## Pythagorean Triples? (Solution #1, Part 1)

(If you haven’t read the “Problem” post with the same title, go there first. This will make more sense if you do.) We want to find all the Pythagorean triples (a,b,c). The first thing a mathematician would probably do is to try some small examples, gather some information, and then look for patterns within thatContinue reading “Pythagorean Triples? (Solution #1, Part 1)”

## From Numbers to “Pure” Math: Ancient Greece

In my previous post, I talked about the conceptual progression from the most basic intuitions about counting to the more general idea of number that transcends any particular physical situation. As big a development as this is, I would say this not mathematics proper. In most civilizations where the number concept developed, the most complicatedContinue reading “From Numbers to “Pure” Math: Ancient Greece”

## Where Did Numbers Come From?

In my last post, I argued that a distinction needs to be made between calculation and math. But certainly these are related, because calculation is about numbers, and math uses a lot of numbers. So what exactly is the connection? Working from my own experience being trained to be a mathematician and educator, as wellContinue reading “Where Did Numbers Come From?”