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Tag Archives: factorization
Fast and slow machines
In my previous post, I presented three hypothetical machines which take a positive integer as input and give us something else as output: a factorization machine gives us the complete prime factorization of ; a factor machine gives us one … Continue reading
Posted in computation, number theory, primes
Tagged algorithm, division, efficiency, exponential, factor, factorization, machine, polynomial, primality, testing, trial
1 Comment
A tale of three machines
The Fundamental Theorem of Arithmetic tells us that any positive integer can be factored into a product of prime factors.1 Given a positive integer , this leads naturally to several questions: What is the prime factorization of ? This is … Continue reading
Posted in computation, number theory, primes
Tagged factor, factorization, machine, primality, testing
11 Comments
The Riemann zeta function and prime numbers
In a previous post I defined the famous Riemann zeta function, Today I want to give you a glimpse of what it has to do with prime numbers—which is a big part of why it is so famous. Consider the … Continue reading
Games with factorization diagram cards
Since I published a deck of factorization diagram cards last September, a few teachers have picked up copies of the cards and started using them with their students. I’ve started collecting ideas for games you can play using the cards, … Continue reading
Posted in arithmetic, counting, games, pattern, pictures, primes, teaching
Tagged cards, diagrams, factorization, games, SET, war
4 Comments
Factorization diagram cards are here!
It’s been a long process, but factorization diagram cards are finally available for purchase! If you just want to purchase a set right this minute, then click the above link! If you want to learn more, keep reading. History As … Continue reading
Posted in arithmetic, counting, pattern, pictures, primes, teaching
Tagged cards, diagrams, factorization
2 Comments
Factorization diagram card redesign: feedback welcome!
After getting a printed set of factorization diagram cards, I decided there were a few design tweaks I wanted to make. I’ve gone through a few iterations and I think they are definitely better now. Here are some representative samples … Continue reading
Posted in arithmetic, counting, pattern, pictures, primes, teaching
Tagged cards, diagrams, factorization
6 Comments
Factorization diagram cards!
I’ve designed a set of factorization diagram cards and had them actually printed. This is one of the first times in my life when I have caused Actual Physical Objects to be created (other than using a printer I guess) … Continue reading
Posted in arithmetic, counting, pattern, pictures, primes, teaching, video
Tagged cards, diagrams, factorization
5 Comments
Factorization diagram posters!
I’ve finally gotten around to making a nice factorization diagram poster: You can buy highquality prints from Imagekind. (If you order soon you should have them before Christmas! =) I’m really quite happy with imagekind, the print quality is fantastic … Continue reading
Posted in arithmetic, counting, geometry, number theory, pattern, pictures, primes
Tagged diagrams, factorization, posters
7 Comments
Factorization diagram cards: help?
The other day I got a lovely email from Malke Rosenfeld thanking me for creating factorization diagrams and linking me to her blog post about “factor dominoes”: she printed out some factorization diagrams, glued them to cardstock, and used the … Continue reading
More factorization diagrams
My post on factorization diagrams from a month ago turned out to be (unexpectedly) quite popular! I got ten times as many hits as usual the day it was published, and since then quite a few other people have created … Continue reading
Posted in arithmetic, links, pictures, primes, programming, recursion
Tagged diagrams, factorization, Haskell
15 Comments