\input zb-basic \input zb-matheduc \iteman{ZMATH 2016a.00587} \itemau{Griffiths, Martin} \itemti{Squeezing bubbles into corners.} \itemso{Math. Teach. (Reston) 107, No. 6, 473-477 (2014).} \itemab From the text: I always seek activities that might stretch my students yet would be accessible to them; that might require logical thought yet would contain counterintuitive elements; that might provide the opportunity to venture into new mathematical realms yet would have a simple starting point. This article and the activity that inspired it did indeed arise by way of a relatively straightforward problem that I proposed to one of my classes. I asked students to draw a square $S$ of side length 2 units containing a circle $C_1$ of radius 1 unit. The challenge was to find the radius $r$ of the largest circle $C_2$ that could fit into one of the corners" between $S$ and $C$. This problem can be solved in several ways. One approach is to imagine an infinite series of ever-decreasing circles. Later we deal with the extended problem of finding the total area of the infinite number of circles that cover $S$. Moving into three dimensions gives rise to the bubbles" referred to in the article's title. And this problem generalizes beautifully into $n$ dimensions. \itemrv{~} \itemcc{G40 I30} \itemut{filling a square with circles; total area; geometric series; plane geometry; solid geometry; filling a cube with spheres; total volume; generalization; multidimensional spaces; hypercubes; hyperspheres; student activities; discovery learning} \itemli{http://www.nctm.org/Publications/mathematics-teacher/2014/Vol107/Issue6/Delving-Deeper\_-Squeezing-Bubbles-into-Corners/} \end