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Explaining why volume of cone is a third of cylinder

A possibility may be to show how a cube consists of 6 equivalent pyramids. The picture below shows three of them, and has empty slots in between for the missing three (I felt this would make the ...
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2 votes

Geometry with a view towards differential geometry textbook

Saul Stahl's ** A Gateway to Modern Geometry: the Poincare Upper Half Plane ** looks extremely promising. I haven't read it, but based on the table of contents, it seems to begin with Euclidean ...
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5 votes

Explaining why volume of cone is a third of cylinder

Without Calculus, you can still be sort of rigorous. With Euclidean geometry we can find the centroid of a right triangle by finding the point where all the medians intersect. A cardboard triangle ...
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Explaining why volume of cone is a third of cylinder

One framework of understanding and building towards proof that we teach to mathematics teachers at primary school level is (and translated to English on fly): Naive empiricism: The pupil tries an ...
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Explaining why volume of cone is a third of cylinder

This is an experiment which can lead you to guess that the volume of a cone is approximately $\frac{1}{3}$ the volume of a cylinder with the same base and height. It is not a proof in any sense of ...
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8 votes

Real-world applications of taxicab metric

A variation on Matthew's bakeries: The taxicab Voronoi diagram shows which firestation can reach a fire fastest in a city whose roads follow an orthogonal grid. The dots below are firestations, and ...
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7 votes

Real-world applications of taxicab metric

I would argue that the taxicab metric as such is actually carrying its weight if it is a "fun exercise for students" that points out that there are real-world applications where the ...
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