math
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The lie at the heart of the Eiffel Tower
This is a bit of a departure from the usual content of this blog, more a musing on an odd bit of trivia regarding mathematical history, nation building, and an iconic landmark at the heart of one of the world’s most famous cities. Named after Gustave Eiffel – his company completed the tower in 1889… Continue reading
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the earth is actually a donut: part ii
In our previous post we figured out how much of a donut planet had the planet directly overhead. This was done for the regime in which the major radius was larger than the smaller radius . What about the case when , called a “spindle” torus? When the circles intersect, they do so at ,… Continue reading
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the earth is actually a donut: part i
I recently saw this meme. Below is a transcript of my thoughts. As usual, a shoutout to my coauthor D.G. for his contributions to the calculations. First thought: …that’s silly Second thought: Most of the Earth couldn’t see the ocean above them, so that can’t possibly be the reason. Third thought: Actually, I wonder how… Continue reading
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The longest arc: Part II
Last time we saw that the problem of finding the circle with the longest arc-length wasn’t possible analytically, and we had to resort to numerical or graphical methods. Now we extend the problem to find the sphere centered at the origin with the largest surface area inside a unit sphere shifted vertically by one unit.… Continue reading
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The largest area: Part I
This adventure started when I attempted a harmless looking problem from the Facebook group “Actually Good Maths Problems”. The answer, which any motivated high school calculus student could find, is a sort of joke or prank on the solver, and I enjoyed it enough that I sent the problem to my good friend David Galea.… Continue reading
Hi there! I’m a content creator with a background in maths education and a passion for making complicated ideas simple, with intuitive animations and visual explanations.
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The Calculus of Explanations 