Exhibition commissioner: Montserrat Alsina Text & Edition: Montserrat Alsina Formatting: Salvador Garriga Manresa, 2nd ed. December 2014 With support and collaboration of

If people do not believe that mathematics is simple, it is only because the do not realize how complicated life is. J.L. von Neumann (Mathematician 1903-1957)

Did you realize through THE QUESTIONS that Mathematics surrounds us and it is part of our lives? The exhibition at the mNACTEC lead you through a usual day at the street, at the park, at work â&#x20AC;Ś to discover SOME ANSWERS ! M. Alsina, Coordinator

Are you ready to discover How mathematics is part of your life?

1. Mathematics in everyday life Mathematics surrounds us, when we get up, when we go to bed and throughout the day. If we close our eyes and imagine our bedroom, we will find objects that use mathematics, as: The alarm clock, a calendar, a “termostat”, tiles of the floor, the mobile, a music reproducer, …

From the moment we get up until we go to bed, mathematics surrounds us.

The alarm clock rings, we tune into music or the news, cross the street, scan our bus ticket or turn the ignition key in our car, stop at the red light that controls the traffic and plan our route using the GPS, answer the mobile... â&#x20AC;Ś all day Mathematics help us in different ways.

2. Street Mathematics Let us think what geometry can we find under our feet, when we walk on the streets. We can find mathematics there! Why are lids circular? Circular lids are easy to fit and are guaranteed not to slip down the hole. Moreover, they also save perimeter material in the shaft.

Can we tile any flat surface with any polygon?

If we observe the pavements, we will see that triangles, squares or hexagons allow us to cover flat surfaces in a continuous and well-organised way.

3. Nature Mathematics Natural numbers are used to count: flower petals, tree branches, root patterns... , Counting the flower petals in the panel, we get { 1, 2, 3, 5, 8, 13, 21, . . . } the Fibonacci sequence Numbers with special relations among them !

The number of petals on a flower, the patterns of stems and roots, the number of spirals in sunflowers. . . All of these follow the pattern of Fibonacci's sequence.

At the Fibonacci sequence, each term is the sum of the two previous. The ratios tend to the golden number.

4. Mathematics and Security In today's information society, all of us speak by mobile and use the internet. The privacy of the data that circulates, its integrity, its authenticity and the fact that it cannot be challenged, are questions of interest to us all. Mathematics gives us methods and keys to secure information transfer, digital signatures, electronic voting systems ...

Caesar's cipher (1st century AD) consisted in substituting the letters of a message for others, following a given corresponding ordered shift in the alphabet. By changing the degree of shift, different values are obtained. We can decrypt to obtain

ESLZWESLAUK SJW XMFFQ Mathematics are funny

guessing that the degree of the shift is 18.

5. Mathematics and health In health matters, mathematics also provides tools and models to interpret the way our body functions. Mathematical tools are frequently used in the devices for records and health check-ups. For example, a electrocardiogram (ECG) is a graphic of the intensity of the heart's electrical activity in relation to time.

Fractals play a fundamental role in our body. The fractal pattern of the respiratory airways and blood circulation routes ensure a good exchange of oxygen and nutrients. We are lucky our alveoli provide a big surface for gas exchange. In the lungs it is an efficient way to compress an area equivalent to a half tennis court inside the ribcage.

6. Letâ&#x20AC;&#x2122;s go shopping The shape of containers is important. It conditions the way they are stacked and influences their cost, with regards to the quantity of material used. Count how many products of same volume are on equal shelfs, varying the shapes: sphere, cylinder and cuboid (tetrabrik).

To detect and avoid errors, codes come into action. Redundant data is added, satisfying some relation. If the relation fails, error is detected. The NIF is an example of a detector code. A letter is added to the DNI as a control digit. Divide the number by 23, and identify which letter corresponds to the residue, according to the table.