A book where I talk about math knowledge/fact/etc that I find interesting.
If you guys also have some interesting math facts, feel free to let me know! I might as well put them in this book.
[This book is best read with white background, sorry dark...
Take an A4 paper, and measure its long and short edge.
Now, get a calculator and divide the long edge by the short edge.
You'll probably get around 1.41
Now, fold your A4 paper in half in the middle of the long edge. It now becomes an A5 paper.
If you then measure its long and short edge, and divide the long edge by the short edge, you will again get a number around 1.41
That number, is the square root of 2.
The reason why they do this, so that they can easily scale the papers up and down without it being disproportionate. And square root of 2 is the only ratio that works. And now, I want to show you why is that.
So here's an illustration of what we've been doing so far
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As you can see, we started of with a long edge a and a short edge b. And when we cut our paper in half, the long edge becomes band the short edge becomes ½a.
So the ratio between the long edge and the short edge for our starting paper and second paper are a/band b/(½a), respectively.
Now, we want to easily scale up and down these papers. And since we also want these two papers to be proportionate to each other, we need to equatiate these two ratios.
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And with some algebra, we can rearrange this equation like this.
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And as you can see, the only ratio for this whole thing to work is the square root of 2!
Here is a diagram of A Series Paper
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That big A0 paper is defined to be a paper with an area of 1 m^2 and the same long edge short edge ratio we got before, the square root of 2.
And since we just cut the paper in half to scale down the paper, this means that A1 paper has an area of half of A0, A2 paper has an area of half of A1, A3 paper has an area of half of A2, and so on!
