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 Notes on Representation  The Number Line
 Operators, Functions, and Properties  part 42
 Running the Math Gauntlet
 Making Change  A Sam Lloyd puzzle
 Notes on Deferred Computation  the Pythagorean Spiral
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 Operators, Functions, and Properties  part 35
 Operators, Functions, and Properties  part 38

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Tag Archives: whole vs. parts
Operators, Functions, and Properties – part 43
In the last several posts in this series, we’ve looked at cyclical patterns of behavior of numbers and operators. For example, in the previous post we saw that when counting up, the last digit of a number consistently repeats after … Continue reading
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Tagged black box, equivalence, models, representations, reverse engineering, whole vs. parts
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Operators, Functions, and Properties – part 37
In this series we’ve looked at boxes that take certain inputs and then produce an output. We’ve called such boxes operators, and we’ve thought of them in many different ways. In some cases, the boxes perform arithmetic; in other cases, … Continue reading
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Tagged black box, equivalence, extending patterns, invariants, models, representations, reverse engineering, whole vs. parts
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Operators, Functions, and Properties – part 33
In this series we have looked at various examples of operators, and most of our attention has been on operators where what comes out is a number, and what comes in is one or two numbers. Some examples of twonumbers … Continue reading
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Tagged black box, denominations, equivalence, extending patterns, models, reverse engineering, whole vs. parts
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Operators, Functions, and Properties – part 31
In the prior post in this series, we looked at the kind of operators typically encountered in school (K12), whether or not they are called operators. Many of them are single number input – single number output, but not all. … Continue reading
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Tagged black box, equivalence, models, naming, reverse engineering, whole vs. parts
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Operators, Functions, and Properties – part 30
In many of the posts in this series we’ve shown operators that work on a single number coming in and that produce a single number coming out. This is a hugely important subcategory of operators, but singlein singleout operators aren’t … Continue reading
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Tagged extending patterns, models, unlearning, whole vs. parts
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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