Tag Archives: Conic

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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Copernicus Science Centre

Photography by Carlos Dorce

Photography by Carlos Dorce

We went to the Centrum Nauki Kopernik in our last day in Warsaw which is a very interesting science museum. The building design was developed by young Polish architects from the firm RAr-2 in Ruda Śląska, who won an architectural competition in December 2005.

There are a lot of different rooms and interactive exhibitions and… there are also a lot of mathematical objects which you can touch and play with them. For example, you can see the Archimedes screw:

Photography by Carlos Dorce

Photography by Carlos Dorce

Water flows forwards and upwards in this simple hand pump, which works just like the rotating blade in an old-fashioned meat mincer. Many places around the world still use such a device to pump water, and it is frequently used to pump sewage in modern sewage systems. It was used for reclaiming land from under sea level in the Netherlands, and it was even used instead of traditional caterpillar tracks on Soviet armoured vehicles! Its key advantage is very simple: it doesn’t contain any complicated mechanisms that may break down.

You can also play with a Möbius band…

Photography by Carlos Dorce

Photography by Carlos Dorce

…or discover the conics rotating a cone full of blue water:

Photography by Carlos Dorce

Photography by Carlos Dorce

Here you have a beautiful parabola:

Photography by Carlos Dorce

Photography by Carlos Dorce

You can also play with the parabola using it as a communication device. Outside the museum there are two parabolas: you talk in one of them and you listen the message in the other:

Photography by Carlos Dorce

Photography by Carlos Dorce

There are models of the Solar system, astronomical and optical experiments… and in the cinematic corner, the cycloid is very important because its property of… play with it! I’ve talked about it before!

Photography by Carlos Dorce

Photography by Carlos Dorce

Finally, the museum receives the visitors with this big Foucault pendulum:

Photography by Carlos Dorce

Photography by Carlos Dorce

It was a very nice experience!

Location: Centrum Nauki Kopernik (map)

The Museum of Mathematics of Catalonia (MMACA)

mmaca04

Last Wednesday I went to MMACA (Museum of Mathematics of Catalonia) with some of my students. This museum is located in Mercader Palace in Cornellà de Llobregat (near Barcelona) since February and we enjoyed a very interesting “mathematical experience”.

Mercader Palace Photography by Carlos Dorce

Mercader Palace
Photography by Carlos Dorce

The museum is not so big but you can “touch” and discover Mathematics in all its rooms. I think that there are enough experiences to enjoy arithemtical and geometrical properties, simmetries, mirrors, impossible tessellations, Stadistics,…

Photography by Carlos Dorce

Photography by Carlos Dorce

For example, students could check the validity of theorem of Pythagoras in two ways. First of all, they coud weigh wooden squares and check that the square constructed on the hypotenuse of a right triangle weighs the same as the two squares constructed on the other two sides of the triabgle. Later, they discovered that the first square could be divided in some pieces of Tangram with which they could construct the other two squares. So the visitors demonstrated the theorem in a very didactic way: playing with balances and playing with tangram.

Photography by Carlos Dorce

Photography by Carlos Dorce

Students also learnt some properties of the cycloid and they could check its brachistochronic characteristic. I imagine Galileo or some of Bernoulli brothers in the 17th century doing the same experiments with a similar instrument. What a wonderful curve! The ball always reaches the central point in the same time and its initial position doesn’t matter!

mmaca07

Photography by Carlos Dorce

Another of the studied curves is the catenary which is one of the emblematic mathematical symbols of Antoni Gaudi’s architecture in Barcelona.

Photography by Carlos Dorce

Photography by Carlos Dorce

Of course, polyhedra are very important in the exhibition and visitors can play with them so they discover some of their most important properties. For example, which is the dual polyhedron of the dodecahedron? Playing with it the students could see that the hidden polyhedron is a… You must visit MMACA and discover it!

Photography by Carlos Dorce

Photography by Carlos Dorce

Another example: look at these three wooden pieces…

mmaca12

The dodecahedron has an ortonormal symmetry and we can check it with an ortonormal set of mirrors:

Photography by Carlos Dorce

Photography by Carlos Dorce

There are more mirrors and more wooden pieces to play and construct other different Platonic and Archimedian polyhedra.

And… did you know that it’s possible to draw a right line playing with two circles? If the red circle rotates within the black one… what figure is described by the yellow point?

Photography by Carlos Dorce

Photography by Carlos Dorce

In the 13th century, the great Nasîr al-Dîn al-Tûsî had to build one similar instrument to improve the astronomical geometrical systems with his “Al-Tûsî’s pair”:

Source: Wikimedia Commons

Rotating a circle within another one, he could move a point in a right line without denying Aristotelian philosophy. This dual system was used by al-Tûsî in his Zîj-i Ilkhanî (finished in 1272) and Nicolas Copernicus probably read this innovation together with other Arabic astronomical models. Thinking about them, he began to improve the astronomical system of his De Revolutionibus (1543). Al-Tûsî’s pair was very famous until the 15th century.

In Erathostenes Room there are some Sam lloyd’s puzzles, games about tesselations, Stadistics, Probablility and this quadric:

Photography by Carlos Dorce

Photography by Carlos Dorce

I didn’t know that it could be described only with a multiplication table! Is its equation z = xy? Yes, of course! My students also played to build the famous Leonardo’s bridge and they could see that there isn’t necessary any nail to hold a bridge.

Photography by Carlos Dorce

Photography by Carlos Dorce

Ah! And I can’t forget to say that if you visit MMACA with a person that don’t like Maths, he/she can always admire this beautiful XIX century Mercader Palace:

Photography by Carlos Dorce

Photography by Carlos Dorce

Furthermore, one of the rooms of the palace is decoratd by a chess lover!

Photography by Carlos Dorce

Photography by Carlos Dorce

So… you must go to MMACA and enjoy Mathematics in a way ever done!

mmaca13

Location: MMACA in Cornellà de Llobregat (map)

The Science Museum in London (VI)

Photography by Carlos Dorce

Photography by Carlos Dorce

Let’s play with Topology! The exhibition is full of polyhedra, curious surfaces,… and Möbius strips:

Photography by Carlos Dorce

Photography by Carlos Dorce

August Möbius (1790-1868)

Professor Möbius discovered the surface now known as the Möbius strip in the course of an investigation of the properties of polyhedra. The discovery was made in 1858 but was not published until 1865.

There is certainly also the Klein’s bottle:

Photography by Carlos Dorce

Photography by Carlos Dorce

We can imagine what a wonderful surface we can get if a plane is deformed!

Photography by Carlos Dorce

Photography by Carlos Dorce

Sometimes, it depends on our point of view and there are surfaces which are homeomorphic to other ones that seems very different to them! If we look at the example of the conics, the circumference, the ellipse, the hyperbola and the parabola are different points of view of the same reality, aren’t they?

Photography by Carlos Dorce

Photography by Carlos Dorce

LocationScience Museum in London (map)