# 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!

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

# Some caricatures of famous mathematicians

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:

Halley and Hevelius:

Galileo:

Sir Isaac Newton:

and Albert 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

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 the monument was moved to the green square in front of the hotel Mercure Gdańsk Old Town (formerly Hotel Hevelius) in 2004.

**Location**: Monument to Hevelius (map)

# Monument to Hevelius

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.

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.

**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

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…

…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:

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

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

**Location**: Hewelianum Centre in Gdansk (map)

# Cryptography in the NTM (Prague)

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.

The Caesar code is also explained:

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.

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.

**Location**: National Technical Museum in Prague (map)

# Hewelianum Centre in Gdansk

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:

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

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

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!

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:

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

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

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!

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

**Location**: Hewelianum Centre in Gdansk (map)

# Jan Hevelius’ tomb

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.

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:

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”.

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

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

# Gdańsk astronomical clock

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.

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:

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.

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

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

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