Geometry

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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Eratosthenes Measures the Earth

Last time we looked at a couple questions about proving the earth is round, which led into questions about how Eratosthenes measured the earth (though that in itself did not prove the earth is not flat). Let’s look at two questions about that project itself.

Proving the Earth is Round … or Not

Can you use mathematics to prove that the earth is round? That’s a question we get from time to time, sometimes from people who want to prove the earth is flat, sometimes from people who want to convince their friends otherwise, and sometimes just from students. Let’s think about it.

Area of Pyramids and Cones

We’ve looked at the volume of a pyramid, the formula for which can be found geometrically by a couple very different methods. Cones can be handled the same way, so we can skim over them. Let’s finish up by considering the surface areas of both cones and pyramids.

Making a Sphere from Flat Material

(A new question of the week) A recent question asking how to make a sphere out of flat material called for a look at an old question on the same topic, and some new ideas, including thoughts about approximation. And we actually get to see the physical result of our assistance, which is rare!

Volume and Surface Area of a Sphere – Without Calculus

We often get questions about deriving formulas for area and volume; usually when the question is about a sphere, the context is calculus, so we talk about integration, the usual modern method. But for students who only know geometry, “wait until you learn calculus” can be unsatisfying. Fortunately, there are a couple ways to do …

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Choosing the Most Appropriate Unit

We’ve been looking at measuring and drawing devices (compass, ruler, protractor); let’s move on to units of measurement. A fairly common question for students learning about measurement is, “What is the most appropriate unit for measuring ___?” The answer is not always clear, as we’ll see.

Using a Protractor

Last time we looked at how to use a ruler to measure distances. This time, we’ll consider another common question over the years: how to use a protractor to measure angles. We’ll also consider the relationship between protractors and the compass and straightedge constructions that started this series on geometry tools. And just like last …

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