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)
Weil der Stadt is located near Stuttgart. Johannes Kepler was born in this very veautiful town on December 27, 1571 and his memory is still there: this big statue is in the middle of the Market Square…
… and Copernicus, Mästlin, Tycho Brahe and Jobst Bürgi are with him in this monumental sculpture.
The four scientists are in the corners of the base of the statue and the words “Astronomia”, “Optica”, “Mathematica” and “Physica” are graved on each of the four sides.
I must say that here we have the first (imaginary) bust of Bürgi that I know. Bürgi was one of the originators of the logarithms because Kepler said that he had seen Bürgi using logarithms in astronomical calculus (Rudolphine Tables (1627)) before their “official” first occurrence in Napier’s Mirifici Logarithmorum Canonis Descriptio (1614). Furthermore, Bürgi published his logarithms in his Aritmetische und Geometrische Progreß tabulen (1620) but his “red numbers” and “black numbers” couldn’t never win the “logarithms” which were the first calculator in all history.
Notice that this statue is not very similar to this other portrait from 1620:
The base of the statue also have four graved images representing moments in Kepler’s life like thispicture with Kepler in the middle explaining the Copernican system…
… with Hipparchus and Ptolemy watching how a central Sun brights in the middle of the universe.
Can you imagine Kepler investigating about his elliptical orbits?
Next to Market Square there is his bithplace which hosts… no, no, no! Tomowwor will be another day!
Location: Weil der Stadt (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 doodle was published in August 25, 2009, to celebrate the 400th anniversary of Galileo’s telescope.
In a previous post I began to talk about this museum located inside Frombork castle. You can learn almost everything about him, his life and his works on medicine, economies and, of course, astronomy, including the replicas of his instruments (we saw them also in Warsaw). For example, it’s possible to see some facsmile editions of his works and also a recreation of his desk:
Among the references about his publication of his works, we can find this engraving showing Copernicus in a lecture for the Cracovian scientists in 1509:
Or this other wonderful one (1873) with Copernicus in he middle of the picture talking about his heliocentric system:
How proud he is of his heliocentric theory!
And who are his guests? First of all, Hipparcus (with the armillar spher) and Ptolemy (with his geocentric system) are listening the theory which will finish theirs. Ptolemy looks askance at Tycho Brahe meanwhile Newton is looking at Laplace:
Galileo Galilei is behind Copernicus looking at him with great reverence:
And Hevelius, the other great Polish astronomer, agrees Copernicus’ theories although he never had the telescope to check them.
Finally, Johannes Kepler seems to be bored of listening this obvious theory although his ellipses will be the curves which will change the astronomy.
A beautiful picture for a beautiful museum. Next step: the cathedral!
Location: Frombork castle (map)
My trip to Poland and Praghe finished yesterday and I remember that in my first post about the Museum of Technology of Warsaw I didn’t talk about the astronomical room in the second floor of the museum. It has some telescopes, reproductions of satellites and a lot of information about the space and we can also find the corner dedicated to Copernicus and his De Revolutionibus Oribium Coelestium and Hevelius.
There are three reproductions of Copernicus’s astronomical instruments which we can imagine in the hands of this Polish astronomer. First of all, the armillary sphere…
…the paralactic triangle (triquetum) for measuring the angular heigh of the Moon…
… and the solar quadrant used by Copernicus in 1510-1520 in order to watch the Sun:
Johannes Hevelius’ instruments are represented by some old images…
…and there is a representation of his observatory in Gdansk:
Alexanderplatz is one of the most emblematic squares in Berlin. It’s a very importnat center of communications and transponts of the German capital although it was created for hosting a cattle market until the end of the 19th century. The current square was designed by the former DDR rulers in the 60’s and nowadays it’s always full of people eating, buying, walking or simply having a beer or a coffee.
If you walk to Alexanderstrasse 9 you will see the great mosaic in the Haus des Lehrers (the Teachers’ House).
The rest of the mosaic is wonderful. It’s a pity that it was only a propagandistic set of pictures!
The Whipple is a University of Cambridge museum within the Department of History and Philosophy of Science. During the 1930s and 1940s, there were strong initiatives to establish history of science within the University and an exhibition of the historical scientific apparatus owned by various colleges was held in 1936. Soon after, a History of Science Lectures Comittee was established which, together with the Cambridge Philosophical Society, negotiated in 1944 a donation of antique scientific instruments and rare books from Robert Stewart Whipple (1871-1953), former Director of the Cambridge Scientific Instrument Company.
So, let’s start our visit in the main room:
The astronomical objects are very usual in this kind of museums and here you have a Newtonian “Herschdel Telescope” (c.1790) which was presented by George III to the Duke of Marlborough and it was placed in the Observatory at Blenheim Palace until it was given to Herschel’s great-grandson, Mr. Joseph A. Hardcastle (1816-1911).
Sir William Herschel achieved public acclaim and royal favour through his discovery of the planet Uranus, which he originally called Georgium Sidus, to honour King George III in 1781. A few years later George III requested that he make a number of telescopes. This is one of five 10-ft reflecting telescopes made in response to that request. Following Herschel’s standard design, the King’s cabinet-maker constructed the mahogany stand and tube. Herschdel made the optical parts himself.
There also are polyhedral sundials, more telescopes, astrolabes,…
… and this wonderful planetarium made by George Adams around 1750.
This grand Orrery, which is not to scale, displays the Sun in the centre, and the 6 then known planets and their satellites; 4 around Jupiter and 5 around Saturn. The planets Uranus, Neptune and Pluto had not yet been discovered.
Now, let’s teke a look at the collection of astrolabes and sundials but… it will be done in the next post!
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!
The third step in the visit to the Royal Observatory of Greenwich is Flamsteed House.
The Royal Observatory of Greenwich was founded in 1675 when Charles II ordered that a small observatory be built in Greenwich Park and appointed John Flamsteed as his ‘astronomical observator’. Flamsteed’s task was to make observations that would improve astronomical navigation, in particular providing a means of finding longitude at sea.
The ceiling of the first room is painted with a map of the night sky and there are portraits of the ten Astronomers Royal who lived here between 1676 and 1948:
Christopher Wren was responsible for building the Observatory. He later said that it was designed ‘for the Observator’s habitation & a little for Pompe’. The following four rooms were Flamsteed’s living quarters. They were incorporated into the enlarged home of the Astronomer’s Royal over the next two and a half centuries. Beyond these, upstairs, is the magnificient Great Star Room, or Octagon Room.
The Octagon Room is one of the few surviving interiors designed by Wren and it was used mainly for observing eclipses, comets and other unusual celestial events.
The 32-inch Astronomical Quadrant is located in this room. It is signed by John Bird but the telescope which was once attached is missing.
The engraving of the Octagon Room by Francis Place shows a similar, earlier quadrant standing on a wheel-tripod platform, which allowed the astronomer to roll it from window to window.
On the wall behind the quadrant we can see three replicas of the clocks which were made in 1676 by Thomas Tompion and sold by Flamsteed’s widow some years later. There is also a replica telescope tube of the kind used here until 1765. Will my daughter be able to discover a new planet?
If we go downstairs now we’ll discover an exhibition about the determination of the longitude at sea:
Where am I?
At sea, navigation is a matter of life and death. Out of sight of land, how can you tell where you are?
By 1700, skilled seamen could find their position north or south (their latitude), but still lacked accurated instruments or methods to calculate their east-west position, known as longitude.
With growing international trade, the lives and valuable cargoes lost in shipwrecks made solving this ‘Longitude Problem’ urgent for all sea-going nations.
The exhibition starts with these two 17th-century globes from North Africa (left) and Persia (right) and then you meet the star of the ‘Longitude Problem’:
Finding longitude – the timekeeper method
One solution to the Longitude Problem was an accurate and portable sea-going clock. By 1726, news of the Longitude Prize had reached John Harrison, a carpenter and self-taught clockmaker from Lincolnshire. Harrison was already making highly accurate land-based clocks and had solved major problems to do with temperature change and friction.
Harrison spent the next 45 years of his life developing portable sea-going timekeepers that would accurately, in spite of a ship’s motion and temperature changes. Each timekeeper represented years of obsessive labour.
By 1760, Harrison had solved the Longitude Problem with his fourth marine timekeeper, now known as H4. It is one of the most important machines ever made.
Harrison’s first timekeeper [H1]
This timekeeper took five years to build. In 1736, it was tested on a sea voyage to Lisbon and back. Harrison was very seasick, but the timekeeper worked. It was the most accurate sea-going clock then known, though not quite accurate enough to win the 20.000 pounds prize.
This prize was offered in 1734 by the British government for a ‘practical and useful’ method enabling ships to determine their longitude at sea.
In the exhibition there are also some timekeepers more and the portraits of some of the most important scientific men which lived in the same time as Harrison: Halley succeeded Flamsteed as Astronomer Royale and his major programme was to replace all the astronomical instruments which were sold by Flamsteed’s widow, and to chart the Moon’s 19-year cycle.
Newton advised the Parliamentary committee that established the Longitude Prize and became a member of the Board of Longitude:
Finally, apart of the camera obscura, we can find outside the Family Tombstone of Halley which was moved to the Observatory from the churchyard of St. Margaret’s in Lee when Halley’s tomb was restored in 1854. The tomb itself is still located at St. Margaret’s with a replica tombstone in place:
As you have seen, you must visit the Royal Observatory in Greenwich if you visit London: it’s only a few metro stops from the center of the city!