Tag Archives: Pascal

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)

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The Pascaline

Pascaline (1652). Musée des arts et métiers (París).

When Blaise Pascal (1623 – 1662) was only 17 y.o., his father Etienne Pascal (another great mathematician) was appointed chief of the taxmen in Normandy, France. What did this clever teenager think when saw his poor father calculating everytime? Well, as good son as he was, he decided to give him the best present which Etienne could receive: a calculating machine (1652) which was recalled with the name Pascaline a lot of years later. This analogic machine was only able to add numbers but Etienne’s work became easier than before. Pascal introduced several improvements to his invention and the Pascaline was patented. Unfortunately, the manufacturing of the machine was too expenseive and Pascal’s small business could only make fifty calculators and one of them still survives in the Musée des arts et métiers in Paris.

In addition , we also report the visit to see some of the instruments that Pascal used to study the atmospheric pressure.

Location: Musée des arts et métiers in Paris (map)

The Science Museum in London (II)

Photography by Carlos Dorce

Photography by Carlos Dorce

There is asection dedicated to Mathematics and it’s a paradise for the mathematical freaks! It’s full of calculators, Klein’s bottles, polyhedra,… and it’s possible to learn a lot of things only reading the information next to them. Shall we begin?

After the Second World War, the teaching of arithmetic to children in Britain became less focussed on repeated sums and tables, and more orientated towards understanding through experience. The use ofcalculators was always controversial.
In 1971, the rapid introduction of silicon chips ushered in the age of the pocket electronic calculator. However, in Japan, use ofthe ‘soraban’ or Japanese abacus was so instilled that, even a generation later, older people relied on them.

Educational toys became increasingly popular during the 20th century as parents realised they could improve their children’s performance and manufacturers realised there was a large potential market. For example, we can see the ‘Tell Bell’ educational toy from c.1930 in the first picture of this post.

All these first calculators also have their space in the museum. Here we can see some examples. The first one is the ‘Addiator’ mechanical adder from 1924. Until the 1970s mechanical adders remained essentially the same as those made in the 19th century but used new materials and designs:

Photography by Carlos Dorce

Photography by Carlos Dorce

The ‘Alpina’ mechanical adder was produced in Germany in c.1955:

Photography by Carlos Dorce

Photography by Carlos Dorce

From c.1950 we find the ‘Baby’ and the ‘Exactus’ mechanical adders and the ‘ Magical Brain’ mechanical adder is from c.1960:

Photography by Carlos Dorce

Photography by Carlos Dorce

But… when did everything begin? The first known attempt to make a caclulating machine was by Wilhelm Schickard (1592-1635), Professor at the University of Tübingen. Sketches of the machine appear in two of his letters written to Johannes Kepler in 1623 and 1624. Unfortunately the machine was destroyed by fire and there is no record of a replacement. Two decades later, Blaise Pascal completed a calculating machine in 1642 when he was 19 y.o. It was designed for addition and subtraction, using a stylus to move the number wheels:

Photography by Carlos Dorce

Photography by Carlos Dorce

The crude constructional methods of the time resulted in unreliable operation. Although several machines were later offered for sale, the venture was not a commercial success.

Photography by Carlos Dorce

Photography by Carlos Dorce

Sir Samuel Morland was the first Englishman to venture into the field of calculating machines designing this one (1666) on Pascal’s invention.

Photography by Carlos Dorce

Photography by Carlos Dorce

Gottfried W. Leibniz continued the construction of new calculating machines with this new one which wasn’t on display when I was in the museum. The mechanism was based on the stepped reckoner which eventually became the foundation of the Arithmometer:

Photography by Carlos Dorce

Photography by Carlos Dorce

It is unworthy of excellent men to lose hours like slaves in the labour of calculation, which could be safely relegated to anyone else if machines were used.

Leibniz, 1671

Finally, we must take a look to the Facit:

Photography by Carlos Dorce

Photography by Carlos Dorce

Was it really the World Champion in its class?

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationScience Museum in London (map)

Christiaan Huygen’s birthday

Today is  Christiaan Huygens’s birthday and this is the doodle dedicated to Huygen’s birthday in April 16, 2009.

Huygens (1629-1695) as one of the first mathematicians to study Probability. He published his De ratiociniis in ludo aleae in 1656 in which he established the foundations of the Calculus of Probabilities after Pascal and Fermat’s letters. Furthermore, he worked on the cycloid, the rectification of curves, the pendulum,…

He also made important contributions to Phisics and Mechanics.

Source: Wikimedia Commos