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Tag Archives: lookup
Operators, Functions, and Properties – part 40
In this series, we’ve spent considerable space playing with operators, which we’ve pictured as black boxes with inputs and outputs, often as part of a machine with state. In more recent posts, e.g. this one , we’ve looked at operators … Continue reading
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Tagged black box, denominations, equivalence, invariants, lookup, reverse engineering
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Operators, Functions, and Properties – part 39
In this series, we’ve been looking at operators in various settings, and looked for ways to use them to shine a different colored light on some aspects school math. In the last four posts, we’ve explored the notions of equivalence … Continue reading
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Tagged black box, denominations, equivalence, extending patterns, invariants, lookup, models, naming, recurrence relationship, representations
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Operators, Functions, and Properties – part 36
In the previous post in this series, we broached the subject of equivalence classes. We did so in the context of looking at an addition table and noticing how each value in the table occurred multiple times. We drew a … Continue reading
Operators, Functions, and Properties – part 15
In this series, we’ve been playing with the mathematical notion of an operator, seeing if we could make it useful for making a bridge between arithmetic and algebra. In the previous post, we started to investigate the notion of a … Continue reading
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Tagged black box, denominations, extending patterns, lookup, models, reverse engineering
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Groupings, Shopping Lists, Vectors: part 7
In part 6 of this series, I introduced an operation called inner product between two vectors, as a way to find the total price of an order using a price list. In this post, I want to give a bunch … Continue reading
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Tagged denominations, lookup, math class, models, naming, representations, whole vs. parts
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Groupings, Shopping Lists, Vectors: part 6
In this series on vectors we showed vector addition in this post, and then took a small excursion to show a surprising connection between some vector additions and the distributive property. In this post, I will combine vectors with lookup … Continue reading
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Tagged denominations, lookup, naming, representations, whole vs. parts
4 Comments
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 – Histograms as Sieves
I think I overlooked one interesting example of something like a sieve being used in the typical K12 math curriculum, and this post is intended to remedy that. It is possible and instructive to look at a histogram as a … Continue reading
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Tagged denominations, lookup, math class, models, representations, sieve, sorting
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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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Tagged education, extending patterns, lookup, math class, representations, reverse engineering
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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
3 Comments