Tag Archives: Circle

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)

Omar Khayyâm’s doodle

Omar Khayyam was born in Nishapur on May 18, 1048. He went to school and two of his best friends there were Nizam al-Mulk and Hassan al-Sabbah. The three boys agreed that the first of them who could get a rich position will help his friends in a future. Al-Mulk became vizier in Alp Arslam’s palace and al-Sabbah and Khayyam also benefited of his nrew position although Khayyam got a job which let him to study Astronomy, Literature and Mathematics. Khayyam’s life wasn’t easy but his astronomical studies and his participation in the reform of the calendar were so decisive that he always had a city or a place where being able to life and work. According to al-Arudî al-Samarcandî, Khayyâm died on December 4, 1131.

Stamp issued by Dubai

Khayyâm studied Euclid’s Elements and Data, Apollonius’ Conics and al-Khwârizmî’s Algebra and wrote his major work on Algebra around 1074 whre was able to solve geometrically the cubic equation. The treatise begins with three introductory lemmas:

  1. To find two segments x and y which a/x = x/y = y/b (Khayyâm finds a point (x,y) which is the crossing point of the parabolas x2 = ay and y2 = bx).
  2. To determine the height of a parallelepiped with known squared base b if we know that its volume must be the same as another parallelepiped with squared base a and height (Khayyâm determines a line k such that a/b =b/m and the searched height K is k/a = h/K).
  3. To determine the side of the base of the second parallelepiped.

Khayyâm solves fourteen canonic cubic equations (he didn’t know the negative numbers!) from these three geometric lemmas. For example:

Lemma 1. From lemma 1, we can find x and y such that 1/x = x/y = y/c and this point (x,y) satisfies x3 = c.

The other thirteen cases are solved crossing parabolas, circles and hiperbolas.

In 1857 E.Fitzgerald discovered Khayyam’s Rubâyyât in the British Museum and trabslated some verses from this “new” manuscript. The translation to English was so popular since 1861 and the Khayyâm’s name was very famous in the literary circles. The Rubâyyât contains over 400 quatrains written in Persian and were translated to English again in 1970s by Robert Graves:

Wake! for Morning in the Bowl of Night

Has flung the Stone that puts the Stars to Flight:

And Lo! the Hunter of the East has caught

The Sultán’s Turret in a Noose of Light

Stamp issued by the Federated States of Micronesia

Stamp issued by Guyana

Dreaming when Dawn’s Left Hand was in the Sky

I heard a Voice within the Tavern cry,

Awake, my Little ones, and fill the Cup

Before Life’s Liquor in its Cup be dry.

The mathematical doodle was published by Google in the Arabic countries two years ago to commemorate Khayyâm’s birthday.

Pi Day’s doodle

Today is Pi Day!

Google published this doodle four years ago. We can see some formulas in it related with circles, spheres, trigonometry and the Archimedian value of pi.

The Bullring in Birmingham

Photography by Carlos Dorce

Photography by Carlos Dorce

Bullring is a very big shopping center in Birmingham downtown which is impossible to not visiting if you are in this great English city. In one f the corners of the mall we can see this curved structure which shows a metallic mosaic full of circles. There are a lot of restaurants and shops below it so here you have a very good place to start your day in the shopping center.

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Bullring Shopping Center (map)

Birmingham Central Library

Photography by Carlos Dorce

Photography by Carlos Dorce

Birmingham Central Library is one wonderful example of a mathematical building. Look at their beautiful three mosaics (the white one, the blac one and both together) which we can admire in Centenary Square!

Photography by Carlos Dorce

Photography by Carlos Dorce

So don’t forget to visit it if you are going to Birmingham!

Location: Birmingham Central Library (map)

A very mathematical table

Photography by Carlos Dorce

Photography by Carlos Dorce

Walking along Ostergade Street I found these tables in Holm’s Kaffe Bar which are also found in other cafes of Copenhagen:

Photography by Carlos Dorce

Photography by Carlos Dorce

I think that I’m going to take a coffee (a double espresso with cold milk) here!

Location: map

Khan Shatyr in Astana

Khan Shatyr in AstanaSource: offical site

Khan Shatyr in Astana
Source: official site

This is my first post about Kazakhstan! I am very happy to be able to talk about this country which I’s like to know! Yesterday I was watching TV and I saw this fascinating mathematical structure in a report about Astana.  Which form has this beautiful roof? Searching information in the official web site:

Quote from MikeSefton, Buro Happold’s project leader of the Khan Shatyr. The center’s design came from the idea of creating one vast roof which would house many venues and which would have a real feeling of space. So often in similar schemes there is a sense of individual, boxed-in buildings but by having one large tent accommodate them all. A major challenge with the project was to keep the temperature inside the space even in a climate with extreme weather conditions. We need visitors to be able to move from venue to venue inside the structure without experiencing dramatic changes in temperature.
Another challenge was the asymmetry of the design. To work to a perfect circle creates a full radial symmetry but when you’re dealing with a cone shape that is also on a lean, you only have one line of symmetry – down the central line. This means every cable anchor and cable has a different geometry as they are all at different angles. Tensile structures are all about anticlastic surfaces – surfaces that have opposing curvatures. Flat tensile designs just don’t work, so if you are considering using a tensile structure, you have to accept that it must have curves.Mountain climbers as part of the construction team. The cable net comprises of 192 radial cables and 16 circumferential cables. The installation of the foil cushions onto the cable net structure which is clad in a three-layer ETFE envelope, will take between three and four months as this can only be done during summer and autumn.To ensure the efficiency as well as to complete the installation of the cables within record time of 1 month, 650 professional mountain climbers from 7 different nations formed part of the construction team at this critical stage. They worked under severe conditions up to a height of 100m from the bottom in order to accomplish the mounting.ETFE – for a comfortable microclimate throughout the year. ETFE (ethylene-tetra fluoroethylene),a material that allows daylight to wash the interiors while sheltering them from weather extremes. The perfect material to be used in unpleasant climates.While the buildings within the envelope are fully conditioned, the target temperatures in the landscaped areas are +15 degrees Celsius in winter and +30 degrees in summer. In winter, a key challenge is to prevent the formation office on the inside of the envelope. This is achieved by a combination of temperature control and directing warm air currents up the inner fabric surface, a strategy that also prevents downdraughts. In summer, fritting on the outermost foil layer provides solar shading. Inside, low-level jets direct cool air across the space, while opening vents at the apex induce stack-effect ventilation.Project’s cable net structure is coated with 19,000sqm of ETFE foil cushions, compromising three layers assembled together, with the middle layer inflated. By inflating the cushions with air the material can accommodate a high thermal range. Each cushion is about 3.5m wide and up to 30m long.The flexibility of the ETFE material also makes it well suited to deal with the cable net’s range of movement. As the structure deflects, the cables move closer together and the cushions change shape – from an eye shape to an almost cylindrical shape.
The ETFE cushion panels are connected to the cables using a system of aluminum clamping plates. These are able to tolerate the movements of the cables under wind and snow loads.

Source: CNN

The 16 circumferential cables hold a picturesqueness structure which must be photographed if a lucky person can travel to Astana. Khan Shatyr Shopping and Entertainment Center is the new symbol of the capital of Kazakhstan. It was designed by Norman Foster and it’s the biggest tent in the World which features shopping and entertainment under the mathematical roof.

Location: Khan Shatyr (map)