Le tabelline sono state probabilmente il nostro primo incubo. Dover memorizzare e saper ripetere a uno schiocco di dita tutte quelle moltiplicazioni sembrava un’impresa titanica. Dopotutto, che cosa l’hanno inventata a fare la calcolatrice, se non per risparmiarci il tempo e la fatica di fare calcoli a mente? Domande come questa sono i dardi da cui si devono difendere i docenti quando mettono piede in una classe di discenti scettici dell’utilità della matematica nella loro vita quotidiana. L’insegnamento delle scienze si muove sempre su due livelli, quello teorico e quello pratico; l’uno non può prescindere dall’altro. Ma forse, troppo spesso, la matematica rimane una disciplina prettamente astratta, un linguaggio per pochi iniziati, quasi esoterico, che sta alla base delle altre scienze e permette di sviluppare astrusi calcoli di derivate, integrali, logaritmi, e compagnia. “Tanto io voglio studiare storia dell’arte”, c’è chi può obiettare. Certo, non tutti noi finiremo per usare le derivate nella nostra vita quotidiana. Eppure, senza nemmeno rendercene conto, usiamo la matematica in tante occasioni giornaliere: dalla spesa alla cucina, alla contabilità, alla banca, ai giochi di carte o da tavolo.
There is discount and discount
What greater satisfaction is there than going shopping, filling a cart to the brim and knowing that between the 2×1 and other one-off discounts, this week we will be shelling out just a few cents for hearty meals fit for a king?. Supermarkets adopt a whole series of strategies to attract or retain customers, including discounts: 2×1, 3×2, 50% on the second unit, 20% on the original price with the loyalty card, and so on. It is true that the discounts are indicated on the tags, which show the original price crossed out and the discounted price next to it; but if this were not the case, it would be useful to know the formula for calculating the percentage (for example, 30% of €90 would be 30×90÷100=27 €). This can also be advantageous in other contexts, such as when we issue an invoice or ask for a loan from the bank. If we are freelancers, perhaps we are interested in giving a small gift to a recurring customer and applying a discount to the total price of the invoice: instead of €570, we want to make €550. What will that €20 reduction be, in percentage, that we have to indicate in the details on the invoice? What is the formula to use to calculate it? Or we are short of liquidity and, nevertheless, we need a new car. We ask for a loan from the bank, which however applies an interest rate of 2%. It is advisable for our finances that we know how to calculate how much more money we will return to the bank when we pay off the debt.
Maybe I'll win
Mathematics also teaches us the calculus of probabilities. What is the probability that it will rain today and that I will therefore have to carry an umbrella? What is the probability that my credit card will not work at least once in five purchases in five different stores? Knowing the principles of probabilistic calculus could help us adopt game strategies to beat our friends at Risk, or to win at roulette. In all fairness, probabilistic calculus can be traced back to a 1654 exchange between Pascal and Fermat on a game of chance; then it was called game theory. In the roulette, a game that was born in France in the 1600s, Probabilistic calculation can be particularly useful, since the aim of the game is to predict the result that will be obtained when the wheel stops spinning. Physics can also give us a hand. The bets that players can make are various and each one involves a certain probability. You can bet on a color or on a number, even or odd as you choose. There are statistics that indicate where the ball stops most frequently that can guide us in our bet: straight¸ on a single number; split on two adjacent numbers; square on four numbers, and many others.
Do it yourself. Even the calculations!
The daily application potential of mathematics does not end with shopping, bills, loans and roulette. If we wanted, we could draw up a long list of circumstances in which to apply it. Remaining in fairly familiar territory, we can't help but think about DIY. Not everyone has golden hands, so some people prefer to entrust the work to experts; but if we like to get our hands dirty and be resourceful in building what we need, hammering nails, assembling shelves or repainting walls, then we should know how to do the calculations precisely. To get the right color, we need to mix the right proportion of each color. To build a part, we need to know how to calculate angles: the protractor is used for much more than making fun drawings, and the sine and cosine formulas leave the page on which we have drawn a graph and enter the reality of plasterboard. To hang a shelf, we need to know how to take the right measurements of height, length and depth to avoid having an unusable surface, because it is tilted and from which objects rain down. Or again, to be able to buy the right roll of fake grass for the garden, we need to make sure we know how to adequately measure the area of the quadrilateral to be covered with synthetic greenery.
Often overlooked, neglected, ignored, mathematics comes back for its revenge and forces us to rethink the relationship we have with it. Whether we are baking a cake with two thirds flour and one third starch, taking out a mortgage with a fixed rate of 1,79%, calculating the remaining kilometers before the car turns off, mathematics with its more or less complex formulas lends us a helping hand. Maybe it's time we started appreciating it.
Article published on 17 December 2018 - 15:11
