Estimation

How Far Can I See?

We have been looking at questions about the roundness of the earth, starting with the general fact, and then the determination of the size of the earth. A very common question is about how that roundness affects what we can see, sometimes as a challenge (“If I can see this, then how can the earth …

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Distances to an Arc: Exact and Approximate Formulas

(A new question of the week) It can be an interesting challenge to be presented with a formula and asked how it was derived. This becomes a bigger challenge when the formula is only approximate, so we have to figure out how to arrive at this particular approximation. But it is impressive when several different …

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A Fermi Problem

(An archive problem of the week) A couple weeks ago, in discussing the value of estimates, I included one example of a (very simple) Fermi problem: one in which it is necessary to invent the data as well as the method of solution. Today, I will examine one answer in which we dug deeper into …

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Evaluating Square Roots by Hand

Square roots commonly are irrational numbers, so that it is necessary to estimate them. Usually today, we use a calculator to find them. Many students, however, are curious about how they could do it without a calculator. Here I want to reverse the usual format of this blog, presenting a summary I have written that …

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