On the scale of my globe, it would hit the arm that holds the ball in place. It is a mere 350km above the surface.Some of these are little known. If you have more or if you have evidence for errors in this page, please tell me!
Humans are great! They have conquered space! Through an international effort we have built a space station, our first permanently occupied outpost, away from the Earth.
How far out is the ISS?
On the scale of my globe, it would hit the arm that holds the ball in place. It is a mere 350km above the surface.
The ISS is a great effort and we should probably do much more. The fact that it is so near should convince us that we are quite stuck on this planet and should do everything we can to save it. One day we may find easy ways to get into deep space, maybe even to other star systems. Until then we must take care of our home.
Most of the world uses paper for writing and printing in a size called A4. A4 is metric, but its size is 297mm x 210mm. Where do these crazy numbers come from?
When you enlarge or reduce a document, you want the result to appear with in same proportions or aspect ratio: the ratio of length over width should not change. Similarly, when you fold a piece of paper in two, it is more often than not useful to end up with the same aspect ratio.
If you start with a square piece of paper (ratio 1/1) and fold it in two, you get two halves that are 2/1 in aspect: they are twice as long as wide:
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So a square is not a good shape to start with.
Is there a ratio that is preserved when cut into two?
Yes, and we can calculate it.
Say its height is a and the width is b, therefore the ratio is a/b:
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Then its halves will have a ratio b/(a/2). What we want is a/b = b/(a/2) so that the folding and cutting has not changed the aspect. This requirement tells us, with a little algebra, that a2=2b2 or that a=1.4142 x b where 1.4142 approximates the square root of 2.
We standardise paper sizes on this aspect ratio: it is then easy to cut paper to different sizes, because each time we cut a stack of sheets in two, we get a stack in the next smaller size, and they have the same aspect.
But where do we start? Obviously with a sheet that is one square meter in surface area. This sheet has to have a height h and a width w such that h x w=1m2 and that h=1.4142xw. Now we apply another little bit of algebra to find the values of h and w that satisfy these requirements, and we find that h=1.189m and w=0.841m. That then are the dimensions of a sheet of format A0 (pronounced "a-zero"), or 118.9cm by 84.1cm.
If we fold it in two and cut, we get two sheets of A1 ("a-one"). Obviously, these are 84.1cm by 59.5cm since they have a height equal to the width of the A0 sheet and a width which is half of the A0 height.
Fold it again, and we obtain sheets of A2 which are 42cm by 59.5cm (we ignore the 0.05cm). Continue to cut in two: A3 is 42cm by 29.7cm; A4 is 21cm by 29.7cm, A5 is 19.8 cm by 21cm etc.
And that explains why A4 has such seemingly crazy dimensions. But think about it next time you make a photocopy at half size, or you fold a sheet in two and discover it fits perfectly into the smaller envelopes.
As companions to the basic "A" sizes, there are "B" and "C" sizes for envelopes and other items that need to accomodate A size paper.
One aspect of paper quality is its weight. Paper for laser printers is usually 80g/m2. Since we know that one A4 sheet has been obtained by cutting an A0 sheet into 16, and an A0 sheet is 1m2, it follows that 16 sheets should weigh 80 grams. There are 500 sheets in one pack, 5 packs in a box. A pack then weighs 80x(500/16)g or 2.5kg and a box 5x2.5kg = 12.5kg (plus something for packing).
I once read an agument against the metric system that ran more or less as follows:
Floppy discs are 3.5", and nobody would like to speak about 88.9mm discs, or even, if rounded, of 89mm discs.
The fact is that floppy discs are 9cm exactly. The 3.5" is an imperial-units approximation.
