Packing for Hyperspace


Given 3 mutually touching unit circles (or disks) in a (2D) plane, what is the largest circle that will fit in the gap?

Given 4 mutually touching unit spheres (or balls) in (3D) space, what is the largest sphere that will fit in the gap? 1,521 more words


Week 44



My breathing space was limited with the back of my palm on my forehead. I let out an audible groan as I was facing down towards the floor but just a few inches off.

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My Career

Dante's Big Bang

Un punto vidi che raggiava lume…

One of my favourite scenes in the Commedia is that of Paradiso 28 where Dante, arriving in the proto-heaven of the Primum Mobile, describes his experience of reaching the engine of the universe, a place of strong ontological instability, thus pushing the envelope of poetic expression to the limit. 531 more words

Much ado about Hyperspheres

What’s a sphere?

Geometrically, a sphere is the locus of points equidistant from a given point (which we call the ‘center’. Algebraically, it is the solution set to the equation… 723 more words