Month: October 2019

Compass and Straightedge: Why?

Some time ago I looked at questions about trisecting an angle by compass and straightedge, which entailed discussing the rules for such constructions. We left open another common question: Why are such constructions important, and why do we use those particular tools? This probably isn’t explained as often as it should be. Why does it …

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Order of Operations: Fractions, Evaluating, and Simplifying

(An archive problem of the week) Last time we looked at the subtle distinction between the order of operations, which defines the meaning of an expression, and properties that allow us to do something other than what an expression literally says. Here I want to look at one longer discussion that brings out these issues …

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Order of Operations: Subtle Distinctions

Some questions we have been asked about the order of operations go beyond the what and why, pondering the relationship of the conventions both to theoretical matters (properties of operations) and to practical matters (evaluating and simplifying expressions). We will see here an important distinction between meaning and processes. PEMDAS vs properties, I: Meaning vs. …

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