Curry's Paradox and the Notion of Area

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Curry's Paradox and the Notion of Area: Part I
Here is a wonderful paradox due to Paul Curry that challenges our beliefs on how area behaves. In this video I show the paradox, resolve paradox, and then in parts II and III of the video show how I use the paradox in teaching. Curry's Paradox and the Notion of Area: Part II
Here's how to use a paradox (part I) to begin a theory of area Curry's Paradox and the Notion of Area: Part III
In this third part, we finish off the pedagogical component of our discussion on how Curry's paradox leads us to our beliefs on how area should behave, and how from basic principles we can find the areas of figures.