SPANISH and German scientists have discovered two exo-planets which may hold water and have a mild, Earth-like climate, meaning potentially, the conditions are right for extra-terrestrial life. Both planets orbit the...
Second Maths Museum for Spain counts on making learning fun
FOR the majority of us, 'maths' conjures up images of grappling with sums in exercise books of squared paper, being shouted at for not using a ruler, and stabbing compass points into rubbers when you got bored, Those who continued the subject past the obligatory school level at 15 or 16 will probably, however, be able to explain to you some of the magic involved – maths, after all, is the foundation for any form of engineering, and is heavily present in art. It's not all number-related, either – shapes, lines and other visual symbols feature largely in maths, as do probabilities and frequencies, weights and measures.
All in all, it's a fascinating subject, and what we learnt in compulsory schooling is merely the very bare bones of it.
This may be a sore point for the protesting students in Valencia yesterday (Friday) who have started a petition after the maths section in their Selectividad, or university entrance exam, turned out to be so difficult many could not do it and now, thousands of sixth-formers fear their marks may be too low to get them into college (although the regional education authority urges them not to panic as they intend to launch a full inquiry). But if they don't want their skills to languish over the summer, and suspect they may have to repeat their exam, a fun way to do so is at a maths museum.
At present, there are only five in Europe – in Florence (Italy), Quaregnon (Belgium), Beaumont-de-Lomagne (France), Giessen (Germany) and Cornellà de Llobregat (Barcelona province, Catalunya) although the good news is that the latter is very cheap, with a €2.50 entry fee for booked visits and a voluntary donation of the same for non-booked trips during main opening hours, which are 17.00 to 20.00 on Wednesdays and 10.00 to 14.00 on Sundays. You can find it in the Can Mercader Palace Museum in the Can Mercader Park.
Despite its restricted opening times – necessary, because it's quite small – the Maths Museum in Cornellà gets around 10,000 visits a year, so it's clear there's a demand for this type of interactive edutainment.
For this reason, a new one is due for opening later this year at the 12th-century Santa María monastery in Casbas (Huesca province, Aragón), a beautiful venue (second picture) which has featured in Spanish films, including La Novia ('The Bride') by Aragonese director Paula Ortiz, and Incierta Gloria ('Uncertain Glory') by Agustí Villaronga, and which was actually lived in until the early part of this century.
The brainchild of Professor Julio Bernués, who teaches maths at Zaragoza University, the future Maths Museum will open firstly to the public, then start taking in school groups from the autumn.
A grant from the ministry for science and universities will help get it under way, although more is needed, so the organisers are crowdfunding the balance via vkm.is/matematicas. Anyone who donates will get free gifts, discounts and free museum entry.
This means two Maths Museums for Spain, more than any other country in Europe – and, although the actual format of the workshops, exhibitions and activities in the Casbas one have not been fully revealed, a swift look at what goes on inside the Cornellà version gives an idea of what you can expect to find there.
Cards are placed in a four-loop serpentine, reflecting rocks in a river. Choose a card in your head, but without telling anyone what it is. Leap forward the number of 'rocks' corresponding with the number of your chosen card. When you reach it, leap forward the number of rocks corresponding with the number of the card you landed on. Repeat until you reach the end.
The computer will tell you which card you picked in the very beginning. Magic? Actually, no. Invented by physicist Martin David Kruskal, it's all about probability, and the card-dealer and number-guesser does his or her own counting before you start, meaning they can predict which card you will land on at the very end and work their way backwards to the one you originally selected.
The computer deals out 12 cards and places them in a 4x3 grid (third picture). Each card is a chamber in a labyrinth with doors between them, which can only be reached by moving horizontally or vertically, never diagonally. Each time you pass through a 'chamber', this disappears. You go through as many doors as the number on the card of the first 'chamber', then stop and click. Whichever way you move, you'll always end up trapped in one room after each move. Again, a question of probability and number formulae, not really magic.
Coloured discs in different sizes, widest at the bottom and narrowest at the top, stand on one of three poles (fourth picture).
You move one at a time, always from the top, onto the others until you manage to get all discs in the right size order onto one of the two poles that were empty at the start. A bit like a towering version of a Rubix cube.
Differently-coloured pyramids are held together by magnets to form an octahedron, an eight-sided shape. Your job is to take them apart and put them back together in the form of a cube. In theory, this should be simple, since a cube has half as many sides as an octahedron...but depending upon your level of spatial skills, you might end up lobbing it out of the window in frustration.
A 'catenary' is a tall, narrow arch, the shape of which resembles that of half a chain link. You're given 11 differently-coloured parts, which you need to put together to build the arch. Sounds simple? Really? Well, best of luck...
Eight balls, 15 holes...and why is my birthday on the same day as yours?
The best way to illustrate this is to have eight different people drop one ball into a random hole, although if you're visiting alone, you'll have to drop all eight yourself and try to forget where you put each. These run through an internal pipe and drop out of one of 15 exits into a groove. If you repeat the exercise several times, you'll see that at least two balls always come out of the same hole.
How does that work, when the pipe inside is not slanted towards one particular channel, and all the balls are evenly-weighted? Again, it's based upon the table of probability, which shows the likelihood of two or more items out of eight coinciding with one of 15 or more possibles is 89.9%. This same table of probability can show you how likely it is that more than one of a group of randomly-selected people have the same birthday: with 365 choices (let's assume none of you was born in a leap year), in a group of four people, there's only a 2% chance any of you will have come into the world on the same day. By the time the group rises to 30 people, the probability is 71%, and if there are 50 or more of you, it's almost a certainty at least two of you will share a birthday, since the chances are 97%.
How we can make this apply to the El Gordo Christmas lottery jackpot is unclear, although no doubt there's a formula for it – and one that involves collecting a rather huge number of friends to go into a syndicate with you.
Coloured ball dispenser
A rotating cylinder filled with 2,500 tiny balls – of which the vast majority are yellow and a very tiny number blue – yields 50 random balls onto a tray each time you turn it.
Mathematicians can predict, with 95% certainty, how many blue balls will appear on average with each 'release' – a certainty which increases with the number of times you let them out, so by around 100, 200 or 500, you'll start to see a pattern forming. This all relates to applied statistics and interval data, used in quantitative research of all types, even working out possible election results, consumer behaviour, or how likely it is to rain next time there's a fiesta and you were planning to go the beach.
Mors tua vita mea
Latin for 'your death is my life', this intriguing board game features green chips and red chips in square shapes on a grid. Following the instructions, the numbers of each increase and decrease randomly, reflecting a population of a species, such as humans. You have to try to work out the best route to 'sustainable growth' to keep your colour chips 'alive', at the expense of your opponent's 'population'. It's a cut-throat world out there – it's all about survival of the fittest coloured squares.
You can buy your own version to try at home if your attempt at it in the museum is successful. Inter-slotting wooden pieces, like meccano parts without the holes or jenga bits that click together, are combined to make a Leonardo da Vinci-style dome with approximately a four- or five-metre diameter base and about a metre in height. Then you can pop inside it and take a selfie. A great group activity for kids, adults or a combination of the two.
Game of Skyscrapers
The Hanoi Towers, Kruskal Count and Mathemagic Labyrinth are also available in virtual as well as physical format, but the Game of Skyscrapers is only playable here on screen. A surefire hit with sudoku-addicts, you have a 4x4 grid and sets of four types of building – green, red, yellow and blue – and have to put them into the squares, but with no two buildings the same in any horizontal or vertical line. Just to add complications, the numbers one to three at the start of each column and row tell you how many buildings you should be able to see when 'standing' at that point. Each skyscraper is a different height, so you need to arrange them so that the taller ones mask – or don't mask – the smaller ones to get the right number of buildings per column or row. Colourful sudoku with a vengeance.
Photograph 2: Románico Aragonés
Photographs 3, 4 and 5: Cornellà de Llobregat Maths Museum
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