Top Posts
 Notes on Representation  Tally Marks
 Math in the Comics  part 1
 Groupings, Shopping Lists, Vectors: part 14
 Notes on Deferred Computation  the Pythagorean Spiral
 Operators, Functions, and Properties  part 37
 Notes on Divisibility  Common Divisors
 Groupings, Shopping Lists, Vectors: part 16
 Notes on Operations  Unary Minus
 Notes on Lookup  Eratosthenes and Other Sieves
 Notes on Lookup  A Sieve for the Collatz Problem

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 Mathematical Notations and Schools – 15
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 Mathematical Notation and Schools – 2
 Mathematical Notation and Schools: The Series
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Monthly Archives: July 2010
Operators, Functions, and Properties – part 12
In this series, we’ve been looking at operators as something that takes an input and turns it into an output, and we’ve been looking at chains of such operators, which we’ve called trains. In the last post, we posed the … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, representations
3 Comments
Operators, Functions, and Properties – part 11
In the prior post of this series, we looked at pairs of operators in which one of the pair cancels out the effect of the other. We call one of these the inverse operator of the other one. For example, … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, representations, reverse engineering, whole vs. parts
2 Comments
Operators, Functions, and Properties – part 10
In the prior post in this series, we looked at chains of operators for which the net effect was to do nothing. We started by comparing the picture on the left with the picture on the right, below, and noticing … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, extending patterns, invariants, models, representations, reverse engineering
2 Comments
Operators, Functions, and Properties – part 9
In the last few sessions in this series we’ve looked at operators that do things like “add 2″ or “multiply by 3″ or “divide by 10″. Each of these operators takes a number as its input and produces a number … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, equivalence, extending patterns, models, representations, reverse engineering
3 Comments
Operators, Functions, and Properties: The Series
This series of posts introduces the notion of an operator as something that changes the state of some machine or device. Often, an operator is invoked at the press of a button. A special case of an operator is one … Continue reading
Operators, Functions, and Properties – part 8
In the prior post, I played with putting together little boxes that perform actions on numbers coming in – simple actions like adding two – and reported on an experiment with seventh graders to find equivalent boxes. I’m going to … Continue reading
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3 Comments
Operators, Functions, and Properties – part 7
Continuing on from the last post, where we introduced some simple operators that operate on a number, like “add 2″, I want to show more examples of composition of these operators. The figure above shows five pairs, each pair consisting … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, models, representations, reverse engineering
2 Comments
Operators, Functions, and Properties – part 6
In this series, we’ve been playing with the idea of operators as some kind of action that alters the state of some device or some system, perhaps invoked at the press of a key or a button. We’ve emphasized that … Continue reading
Posted in Uncategorized
Tagged equivalence, extending patterns, models, representations, reverse engineering
5 Comments