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Tag Archives: lookup
Notes on Divisibility – Common Divisors
In an earlier post I introduced the notion of a divisor without relying on division, instead thinking of it as a mark that was left during skip counting. This is a very old notion, dating at least to the times … Continue reading
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Tagged denominations, extending patterns, lookup, models, naming, puzzle, reverse engineering
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Notes on Divisibility – Eratosthenes and Euclid
You will want to read the Notes on Divisibility post first. In the figure below, I’ve shown the first 22 mile markers, and the red marks on each. Skip counting by twos leads to the red “2” marks, skip counting … Continue reading
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Tagged denominations, extending patterns, lookup, models, naming, recurrence relationship, sieve
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Notes On Divisibility
Imagine the numbers 1, 2, 3, … laid out in a regular linear sequence, like mile markers on a long road. The markers don’t need to be a mile apart, you can put them closer if you like, but you … Continue reading
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Tagged denominations, extending patterns, lookup, naming, unlearning
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Skinny Multiplication Table
This is a puzzle. Imagine a lookup table like this: and that this table is used for multiplication. Obviously, this multiplication table must be used differently from the usual one, because it is a onedimensional table, long and skinny. To … Continue reading
Napier’s Logs
(In an earlier post, I referred to a way to understand the invention of logarithms by John Napier. This post fleshes this out.) Imagine an era long ago where calculators and computers didn’t exist, and the engineers and crafts people … Continue reading