Category Archives: counting

do go no to

Posted on January 7, 2020 by Brent

dodo do go on do no harm do to others go do likewise go-go music go no further goto considered harmful no can do it’s a no go a big no-no say no to drugs what to do here or … Continue reading →

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A new counting system

Posted on December 30, 2019 by Brent

0 = t__ough 1 = t_rough 2 = th_ough 3 = through So, for example, trough through tough though though. English is so strange.

Posted in arithmetic, counting | Tagged , , , | 1 Comment

Computing the Euler totient function, part 4: totient of prime powers

Posted on July 2, 2019 by Brent

I’ve been on a bit of a hiatus as I’ve been travelling with my family for the past month. So here’s a recap. Our story so far Recall that the Euler totient function, , counts how many numbers from to … Continue reading →

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Computing the Euler totient function, part 3: proving phi is multiplicative

Posted on May 27, 2019 by Brent

We are trying to show that the Euler totient function , which counts how many numbers from to share no common factors with , is multiplicative, that is, whenever and share no common factors. In my previous post, we looked … Continue reading →

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Computing the Euler totient function, part 2: seeing phi is multiplicative

Posted on May 18, 2019 by Brent

In my last post, I claimed that whenever and are relatively prime. (Recall that counts how many numbers from to share no factors in common with .) Let’s get some intuition for this by looking at some Chinese remainder theorem … Continue reading →

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Computing the Euler totient function, part 1

Posted on May 9, 2019 by Brent

Recall that Euler’s totient function counts how many of the integers from to are relatively prime to , that is, share no factors in common with . For example, , since only , , , and share no factors with … Continue reading →

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Games with factorization diagram cards

Posted on February 17, 2017 by Brent

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 , , , , , | 4 Comments

Factorization diagram cards are here!

Posted on September 11, 2016 by Brent

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 →

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Factorization diagram card redesign: feedback welcome!

Posted on August 24, 2016 by Brent

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 , , | 6 Comments

Factorization diagram cards!

Posted on May 31, 2016 by Brent

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 , , | 5 Comments