as much of the glitter-glue away as you can while it’s still wet – it’s trickier to remove when it’s dry, especially if the piece of pottery isn’t glazed. Try not to get too much of the glitter on you as well. This is a fairly messy process, but the results can be rather lovely. The most valuable thing you will ever own is your time. Using some of it to make a thing of beauty cannot be a bad thing – and reminding yourself that broken things can be fixed is always worthwhile.
We all learn a simple way to tie shoelaces when we are kids. This technique – sometimes called a butterfly knot – is at least twice as fast. You appear to tie the knot in one quick movement, which impresses onlookers. It might look tricky, but it’s one you can learn very quickly. Once you have done it a few times, you’ll never go back to the old loop-loop-knot method again.
Note: This is much easier to do than to describe! Follow these instructions while you try to tie the knot on an actual shoe. Just as when you first learned to tie a shoe – it gets much easier.
1. Begin with the traditional cross-over. Regardless of how you tie your shoes, you might want to put one lace through a second time. It forms a triple, which has more friction and so locks every knot in place. Your shoes will come untied less often if you take nothing but this away.
2. Note and practise the finger positions in the next pictures until they are second nature. Thumb and middle on the right hand, index and middle on the left. The idea is to form and bring both loops together in the same movement, completing the knot in one swift tug.
3. Rotate each hand – the left clockwise to bring the thumb underneath, then anticlockwise to form an upside-down U or open loop.
4. The right hand moves anticlockwise to bring the second/index finger up underneath, then clockwise to form an upside-down U or open loop.
This probably seems impossibly complex at this point. Just remember – there is nothing wrong with complexity. If something is hard, we don’t give up. We grab it by the throat and throttle it until it’s easier. In this case, that might mean sitting with a shoe on a table and the book propped open next to you for ten minutes, but the principle is clear enough.
5. It helps to form exaggerated open loops when you are learning. Bring them together, right hand over the left hand, holding the four points taut – the two bends and two grips.
6. When the right-hand lace is brought over to the left hand, it forms a capital letter A.
7. With the thumb and forefinger of the right hand, grasp the crossbar of the A.
8. With the thumb and forefinger of the left hand, grasp the lower left leg of the A.
9. Pull gently – and the familiar twin loops will form.
If you want pinpoint accuracy, there are laser devices on the market that will give you precision in a split second. This is more for those who want to know if a tree will hit their roof when it blows down. Or just because the basics of trigonometry are interesting.
YOU WILL NEED
A protractor
A pencil
A bit of Blu Tack
A calculator
Trigonometry has to do with triangles. It’s the branch of mathematics that examines the relationships between the lengths of the sides and the angles. You probably already know that the internal angles of a triangle always add up to 180°. That is one of the first things you learn – so if we know one angle of a triangle is 40° and another is 80°, the last has to be 60°, because 40 + 80 + 60 = 180.
So whether it’s an equilateral triangle, where all the sides and angles are equal:
Or an isosceles triangle, where at least two sides are equal:
… the internal angles always add up to 180°. You might also be interested to know that angles along a straight line also add up to 180°. If you think about it, 180° is half a circle of 360°.
If you drew a straight line and crossed another through it, you would have two right angles of 90° – for a total of 180°. Four right angles, or 4 × 90 = 360 – the full turn.
That means, just as a matter of interest, that if you know any internal angle of a triangle, you can extend a straight line and also know the external angle. That might come in handy one day.
Sadly, there isn’t space enough here to cover all the interesting aspects of triangles. We’ll concentrate on one very specific task – finding the height of something using trigonometry – a word that means ‘triangle measuring’. It might be a tree or a building. In theory, it could be a person, though this is more a method for big objects.
First, pace a distance from the base of your object. Use a little common sense and pace out a fair way – 30, 60 or 90 yards. Those are not accidental choices. One problem with metres is that they have no physical reality, whereas a yard is a man’s pace. It’s possible to pace out a field in yards, for example, but not metres. However, a metre is – as near as makes no odds for our purposes – 3ft 4in. That means that 10ft (3 × 3ft 4in) is very close to 3m. So we chose a distance from the tree that could be expressed fairly easily in both yards and metres. Sixty yards is 180ft, or 18 × 3m = 54m.
You now have the base of your triangle. You are still missing the height of the tree, the hypotenuse (the longest side diagonal) and the angles. Where the tree touches the ground is 90°, which is what will make this work. The next part works for all right-angled triangles – triangles with a 90° angle in them.
Now,
