This picture is in the Gemäldegalerie Alte Meister of Dresden. Archimedes (c. 287 aC – c. 212 aC) is in the middle of a brainstorm reading one of his papers! A compass and a ruler remember us the Geometry and the mirror could be an allegorical detail of his inventions which defended Siracussa from the Roman invaders. There also are a sand clock (the Sand Reckoner?) and a terrestrial globe. As you can see, Rafaello Sanzio’s angels aren’t the only brightning star of the Museum!
Kepler’s last home is this orange house located in Keplerstrasse 5 in Regensburg. Reading the famous Kepler’s biography written by Max Caspar:
[…] On November 2  he rode, tired, on a skinny nag, over The Stone Bridge into Regensburg. He took up quarters in Hillebrand Billj’s house in the street now named after him. This acquaintance was a tradesman and later an innkeeper.
Only a few days after his arrival Kepler came down with an acute illness. His body was weakened by much night study, by constant worry, and also by the long journey at a bad time of year. In the beginning he attributed no significance to his being taken ill. He had often before suffered from attacks of fever. He believed that his fever originated from “sacer ignis”, fire-pustules. As the illness became worse, an attempt was made to help him by bleeding. But soon he began to lose consciousness and became delirious. Several pastors visited him and “refreshed him with the vitalizing water of consolation”. It is not said anywhere that holy communion was afforded him. In the throes of death Pastor Christoph Sigmund Donauer rendered him aid. When, almost in the last moment of his life, he was asked on what he pinned his hope of salvation, he answered full of confidence: only and alone on the services of Jesus Christ; in Him is based, as he wanted to testify firmly and resolutely, all refuge, all his solace and welfare. At noon on November 15 this pious man breathed his last. […].
A plaque on the facade says that this is the house which I was looking for when I have arrived at Regensburg:
Bad luck! This small museum is only open in the weekends and it’s possible to rent a guided visit only for groups! I’ve not arrived here to give up! Finally, I’ve been able to visit it and the first thing that I’ve seen… the magnificent bust of the last owner of the house…
… over a plaque in German language where it’s possible to read a little part of this story:
The museum located in the house is very small and explains Kepler’s life and works focussing the interest in his astronomical discoveries and his three laws.
There is also a representation of the barrels whose volume was calculated precisely by Kepler in 1615:
Another bust representing the great mathematician is in the room of the first floor next to some information about his commemorative monument also in Regensburg.
There are a lot of Kepler’s works (which seem to be original) and this wonderful German edition of Napier’s logarithms (1631) which couldn’t be used by Kepler but exemplifies the great impact that this powerful calculator had in the beginning of the 17th century.
Of course, his Astronomia Nova, his Harmonices mundi,… and his Tabula Rudolphinae are also exhibited.
There also are explanation about his relation with Tycho Brahe and the Copernican system and a lot of astronomical instruments like sextants, globes, compasses,…
Finally, I want to say goodbye looking at this famous portrait. This man discovered the elliptical orbits of the palnets and his obsession with numbers let him find the second and the third law. Copernicus was right and Newton will be confirm all this theories. The World was explained (Wait Einstein, wait!).
Location: Kepler’s museum in Regensburg (map)
Copernicus studied in the Collegius maius between 1491 and 1495. On the list of 69 students matriculated in 1491 at the Cracok Academy were “Nicolaus Nicolai de Thuronia” and aslso his brother “Andreas Nicolai”. The Jagiellonian University consisted offour faculties at the time (the Theological Faculty, the Canonical La Faculty, the Medical Faculty and the Liberal Arts Faculty). Copernicus began his studies learning the grammar of Latin, poetry and rhetoric but he early started to attend lectures on Euclidean geometry and astronomy. During the 15th and early 16th centuries, the University gained importance in Central Europe as a scientific center due to the high level of astronomical and mathematical sciences: the distinguished professors of the time included Marcin Hrol (c.1422-c.1453), Wojciech of Brudzewo (1445-1495), Jan of Glogow (c.1445-1507) and Maciej of Miechow (1453-1523). In the second semester of 1493 he attended lectures of Jerzy Peürbach, with the comments of Wojciech of Brudzewo, and the lectures about Aristotle’s De Caelo. It’s unknown when Copernicus brothers finished their studies n Cracow but they surely didn’t receive their degrees. Perhaps their mother’s death in 1495 caused their return to Prussia.
Thus one of the required mathematical visits that must be done in Cracow is this College:
The building hosts an interesting museum with a lot of old objects which are not directly related to the College but I must recognize that it’s possible to imagine how the academical life was in the 15th century. The first room is a big hall full of shelves with books, statutes, quadrants, portraits, maps and spheres:
Everything takes you back to a ‘kitsch’ Renaissance:
There is space for our Copernicus, of course,…:
…and also for Galileo:
There is a special small room dedicated exclusively to Copernicus with astrolabes, charts, books and copies of some interesting documents:
For example, look at this interesting torquetum made by Hans Dorn in 1480 (the astrolabe was also made by Dorn in 1486)…:
…or this portrait of Kepler from the 18th century:
Furthermore, a bust of Isaac Newton…
… is on the top of the door through which you enter a room full of astronomical and mathematical instruments:
Can you see this little Aechimedes screw?
Before ending the visit, Newton (again!) says goodgye to the visitors in a very modern picture:
And Kepler too!
One thing more… Go to the ticket office and you will see some mathematical objects more like these English Napier Rods from the 17th century:
Location: Collegius Maius (map)
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:
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:
For example, the polyhedrical sundials are so beautiful like this constructed on a cube by German David Beringer around 1750:
Or… what about this other constructed by Mathias Karl Krausler in 1691?
The oldest exhibited astrolabe is this unsigned one from around 1450:
And there also is an unsigned torquetum from the late 16th century:
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:
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)…
… and another is this equinoctial sundial (1585):
Finally, look at this armilar sphere from the second half of the 16th century! It’s a piece of art!
The Temple Bar Memorial (1880) stands in the middle of the road opposite Street’s Law Courts marking the place where Wren’s Temple Bar used to stand as the entrance to London from Westminster.
The monument has two standing statues dedicated to Queen Victoria and the Prince of Wales because both were the last royals to pass through the old gate in 1872.
The reliefs round Queen Victoria contains some allegories which includes the first picture about the Euclidean demonstration of the theorem of Pythagoras. We also find a ruler and a globe with the ecliptic.
Location: Temple Bar (map)
This is Birmingham City Council. I arrived at Birmingham yesterday together with three colleagues and ten students because we are participating in a Comenius meeting organized by the Long Eaton School. This morning we have been wandering in the center of the city and have visited some of its most important buildings as the city council. It has been a rainy day but we have enjoyed the city a lot
Birmingham City Council is in Victoria Square and it’s one of the city hearts. I haven’t found out when it was built yet but I’ve noticed this beautiful mosaic below the main frontispiece:
You can see Science in the left of it. It’s a pity that the picture isn’t so good butit’s possible to distinguish something similar to an armilar sphere.
Furthermore, in the frontispiece located in the left corner of the main facade there are some muses (?) and…
this one is measuring on a globe with a compass:
There always are mathematical objects everywhere!
The forntispiece of Museo del Prado of Madrid is full of allegorical figures of the muses and the arts. If we watch it carefully, we’ll notice Urania with a compass and a globe in her hands counting on a parchment:
The building was designed by the architect Juan de Villanueva (1739-1811) and it had to host the Royal Observatory, a Science Room, the Botanic Gardens, schools, laboratories,… The Spanish king yhought that it could be a very good example of the new illustrated Spain. However, it never was used in this way:
Nowadays thousands of tourists visit the pictures in the Museo del Prado and only a few ones visit outside the building. Among all the statues which decorate this neoclassical structure there are the Architecture…
…and the Symmetry:
There are also some medallions with busts of famous Spanish scientist and writers on each of these statues. Of course, Juan de Herrera is also here:
Indian astrologer’s celestial globe from the 19th century:
This celestial globe is extremely unusual in being inscribed in Arabic, Persian and Urdu, representing a blending of traditions. It was probably designed for astrological use.
English Ptolemaic armillary sphere, by Richard Glynne (c. 1715)
Ptolemy’s cosmology placed the moon along with Mercury, Venus, the sun, Jupiter and Saturn in orbit around the Eart, which stood at rest at the centre of the universe. Although a sun-centred universe was more widely accepted among astronomers in the 18th century, Ptolemaic armillary spheres such as this one continued to be made and sold.
Upstairs there is another exhibition related to globes and armilar spheres and we can find some terrestial globes and Copernican and more Ptolemaic spheres. Here you have one Ptolemaic one dated in 1790:
Finally, I must point to two delicatessen. The first one is this little ivory plaque showing astronomers working with their instruments:
The other is this picture showing a figure pointing to a globe from a section of the Roman mosaic from mid-2nd century (Museo Nacional de Arte Romano):
The National Maritime Museum is another of the touristic attractions which can be visited in Greenwich. Of course, you can see boats, ships, maps,… and all the things related to the sea and the English glorious past. Therefore… what can the mathematical tourist visit here? Navigators used charts, maps, astrolabes, globes,… in their adventures so we can start our mathematical visit with all these mathematical objects!
Brass celestial globe. German, about 1725
This is one of a pair with a terrestial globe. It shows constellations, the Milky Way and the Magellanic Clouds. It contains some mistakes, indicating that it was a luxury item that could adorna wealthy home rather than an up-to-date scientific instrument. Nevertheless, with its calendar ring, it could be used to identify what was seen in the night sky.
There also are terrestial globes which were used by navigators to measure distances on the terrestial surfaces:
The first golden globe is from 1600 and the globe at its right is a French globe from 1625. Behind it there is a German terrestial globe by Johann Reinhold (1588). Of course, sundials also are shown in the exhibition! The first one (left) is an inclining dial for use in Japan before 1872 and the second is an equinoctial dial fou use in Huangzou, China, in the 19th century:
We can also find astrolabes, compasses, quadrants, telescopes, rulers,…
Look at this astrolabe from Islamic Spain (c.1230) by an unknown maker! It’s a jewel!
I am sure that you can find out more mathematical objects if you have enough time to enjoy all the exhibition!