Calculations with Constraints: Multiply and Divide by Numbers with Specific Properties

This chapter presents the techniques need to multiply or divide two numbers that have a particular property. It also introduces concepts such as twin primes and powerful numbers, and shows the classic proof that there are infinitely many primes. Applications include the size of sheets of paper, the radioactivity of bananas, the dimensions of a rugby union playing field, and the units of time and length proposed by Thomas Jefferson. The methods shown here apply mostly to numbers below, or slightly above 100. As they depend on properties of numbers, there is a need to employ pattern-spotting skills; some hints are provided.

Powerful numbers: Exemplary quantitative studies of science that had policy impact

Much scientometric research aims to be relevant to policy, but such research only rarely has a notable policy impact. In this paper, we examine four exemplary cases of policy impact from quantitative studies of science. The cases are analyzed in light of lessons learned about the use of evidence in policy making in health services, which provides very thorough explorations of the problems inherent in policy use of academic research. The analysis highlights key dimensions of the examples, which offer lessons for those aspiring to influence policy with quantitative studies of science.