Tag - sphere

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If i² = -1, what's happening inside i² to get it to -1?

[I wrote the following while I was learning about how the imaginary realm works. It looks like I didn't yet understand how i is a rotation, and was still thinking of it as a vertical-only movement. So it's a lot of kerfuffle about nothing, but I'm keeping here as a reference point on the journey to  […]

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Yes, hyperbolic geometry does describe the inside of a sphere

I tried for years to get a clear intuitive image for the inside of a sphere, as clear as I already have for the outside of a sphere. It's really hard! I've even been inside a large spherical room (there's a church in Boston with one), and of course, as we all do, I can easily imagine being inside of  […]

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