Tag Archives: recurrence relationship

Operators, Functions, and Properties – part 24

In the previous post in this series, we started to model recurrence relationships with state machines: The idea is that we have a device with two buttons and a screen; after we press the Start button, we can press the … Continue reading

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Operators, Functions, and Properties – part 23

In this series, we’ve been looking at operators as something that modifies the state of some machine or device, usually triggered by the pushing of a button.  We’ve looked quite a bit at operators that operate on numbers, for example … 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

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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

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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 – 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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Notes on Deferred Computation – the Pythagorean Spiral

The following figure is quite interesting: Imagine you start out home, in the center at the bottom, and move a distance of 1 to the right to A.  At A, you have traveled a total distance of 1, and you … Continue reading

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