BASIC MATHEMATICAL EQUIPMENT

Mathematics is often associated with a set of drawing and measuring tools. Unlike many language lessons, where you may need little more than a notebook and perhaps a bilingual dictionary, mathematics frequently involves drawing, measuring and constructing shapes, as well as performing calculations. For that reason, we need some special equipment. The basic list includes: 1. A PENCIL We all know what a pencil is, and most of us already use one every day. One of its greatest advantages is that mistakes can easily be erased. For mathematical work, black pencils are usually preferred, but I will happily leave the choice of colour to you. If you want to draw red hearts, yellow suns, orange sunsets or green forests and mountains, please do. Everyone should be free to colour the world with whatever they feel is missing from their own life. Just do not spend all your time drawing money, because that would make me rather sad. Human beings are worth much more than money. Life becomes rather depressing if all we think about is wealth. So, use your pencil boldly. Draw smiles, kindness and positive numbers. There is something rather gloomy about negative numbers, although we shall meet them later. To be fair, we will eventually have a lesson about money. Then I shall give you complete freedom to place as many zeros as you wish after any number you choose. At least for a little while, we shall all become billionaires. 2. A SHARPENER A pencil and a sharpener naturally belong together. In life, however, it is not only pencils that need sharpening. We must also keep our curiosity, imagination, compassion, humanity and love of life sharp. Perhaps the greatest sharpener of all is our determination to resist hopelessness and our desire to prove that, although we are only a tiny part of the universe, we still matter. The macrocosm and the microcosm cannot be separated because each gives meaning to the other. 3. AN ERASER An eraser is an invaluable tool. What would life be like without the ability to erase? So often we wish we could erase painful memories, mistakes, sorrow, tears and suffering. Sometimes we even wish we could erase certain people from our lives. So, whenever you need to erase something, do it boldly. 4. A RULER Use a ruler whenever you wish to draw a straight line. And if your own life seems to be following too many unexpected curves and you begin to lose your direction, perhaps you should reach for an imaginary ruler and measure where you are. It may not be terribly important to know exactly how many centimetres separate you from your cup of coffee, but it is very important to measure your integrity, honesty and humanity. Those should never be far away from you—not even by a few millimetres. For greater distances, you may need a metre rule instead. 5. A SET SQUARE (TRIANGLE RULER) A set square performs many of the same functions as an ordinary ruler, but it also allows us to construct right angles and draw triangles accurately. Right angles are useful in mathematics, just as clear principles are useful in life. Acute and obtuse angles have their place as well—but be careful of their sharp corners. Sometimes they can hurt. 6. A COMPASS At first glance, a compass may look like a strange medieval instrument, and many students find it rather awkward to use. You have to learn how to hold the pencil firmly and adjust it carefully before you can draw perfect circles. Like many worthwhile things, it simply requires practice. If there are moments when your life feels incomplete or out of balance, perhaps drawing circles with a compass is not such a bad idea. Since ancient times, the circle has symbolised perfection, harmony, eternity, the Sun and divine unity. Perhaps more people should spend time drawing happy circles. 7. A PROTRACTOR The protractor is another useful mathematical instrument. Versions of it have existed since ancient Babylon. It consists of a straight edge and a semicircular or circular scale marked with degrees, allowing us to measure and construct angles accurately. Whenever life requires careful planning, clear direction and thoughtful decisions, perhaps we should approach it with the same precision that we use when measuring angles. Clarity is always helpful. 8. A CALCULATOR Whenever possible, it is better to train your own mind before reaching for a calculator. Our brains are capable of performing far more calculations than we sometimes believe. If we rely on calculators for every simple calculation, we risk making our minds a little lazy. Of course, calculators can sometimes be entertaining. You might calculate how much of your salary remains after paying all your bills. After that little exercise, mathematics lessons may suddenly seem much more interesting. Or perhaps you could use the calculator to work out your exact age—if you happen to be one of those people who prefer not to remember it too precisely. 9. GRAPH PAPER Graph paper is covered with small squares arranged in a regular pattern. Do not worry about it just yet. We shall need it only when we begin drawing graphs and studying transformations. Graph paper is especially useful for exploring how shapes move, rotate, reflect and enlarge. Life itself is full of transformations: childhood becomes youth, youth becomes adulthood, adulthood grows into old age, and every ending prepares the way for a new beginning. 10. A BLANK SHEET OF PAPER Every mathematician needs a blank sheet of paper. You can use it to make rough calculations, test ideas or simply doodle while trying to persuade your compass to draw a perfect circle. Sometimes it may become the place where your thoughts appear before your calculations do. You might even draw the seasons—autumn leaves falling from the trees, flowers blooming in spring, snowflakes drifting through winter or gentle summer rain. 11. A BAR OF CHOCOLATE Strictly speaking, chocolate is not a mathematical instrument. Nevertheless, it is always wise to keep some nearby. Chocolate is an excellent mood booster and, for many people, one of the sweetest sources of mathematical inspiration. Activities Activity 1: Use a compass to create a picture made entirely of circles. Connect the circles in different ways and colour your design afterwards. What ideas or patterns have you created? Activity 2: Use a protractor and try to measure the angle between your chair and the window. Is this actually possible? If not, can you explain why? (Elena S. Lyubenova)