Multiplication: Difference between revisions
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'''Multiplication''' is [TODO] | '''Multiplication''' is [TODO] | ||
== Examples == | |||
My thesis is that multiplication always identifies quantities resulting from a unit-conversion (i.e. a change in unit-perspective) of some sort. | |||
=== Examples which obviously come from unit-conversion === | |||
Suppose you wish to find the number of squares in a rectangular grid. You measure that there are <math>n</math> squares per column, and that there are <math>m</math> columns. In total, therefore, there are <math>nm</math> squares. | |||
Each pack of hot dog buns contains 6 buns, so if I buy 10 packs then I will have enough buns for 6*10 = 60 hot dogs. | |||
=== Examples which don't obviously come from unit-conversion === | |||
The volume of a disk of radius r = 2 meters is approximately 3.14 * 2 * 2 = 12.56 square meters. It could be argued, however, that this ''does'' come from unit-conversion: the derivation consists of finding the area <math>2\pi r \times dr</math> of small annuli (which is done by unit conversion and approximation), then adding their areas together. | |||
A for loop which runs <math>n</math> times, inside of a for-loop which runs <math>m</math> times, will take approximately <math>nm</math> steps to run. Again, I think this ''does'' come from a unit-conversion. | |||
Revision as of 22:24, 12 March 2025
Multiplication is [TODO]
Examples
My thesis is that multiplication always identifies quantities resulting from a unit-conversion (i.e. a change in unit-perspective) of some sort.
Examples which obviously come from unit-conversion
Suppose you wish to find the number of squares in a rectangular grid. You measure that there are squares per column, and that there are columns. In total, therefore, there are squares.
Each pack of hot dog buns contains 6 buns, so if I buy 10 packs then I will have enough buns for 6*10 = 60 hot dogs.
Examples which don't obviously come from unit-conversion
The volume of a disk of radius r = 2 meters is approximately 3.14 * 2 * 2 = 12.56 square meters. It could be argued, however, that this does come from unit-conversion: the derivation consists of finding the area of small annuli (which is done by unit conversion and approximation), then adding their areas together.
A for loop which runs times, inside of a for-loop which runs times, will take approximately steps to run. Again, I think this does come from a unit-conversion.