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Tag Archives: whole vs. parts
The Whole and the Parts – The Series
I’ve written a number of posts where the main theme is a whole that is more than just the sum of the parts. Whenever you have a whole, it is worth looking to see if the nature and the behavior … Continue reading
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Tagged education, models, naming, reverse engineering, whole vs. parts
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Quantity – The Series
In this series, we take a leisurely look at quantities of different kinds. It is rather interesting to find out that there are more than one kind of number, based on what operations make sense to perform on them. For … Continue reading
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Tagged models, naming, representations, reverse engineering, series on math learning, whole vs. parts
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Groupings, Shopping Lists, Vectors: part 24
In this series of posts on the topic of vectors, I’ve been primarily interested in playing with situations in which the notion of a vector naturally arises. Looking at shopping lists was one of those. A shopping list is … Continue reading
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Tagged denominations, extending patterns, matrix multiplication, models, naming, whole vs. parts
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Groupings, Shopping Lists, Vectors: part 23
In this post I’m going to look at something usually referred to as linear combinations. In the prior post, we had an occasion to look at coordinate systems where the axes are not at right angles. We saw that you … Continue reading
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Tagged denominations, extending patterns, matrix multiplication, models, naming, representations, whole vs. parts
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Groupings, Shopping Lists, Vectors: part 22
In the last few posts in this series I’ve examined some consequences of British values, where we have pounds and shillings (and also pence) – but then have this other value, the guinea, which equals one pound and one shilling. … Continue reading
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Tagged denominations, extending patterns, matrix multiplication, models, naming, representations, whole vs. parts
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Groupings, Shopping Lists, Vectors: part 21
In the previous post in this series, part 20, I showed a matrix multiplication to convert a value stated in guineas and shillings into one stated in pounds and shillings. We were interested in the same value, expressed in different … Continue reading
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Tagged denominations, extending patterns, matrix multiplication, representations, whole vs. parts
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Groupings, Shopping Lists, Vectors: part 20
In England, the main currency is called the pound. Smaller units are called shillings and pence. A pound is 20 shillings, a shilling is 5 pence, hence a pound is 100 pence. This system has been in place since 1971; … Continue reading
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Tagged denominations, extending patterns, matrix multiplication, models, naming, representations, whole vs. parts
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Groupings, Shopping Lists, Vectors: part 19
In this post, I will try to connect a set of equations with matrices and vectors in a way that isn’t simply a notational shift. In part 18 of this series, I brought up the vast preponderance of square matrices … Continue reading
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Tagged denominations, matrix multiplication, models, naming, representations, whole vs. parts
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Groupings, Shopping Lists, Vectors: part 18
If you have read earlier installments of this series – and I know it has gotten long – you may have noticed that very few of the matrices that appeared there have the same number of rows and columns. A … Continue reading
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Tagged denominations, extending patterns, math class, matrix multiplication, models, naming, representations, whole vs. parts
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Groupings, Shopping Lists, Vectors: part 17
In this post I will show a fullfledged matrix multiplication done in a spreadsheet, Excel. (This series starts here; two recent posts part 15 and part 16 introduce vector inner products done in Excel.) Above you see one approach, though … Continue reading
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Tagged education, extending patterns, matrix multiplication, models, naming, representations, whole vs. parts
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