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Author Archives: Ofir
Summing the prime reciprocals
In the previous post we saw why primes are so important, and used Euclid’s proof to show that there are infinitely many primes. We further conjectured that not only there are infinitely many primes, they are also “nicely” distributed among … Continue reading
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How many primes are there?
The prime numbers are one of those basic, yet mysterious, sets in mathematics, that while we know much about them, there are still many interesting open questions waiting to be answered, including probably the most well known conjecture in mathematics … Continue reading
Improper integrals and periodic functions
The idea for this post came from a question I saw in a math help forum about improper integrals. While this problem has a very simple solution using basic tools in integral calculus, I want to show a more geometric … Continue reading
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Random walks on graphs
Imagine going to a new amusement park for the first time. Once you get there, you go to the first ride that you see, and when you finish it, you randomly choose one of the roads leaving it and follow … Continue reading
Radars and the Chinese Remainder Theorem
The radar is a detection system that was developed before and during World War II for military uses, though by today it has many other applications including, for example, astronomical and geological research. The name radar is an acronym for … Continue reading
Billiard tables – and what is mathematical research
Mathematical research is something that most people don’t really understand. They can imagine someone in a lab mixing chemicals or doing experiments with some scientific machinery, but mathematical research? The goal of this post is to share with you a … Continue reading
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Random walks and self similar sets
1. Introduction In this post we consider an interesting mathematical process which can be easily simulated by a computer, and generates interesting pictures. A video version of this post can be seen in here (for now in Hebrew). Let and … Continue reading
How to measure information using entropy
Which text gives us more information – the full body of work of Shakespeare, or 884,647 random words written by 1000 monkeys? To answer this, we talk with our good friend Alice, and ask her to send both of these … Continue reading
Lattice parametrization
We came to the point where we have already seen how lattices appear naturally in problems arising from number theory. In this post we construct a nice space which parametrize the set of all lattices of a certain dimension, with … Continue reading
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Tagged Homogeneous spaces, Hyperbolic space, Lattices, SL_2(Z)
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The rise of algebraic extensions
In the post about number theory and lattices, we tried to determine when is the Euclidean distance in is actually a Euclidean norm and we were led to study the embeddings of rings such as as lattices in . As mentioned … Continue reading
Ofir David 