In recent years, many localization algorithms have been proposed for wireless sensor networks, in which the hop-count based localization schemes are attractive due to the advantage of low cost. However, these approaches usually utilize discrete integers to calculate the hop-counts between nodes. Such coarse-grained hop-counts make no distinction among one-hop nodes. More seriously, as the hop-c...

Our modern system of positional decimal notation with zero, together with efficient algorithms for computation, which were discovered in India some time prior to 500 CE, certainly must rank among the most significant achievements of all time. And it was not easy. As Pierre-Simon Laplace (1923) explained, “the difficulty of inventing it will be better appreciated if we consider that it escaped t...

Arrange three circles so that every pair is mutually tangent. Is it possible to add another, tangent to all three? The answer, as described by Apollonius of Perga in Hellenistic Greece, is yes, and, indeed, there are exactly two solutions [oP71, Problem XIV, p.12]. The four resulting circles are called a Descartes quadruple, and it is impossible to add a fifth. There is a remarkable relationshi...