Some caricatures of famous mathematicians

Archimedes

Archimedes

In my last post about the Hewelanium Centre of Gdansk, I must show you the caricatures of the famous mathematicians and astronomers which you find on the walls (and you also can buy as a puzzle in the shop of the museum). You have pictures of Archimedes, Pascal, Copernicus:

Copernicus

Copernicus

Halley and Hevelius:

Halley and Hevelius

Halley and Hevelius

Galileo:

Galileo Galilei

Galileo Galilei

Sir Isaac Newton:

Newton

Newton

and Albert Einstein:

Einstein

Einstein

These aren’t good pictures but the posters are in 3D and my camera is not the best camera in the World!

Location: Hewelianum Centre in Gdansk (map)

Another monument dedicated to Hevelius

Photography by Carlos Dorce

Photography by Carlos Dorce

 The first monument to Hevelius built in Gdansk was initiative of TPD club Neptune of Gdansk and it was possible because of the donation of the citizens in 1973. The author was Michael Gąsienica Szostak and ihe monument was moved to the green square in fornt of the hotel Mercure Gdańsk Old Town (formerly Hotel Hevelius) in 2004.

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Monument to Hevelius (map)

Monument to Hevelius

Photography by Carlos Dorce

Photography by Carlos Dorce

This monument was designed by Jan Szczypka on 2006 and was unveiled on January 28 to conmemmorate the 395th anniversary of his birth. It’s opposite the Old Town Hall and near the church where he was buried which tower can be seen behind the monument.

Photography by Carlos Dorce

Photography by Carlos Dorce

Hevelis was the last great astronomer who worked without telescopes so he is working with a quadrant in spite of the 17th century modern devices.

Next to him there is a stellar map painted on a large wall waiting to be observed by this great astronomer.

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Monument to Hevelius in Gdansk (map)

Galileo’s telescope in Google

This doodle was published in August 25, 2009, to celebrate the 400th anniversary of Galileo’s telescope.

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)

Cryptography in the NTM (Prague)

Photography by Carlos Dorce

Photography by Carlos Dorce

I hope this is my last post about the NTM in Prague after talking about the astronomical instruments and Kircher’s Organum Mathematicum! Opposite the astronomical exhibition, there is another about secrets and adults and children can play with the cryptography (if they know the Czec language!):

Ché Guevara used a number code when communicating with Fidel Castro. He transposed each letter in the text to a number [...]. He then wrote those numbers one behind the other. Below that line he wrote a second line of numbers, known only to him and Castro, which was used only once. He then added both lines, number per number, and below each set of numbers he wrote (the last digit of) the sum. This give a third line of numbers. Only that row was transmitted. When Castro subtracted the second line from the third, he had the first line as the result.

The Ché method cannot be cracked because the key (the second line of numbers) is random, as long as the message, is only used once.

One of the oldest methods for hidding a message is the Ribbon Code:

The code system of winding ribbons around a shaft was already known to the Greeks of the seventh century BC. The generals of Sparta received a staff in deep secrecy, of which the other half was kept by the magistrates of the city. Messages were written on a leather belt.

The Greek called such a stick a scytale and code experts today still use that name. The scytale is an example of a ‘transposition code’, a code in which the letters of a text are mixed up according to a specified recipe. The drawback of a scytale is that the spy can already guess from the ribbons which coding technique was used. It is then only a matter of patience to find the right diameter of the shaft. Gabrielle Petit, a heroine of the Belgian resistance during World War I, passed messages on silk ribbons, which she camouflaged as part of her clothes.

Photography by Carlos Dorce

Photography by Carlos Dorce

The Caesar code is also explained:

Photography by Carlos Dorce

Photography by Carlos Dorce

And the Mask Code:

The French cardinal Richelieu (1585-1642), a famous and powerful intrigant, fully used this technique to stay in contact with his agents and spies. They were each given a mask, to put over his letters.

In this method, you and your partner each have the same grid with holes. You write a message in the holes, and afterwards you fill in the remaining space with innocent text. This technique is known as the ‘Cardan grille’ after Girolamo Cardano, of Cardan joint fame, who invented the grille in 1550. It is very difficult to crack.

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, a space for the Enigma machine:

The Enigma was the German top coding machine during World War II. The Germans thought their messages to be uncrackable. Which would indeed have been the case, if they operators hadn’t made procedural mistakes and the British hadn’t secured a code book. The mathematical genius Alan Turing designed the first automatic calculators to do the enormous amount of computations needed to check all possibilities. It is assumed Turing and his crew shortened the war with two years.

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationNational Technical Museum in Prague (map)

Hewelianum Centre in Gdansk

Photography by Carlos Dorce

Photography by Carlos Dorce

I visited the Hewelianum Centre when I was in Gdansk and I discovered a new science museum which must be located in all the tourist guides:

The Hewelianum Centre is an educational and recreational centre for all age groups situated on the grounds of the Fort Góra Gradowa. The view from the top of the hill is the panorama of the historic town and the industrial landscape of the shipyard grounds. A picturesque park and a complex of restored 19th-century military remains hosting interactive exhibitions – this is today’s image of the Fort of Góra Gradowa.

Science popularization is the main objective of the Hewelianum Centre. Interactive and multimedia exhibitions and popular science events disclose the mysteries of physics and astronomy, transfer the visitors to the past, making the historic events better understandable in the present, teach how to be sensitive to the beauty of nature, and strengthen in visitors the belief that we are all responsible for our planet. In Hewelianum Centre you can perceive the world, learn about it, and relax yourself in an interactive, creative, and innovative way!

One of the exhibitions is called “Puzzle” (why not “Maths”?) and it’s a place where people can play with Mathematics:

Break the code and discover a new dimension of mathematics!

The “Puzzle” exhibition is a three-dimensional space: mathematical, interactive, and unconventional. It consists of more than 20 stations for experimenting – where mathematics governs, but in an unprecedented way!

By crossing the mathematical “puzzle” threshold, we enter the world of geometry, symmetry, and numbers. The mathematical setting, however, is only a backdrop for interactive learning and fun. A collection of the exhibition’s main attractions includes the multiplication tower, the Pythagorean theorem in liquid form, and the Möbius strip. Here you can also see what your face would look like if it were composed of two left or two right halves or check whether a meter is the same length for all. Visiting the mathematical “Puzzle” is a perfect idea for a unique scientific experience.

The exhibition is located in the Guardhouse over the Mortar Battery postern

The room is small but all the walls and corners are full of Maths experiments:

Photography by Carlos Dorce

Photography by Carlos Dorce

For example, there is a Galton box (or Bean machine) where Pascal’s triangle and the Gaussian function can be observed perfectly.

Photography by Carlos Dorce

Photography by Carlos Dorce

You can also play with the Towers of Hanoi and discover that the minimum number of moves required to solve the puzzle is 2n – 1, where n is the number of disks (this problem was first publicized in the West by Édouard Lucas in 1883):

Photography by Carlos Dorce

Photography by Carlos Dorce

Did you know that it’s possible to construct a byke with squared wheels? Yes, of course. The path for this bike must be formed by contiguous series of inverted catenaries!

Photography by Carlos Dorce

Photography by Carlos Dorce

And had you ever seen such a wonderful way to demonstrate the Theorem of Pythagoras? Water inside the square constructed on the hypothenusa fills perfectly in the two squares constructed on the other two sides:

Photography by Carlos Dorce

Photography by Carlos Dorce

Obviously, there are Möbius strips and Klein’s bottles:

Photography by Carlos Dorce

Photography by Carlos Dorce

And you can play with the light to discover the four conics:

Photography by Carlos Dorce

Photography by Carlos Dorce

There are poster about a lot of mathematical subjects but tha puzzle that fascinatd so much to my son and daughter was this experiment with volumes. They discovered that the volume of a prism is three times the volume of the corresponding pyramid although they played with the red sand preparing cornflakes for breakfast!

Photography by Carlos Dorce

Photography by Carlos Dorce

If you visit Gdansk you must go to Hewelianum Centre and really enjoy Maths!

Location: Hewelianum Centre in Gdansk (map)

Jan Hevelius’ tomb

Photography by Carlos Dorce

Photography by Carlos Dorce

Hevelius is buried in St. Catherine’s Church in Gdansk. The construction of the current church began before 1379 and the consecration of the first phase of the building was on the feast of Pentecost of 1432. In the 15th century a chapel and a tower were added and the church’s vault was finished. One century later the side naves were added to te presbytery.

Photography by Carlos Dorce

Photography by Carlos Dorce

Hevelius was the head Protestant councillor in St. Catherine for 47 years and he often made astronomical observations from the tower of the church. Thus, when he died nobody doubted that he had to be buried behind the altar:

Photography by Carlos Dorce

Photography by Carlos Dorce

His epitaph was founded by his grand-son Daniel Gottlob-Davisson and the work was completed in 1779. You can see some astronomical instruments in the lower part. Under the portrait there is an inscription “To Jan Heweliusz with respect due to such man”.

Photography by Carlos Dorce

Photography by Carlos Dorce

There also is a plaque placed in the same column on January 28, 2011, to conmemorate 400 years of Hevelius’ birth:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: St. Catherine’s Church in Gdansk (map)

Gdańsk astronomical clock

Photography by Carlos Dorce

Photography by Carlos Dorce

This astronomical clock was constructed between 1464 qnd 1470 by the clockmaker Hans Düringer of Nuremberg. It’s 14 metres high and was the World’s tallest clock in the 15th century. It was reconstructed after the damages in the Second World War.

The construction of St. Mary began in 1379 and it’s currently the largest brick church in the World because of it’s 105 metres high and the nave is 66 metres wide.

Photography by Carlos Dorce

Photography by Carlos Dorce

It’s one of the symbols of Gdansk. For example, here you have on German Nazi propaganda poster from 1939 with St. Mary as guest star:

Source: Wikimedia Commons

The clock shows the date, the time, the phases and position of the Moon and the position of the Sun in the Zodiac. On the clock Adam and Eve alongside the Three Kings, the Death and the Apostles.

Photography by Carlos Dorce

Photography by Carlos Dorce

There also are the calendar of the Saints so it’s a very complete clock.

Photography by Carlos Dorce

Photography by Carlos Dorce

By the way, there is a sundial in one of the lateral facades!

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Basilica of St. Mary of the Blessed Virgin Mary in Gdańsk (map)

Copernicus’ tower

Photography by Carlos Dorce

Photography by Carlos Dorce

In the northwest corner of the cathedral of Frombork grounds is Copernicus’ tower. This building was used by the astronomer to observe the sky and now contains an exhibition about the search of his tomb and the investigations made on his cadaver.

Furthermore, there ar a lot of photographies and posters and from his skull…

Photography by Carlos Dorce

Photography by Carlos Dorce

…you can see the reconstruction of his face. Ladies and gentlemen… here you have… Nicolaus Copernicus!

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Frombork castle (map)

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