Real life

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.

Reading Pandemic Graphs

(A new question of the week) Having just discussed several mathematical topics that lie behind the various graphs we have seen in the news lately, I want to depart from our usual style and answer my own current questions. We’ll look at several graphs of COVID-19’s growth and think about what we can learn from …

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Logarithmic Graphing

We’ve been looking at the math underlying some of the graphs associated with the COVID-19 pandemic, starting with exponential growth, and then logistic growth. I want to look in more detail at a feature I mentioned in the first post, viewing a graph logarithmically. This is a powerful technique that goes far beyond a button …

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Logistic Growth

Last time we looked at the meaning of exponential growth, a term commonly used in describing the initial spread of a virus such as the current SARS2 (which causes COVID-19). But exponential growth can’t continue forever, as it would soon exceed the total population. A slightly more complicated model for growth that takes into account …

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Exponential Growth

The term “exponential” has gone viral, so to speak. Do we all know what it means? In the next few posts I’ll look at answers we’ve given to questions about exponential growth and related concepts, some of them about the spread of diseases or rumors. (Disclaimer: I will be writing about the basic math, not …

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Oblique Triangles in Applications

Having just looked at how to solve oblique triangles, let’s look at a couple “word problems” (applications) involving such triangles. We’ll be using the Law of Sines, and also exploring alternative methods of solution.

Solving an Oblique Triangle, Part II

Last time we looked at solving triangles in the ASA, AAS, SSS, and SAS cases. We have one more case, which tends to be a little more complicated: the “ambiguous case”, SSA.

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!