

Units calculation (units, names and values  small calculations with units  (measuresand appareils de mesure)  Disguised percentages  Slopes, degrees and trigonometry (clock and sinusoidal curbs, lunar tides and alternative current) 
The Mega term (see below), is used without understanding in the trade or the popular speech to say
"much"; Mega bass for a radio set which cannot really deliver the powerful bass ones (very limited by the size of
the loudspeakers, the piles and other electronic cicuits).
Name of very large and very small figures ; thousand (a thousand ); a million = 1000 thousands = a
Mega (1 followed up by 6 zero); a Milliard (GB) or a
billion (US) = thousand millions/Mega (no name ? 1 followup by 9 zeros ); one billion (GB) or trillion (US) = thousand milliards (GB) or thousand billion (US) = Tera (1 followup with 12 zeros).
And an astronomical one, well known google (1 and 100 zero)
The same ones but into small now (opposite), is: thousandths = 1 divided per 1000 =
1/1000); one millionth = 1/one million = a micro ; a billionth (US) = 1/un billion = a nano (1 followed by 9 zeros); one (name ?) = 1/one billion =
1/thousand billion = a pico (1 divided by 1 followup by 12 zeros) ; an Angström, unit of length of wave and distances atomic = 1/1 followup by 10 zeros.
These extreme numbers can appear out of the everyday usage, however will know that a printer projects ink drops
calculated in picolitre , that a TGV consumes 5 Megawatts/second and that unit Tera is necessary to measure
the consumption of electricity of Paris over one year (15 Tw/h), equal to that of Eurodif, power station of uranium
enrichment.
Simplification for numbers with a lot of zeros ; example on Angström = 1 divided by ten zeros is also writen 1^{10} (1 power 10)
One multiplied by teén zeros would be writen 1^{10} (1 power +10).
said 1 power 10.
Small calculation with the units : a calculation must utilise
units of comparable nature (one multiple step of the monkeys
with hens, but with eggs, yes, if you wish to have a figure
which represents an average output).
Therefore, if you want to know the thickness of stones that
you would obtain by pouring 50 litres of stones on two
square meters (2 meters by 1 meter) it will be necessary to
convert volume into cubic meters or cubic centimetres (and
similar for the surface ). Calculation: one litre = 10 cm *
10 cm * 10 cm = 1000 cubic centimetres. 50 litres make
50.000 cubic centimetre, which you spread out over 2 square
metre is 2 times 100*100 cm = 20.000 square cm (cm2). 50.000
divided by 20.000 = 5/2 (one removes 4 zeros on each side) =
2,5 cm of thickness. Be not thrown into a panic any more by
seeing a ground heap. Once spread, there is nothing any more
left ! and it is packed afterwards.
Note : the official litre of the bottles would make nothing
any more but some 98 centilitres !
See below meters
The ellipse is the curve all planets and stars follow in the their race around another
one larger, whose retains them by his enormous gravity (attraction due to its mass); like the moon around
the earth, earth around the sun and so on.
An ellipse can be drawn by planting two drawing pins or points on two points (called focus) and by
fixing on each one the tip of a thin thread.
This thread will be cut definitely longer than the space reserved between the points. One tightens then the
thread by pushing a pencil against it while having it run along (one cannot make so only half of the ellipse and it
is necessary to take again on the other side). The shape and the size of the ellipse will thus depend on the spacing
between the points and the length of the thread, which summarizes a mathematical formula.
Let us return to the thread: its length is always the same one (constant)
wherever is the pencil which tightens it. Conclusion, in any point of an ellipse, the addition of
the two distances towards the two points is constant.
The parabola
is the curve that any stone launched in the air in direction of a target makes.
Even the ball of a rifle follows such a curve and it is necessary to regulate the sight (the rise) according to the distance. If the
way is very short, one can't see the curb and one believe, wrongly, that it is a straight line. In fact it is impossible because gravity inevitably draws the
stone or the ball downwards; it thus goes up by the power of the throw, then falls down more and more vertically. It is difficult
building a parabola with a thread because it is necessary that this thread be fixed at a point (the
focus) but slide at the other end along a straight line called director.
In any point of a parabola, the distances between the focus (the point) and a line called director, remain equal.
The chain curves is the curve which any thread tended between two points makes under the effect of gravity ; washing line or powerline, nothing escapes from it. One cannot plot this curve of which the mathematical resolution is complex and inaccurate because one makes in fact numerous estimations. Thus do not think the sag the cable makes to cross the river or to cross the valley could be reduced by tightening it more, either those of the bridges, whose weight for each meter is enormeous. They are already under a very strong tension and with the cold and the weight of snow, ready to break in spite of appearances. You will thus tend "in straight line" and only seemingly, a resistant and light thread on a short distance. It is what the masons practise for tracing a horizontal line on a wall: one coats the wire with a coloured powder, one tightens it well and one pinch/release it on the wall so that it deposits its color onto.
The curve of the dog is so called by reference to four dogs which would keep chasing while leaving each one the corner of a square. At every moment, the race of the one of the dogs is perpendicular to that of the pursued dog because it is the shortest way to reach it. As the dogs run themselves all after, the direction of each dog changes without stop. Each curve describes a kind of spiral. Without studies, without calculation, the dog follows this complex curve which is the best to catch up with the other which must also avoid the other.
This curve is only interesting to underline our aptitude (like the dogs considered), to correct our trajectory automatically in order to maintain a distances minimum (because that corresponds to the minimum effort). This concept of minimum effort and thus of distance minimum always pushes us to take the direct straight line at any moment to reach a spot. of which the pressed lawns whereas a path skakes aside, the reversed fences, angers to have to make a great loop where one passed before straight (motorways, properties), conflicts which go to wounds or dead of man if paths were vital (seen in New Caledonia). Without speaking about the toads one collects to make them cross the motorway at the season of love, of crabs crushed everywhere in the Pacific Islands and besides. All the life is conditioned by that : lots of current roads were old ways of passage, coming from the paths of the bas of the ages, not only from the men but also of the animals. One says in Corsica that to trace the path in the mountain, one follows the goat (which combines shortest with easiest). In the car, you often have two routes, shortest and fastest.