronomy. During his lifetime the great topic of discussion was which world system is correct. Is it the earth or the sun that is motionless at the centre of the universe? Tycho Brahe doubted that it could be the sun. But he resolutely affirmed that the answer had to be sought in careful observations of the positions and movements of the heavenly bodies. During his years on Ven he methodically charted the heavens with the aid of advanced instruments. His findings paved the way for a new scientific world-view.

Tycho’s life was chequered and dramatic. During his time here on the island, Ven became a brilliant centre of European science. He was unconventional in his lifestyle and had a view of women’s ability that was unusual for the time. He was an all-rounder science, with a great talent for organization. Here he shaped the kingdom of Urania.

Welcome to the Tycho Brahe Museum!

Tycho Brahe Museum Photography by Carlos Dorce

Tycho Brahe Museum
Photography by Carlos Dorce

You can learn a lot of things about Brahe’s life and his instruments in the museum. For example, there are reproductions of his quadrant and his famous sextant:

Brahe's sextant Photography by Carlos Dorce

Brahe’s sextant
Photography by Carlos Dorce

When taking measures, the quadrant was turned until it pointed towards the star. The ruler with the sight was then moved along the arc until the star was visible in the sight. The altitude of the star was read off on the scale on the arc and the direction of the star was read off on the circular scale running round the room.

So the sextant was used to measure the angular distance between stars (the stellar distance).

All the instruments were placed in the terraces of Uraniborg main building which was a not so big castle built in the higher point of the island:

For a lord like Tycho Brahe it was important to have a beautiful residence to mark his status. As soon as Tycho arrived on Ven he started building his castle. It was modelled on modern castles that he had seen on his travels in Europe. The castle that stood here was reminiscent of the masterpiece of the architect Palladio, the Villa Rotunda. […]

Tycho called his castle Uraniborg after the Greek goddess of astronomy, Urania. The building was purposefully deseigned in the service of science, and it was Europe’s first astronomical observatory.

Uraniborg main building
Source: Wikimedia Commons

Another of the instruments which Tycho built for his Urania was the Quadrans MAgnus Chalibeus (1588) with which it was possible to measure altitudes and the azimuth of any star.

Brahe's quadrant Photography by Carlos Dorce

Brahe’s quadrant
Photography by Carlos Dorce

Tycho’s achievements as an astronomer were pioneering. He sought to re-establish the high science of classical times through meticulous and direct observations of the heavenly bodies. For several decades he surveyed the heavens with the aid of advanced instruments. His measurements were unique in their accuracy, and would not be surpassed for almost three centuries.

The visit continues in the Observatory of Stjerneborg, next to Uraniborg. The weather of the island is always windy and all the instruments placed in the terraces teetered because of this strong wind. Therefore, Tycho decided to build a new observatory under the ground:

Source: Wikimedia Commons

The current reconstruction of this space takes you back to times of Tycho because you can listen a recreation of one of Tycho’s nights. There are the astronomical instruments placed in the same place as four centuries ago and all the show has been thought to wrap the visitor in this scientific moment.

Brahe's astronomical instrument in aa. Photography by Carlos Dorce

Brahe’s astronomical instrument in Stjerneborg.
Photography by Carlos Dorce

Here he got the best series of observations and astronomical data than any other scientist in those times.

Brahe's astronomical instrument in Stjerneborg. Photography by Carlos Dorce

Observatory of Stjerneborg.
Photography by Carlos Dorce

Here he got the best series of observations and astronomical data than any other scientist in those times. Tycho Brahe was one of the most wonderful scientists of the XVIth century and we must remember that Johannes Kepler deduced his three Physic laws from Brahe’s observations in Prague. So, I have enjoyed Uraniborg and Stjerneborg a lot and I can assure you that today has been one of my most wonderful Mathematical days:

Brahe looking at the nova in Casiopea Photography by Carlos Dorce

Brahe looking at a new nova in Casiopea
Photography by Carlos Dorce

And… that’s all folks. If you visit Malmö or Copenhagen, this is one of the most scientific trips that you must do!

Me in Stjerneborg  Photography by Laura Gómez

Me in Stjerneborg
Photography by Laura Gómez

Localització: Ven island (map)