I see many favorites here, but this one should be mentioned too:
MR1710978 (2000h:00002) Hugo Steinhaus. Mathematical snapshots. Translated from the Polish. With a preface by Morris Kline. Reprint of the third (1983) English edition. Dover Publications, Inc., Mineola, NY, 1999. vi+311 pp. ISBN: 0-486-40914-7
It was first published in 1939 ("Kalejdoskop matematyczny" in Polish).
Here is the summary:
Things like fair division or platonic bodies made accessible for an aunt and a niece alike (I actually gave my copy to my niece a few years ago).