Monthly Archives: February 2009

Notes on Representation – Tally Marks

I’m assuming you are quite familiar with tally marks: As a system of representation of quantity, tally marks play a very interesting role.  You can view it as a number system, yet as a number system it does not compete … Continue reading

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A Collatz-Inspired Puzzle

This is a puzzle. In prior posts, I used the Collatz Problem, restated here: Each counting number n past 1 is assigned a successor number, as follows: The number “1″ is considered home, and when you’re home, you stop.  If … Continue reading

Notes on Lookup – Another Sieve for the Collatz Problem

This post is a follow-up on an earlier post in which I introduced the Collatz Problem and designed a sieve that systematically builds solutions and is very efficient in the work it does.  In this post, I’ll give a version … Continue reading

Notes on Lookup – Histograms as Sieves

I think I overlooked one interesting example of something like a sieve being used in the typical K-12 math curriculum, and this post is intended to remedy that.  It is possible and instructive to look at a histogram as a … Continue reading

Math in the Comics – part 6

Today, there is a follow-up on yesterday’s Non Sequitur comic – in which Danae’s new math system is revealed: henceforth, she will start with the answer and work back to get an equation that fits the problem.  This way, she … Continue reading

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Math in the Comics – part 5

In today’s comics, there is this Non Sequitur one: Comics, to me, are interesting regardless of whether a particular one is funny, since they reveal a lot about the community and the society in which they appear.  Usually, comics make … Continue reading

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Notes on Lookup – A Sieve for the Collatz Problem

This post is meant as a follow-up on this one on look-up and sieves, not on my more recent one pondering the diminished status of look-up in K-12 math. I’ve been playing with different ways to use a sieve to … Continue reading

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Notes on Lookup – Computation versus Lookup in School

In the previous post, I played with sieves some more.  Sieves are a device for getting something calculated.  At least since Eratosthenes, 2200 years ago, this simple and illustrative tool has been part of mathematics.  Yet you don’t see sieves … Continue reading

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Notes on Lookup – Eratosthenes and Other Sieves

The best known sieve in mathematics is the sieve of Eratosthenes, used for finding a collection of prime numbers.  In an earlier post I described a version of that sieve that finds all divisors (and not just whether a number … Continue reading

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Mathematical Puzzle – Hinges

This is a puzzle. Imagine I have three rods of length 1 each, and they are connected together with perfect hinges.  Together, they form a somewhat flexible shape ABCD (with AB=1, BC=1 and CD=1), even if I fix the two … Continue reading

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