Funny Fractions and Ford Circles - Numberphile
Farey Sequences, Ford Circles and a strange addition sign... Featuring Francis Bonahon from the University of Southern California. More links & stuff in full ...
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I thought that we could talk about fractions. So , for instance, one over two. Also known as one half. Okay, so another one would be two over five, or two fifths. And then there are more complicated ones, like eighteen over forty-two, and, well, you know that there is something a little wrong here, which is that the top and the bottom, you can both divide them by two, and then you get that this is nine over twenty-one. And, oh, I'm not done. And so it's three sevenths. I wanted to do this example because all the fractions I'm going to consider are going to be reduced like this. Namely, it's going to be of the form p over q, where p and q are integers, and they are what we call coprime, namely that they have no common divisor. [Brady]: We've cancelled them down as f...
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I thought that we could talk about fractions. So , for instance, one over two. Also known as one half. Okay, so another one would be two over five, or two fifths. And then there are more complicated ones, like eighteen over forty-two, and, well, you know that there is something a little wrong here, which is that the top and the bottom, you can both divide them by two, and then you get that this is nine over twenty-one. And, oh, I'm not done. And so it's three sevenths. I wanted to do this example because all the fractions I'm going to consider are going to be reduced like this. Namely, it's going to be of the form p over q, where p and q are integers, and they are what we call coprime, namely that they have no common divisor. [Brady]: We've cancelled them down as f...
