Category Archives: Poland

The Museum of Mathematics in the Collegius Maius

Photography by Carlos Dorce

Photography by Carlos Dorce

Another interesting museum located in the Collegius Maius of the Jagiellonian University is an exhibition about mathematics where children can play and learn a lot! There are old calculators from the 20th century…

Photography by Carlos Dorce

Photography by Carlos Dorce

…abacus and slide rulers:

Photography by Carlos Dorce

Photography by Carlos Dorce

Children can play with Geography and learn that straight lines in a map are not the shortest ways for the planes:

Photography by Carlos Dorce

Photography by Carlos Dorce

They can also learn the theorem of Pythagoras scrolling this interesting figure:

Photography by Carlos Dorce

Photography by Carlos Dorce

There are polyhedra and a lot of geometrical and topological games:

Photography by Carlos Dorce

Photography by Carlos Dorce

The museum is very small but all the tourist are inside Collegius Maius so you can be very quiet watching all the exhibited objects and toys, like the Rodin’s Thinker:

Photography by Carlos Dorce

Photography by Cristina Martínez

Finally… here you have my two children playing with Eulerian graphs! They are lovely! Aren’t they?

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Collegius Maius (map)

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The Collegius Maius of the Jagiellonian University

Photography by Carlos Dorce

Photography by Carlos Dorce

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:

Photography by Carlos Dorce

Photography by Carlos Dorce

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:

Photography by Carlos Dorce

Photography by Carlos Dorce

Everything takes you back to a ‘kitsch’ Renaissance:

Photography by Carlos Dorce

Photography by Carlos Dorce

There is space for our Copernicus, of course,…:

Photography by Carlos Dorce

Photography by Carlos Dorce

…and also for Galileo:

Photography by Carlos Dorce

Photography by Carlos Dorce

There is a special small room dedicated exclusively to Copernicus with astrolabes, charts, books and copies of some interesting documents:

Photography by Carlos Dorce

Photography by Carlos Dorce

For example, look at this interesting torquetum made by Hans Dorn in 1480 (the astrolabe was also made by Dorn in 1486)…:

Photography by Carlos Dorce

Photography by Carlos Dorce

…or this portrait of Kepler from the 18th century:

Portrait of Johannes Kepler

Portrait of Johannes Kepler

Furthermore, a bust of Isaac Newton…

Photography by Carlos Dorce

Photography by Carlos Dorce

… is on the top of the door through which you enter a room full of astronomical and mathematical instruments:

Photography by Carlos Dorce

Photography by Carlos Dorce

Can you see this little Aechimedes screw?

Photography by Carlos Dorce

Photography by Carlos Dorce

Before ending the visit, Newton (again!) says goodgye to the visitors in a very modern picture:

Photography by Carlos Dorce

Photography by Carlos Dorce

And Kepler too!

Photography by Carlos Dorce

Photography by Carlos Dorce

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:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Collegius Maius (map)

Copernicus in Krakow

Photography by Carlos Dorce

Photography by Carlos Dorce

This statue is next to the Jagiellonian University in Kraków. It was designed by Cyprian Godebski in 1899 as a top of a well and originally stood in the courtyard of the Jagiellonian’s Collegium Maius (Copernicus studied at the Collegium Maius in the years 1491 – 1495). It was moved here in 1953.

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Copernicus Monument in Krakow (map)

A sundial in St. Mary’s Church of Krakow

Photography by Carlos Dorce

Photography by Carlos Dorce

This sundial is on the south wall of St. Mary’s Basilica of Krakow (also known as Church of Our Lady Assumed into Heaven).

Photography by Carlos Dorce

Photography by Carlos Dorce

This 14th-century church is famous because on every hour the Hejnal mariacki is played from the top of its highest tower. The song breaks doesn’t finish to commemorate the death of trumpeter who was shot in the throat while sounding the alarm before the Mongol attack on the city.

Location: St. Mary’s Church in Krakow (map)

A plaque in the Cloth Hall in Krakow

Photography by Carlos Dorce

Photography by Carlos Dorce

In the ground floor of the Cloth Hall of Krakow there is this modern plaque (2007) designed by Czeslaw Dźwigaj and the selection of the text was made by Jerzy Wyrozumski and Alexander Kravchuk:

1257 Krakow city rights advocates by the German tradition and the situation of the market and the houses and affected courts

It was Bolesław V, “the Chaste One”, (1226–1279), Duke of Sandomierz in Lesser Poland from 1232 and High Duke of Poland from 1243 until his death, who introduced in 1257 the city rights modelled on the Magdeburg law allowing for tax benefits and new trade privileges for the citizens and this plaque was designed to conmemmorate the 750th anniversary of this moment.

The Cloth Hall is one of the most emblematic symbols of Krakow because is probably the oldest shopping mall in the World:

Source: Wikimedia Commons

It’s in the middle of the main square of Krakow and everybody visit it and buy something in the shops of the ground floor.

Photography by Carlos Dorce

Photography by Carlos Dorce

So next time that you visit Krakow look at the floor to this conmemorative plaque:

Location: The Cloth Hall in Krakow (map)

Finally will be the last?

Photography by Carlos Dorce

Photography by Carlos Dorce

We were coming back to our apartment and… another Copernicus! How many Copernicus are in Poland? This is made with 100 kg of chocolate and it must be the sweetest one. It was in the ancent Royal Pharmacy and current Cukierna Sowa:

The Royal Pharmacy

Here was the oldest pharmacy in Torun, established in the 14th century by Arnold, an apothecary from Wroclaw. In 1652 the pharmacy was granted the name “The Royal Pharmacy”. A figure of an eagle was placed over the door in the 18th century. From then on it has been called “The Pharmacy under the Eagle”.

It was a nice present before leaving Torun!

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Cukierna Sowa in Torun (map)

More Copernicus in Torun!

Photography by Carlos Dorce

Photography by Carlos Dorce

There is another monument of Copernicus in Torun designed by Wiktor Brodzki (1817-1904) in 1871. It is inside the Old Town Hall and you can see it in the main entrance of the museum housed there. So, enjoy it! One more monument for the collection!

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Old Town Hall in Torun (map)

Two sundials in Czestochowa

Photography by Carlos Dorce

Photography by Carlos Dorce

These two sundials are on the main door of the Sanctuary of Black Madonna in Jasna Góra in Czestochowa.

Source: Wikimedia Commons

Location: Jasna Góra (map)

Fontanna Cosmopolis

Photography by Carlos Dorce

Photography by Carlos Dorce

This fountain representing the Solar System was totally renovated and redesigned as a part of the Old Town of Torun renovation in 2008. It gushes water out of 115 nozzles in the perimeters of the orbits of the planets up to the height of 5 meters.

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Fontanna Cosmopolis in Torun (map)

Another monument to Copernicus

Photography by Carlos Dorce

Photography by Carlos Dorce

Only five seconds to remember this other monument dedicated to Nicolaus Copernicus and his heliocentric system in Torun!

Location: map