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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
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
A CollatzInspired 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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Tagged models, puzzle, recurrence relationship, representations, reverse engineering
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Notes on Lookup – Another Sieve for the Collatz Problem
This post is a followup 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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Tagged extending patterns, lookup, models, recurrence relationship, representations, sieve
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Notes on Lookup – A Sieve for the Collatz Problem
This post is meant as a followup on this one on lookup and sieves, not on my more recent one pondering the diminished status of lookup in K12 math. I’ve been playing with different ways to use a sieve to … Continue reading
Posted in Uncategorized
Tagged extending patterns, models, naming, recurrence relationship, representations, reverse engineering, sieve
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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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Tagged extending patterns, lookup, models, recurrence relationship, reverse engineering, sieve
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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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Tagged deferred computation, extending patterns, math class, models, recurrence relationship, representations
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