The Historical Background of a Famous Indeterminate Problem and Some Teaching Perspectives

Abstract

This paper proposes a new goodness-of-fit for the two-parameter distribution. It is based on a function of squared distances between empirical and theoretical quantiles of a set of observations being hypothesized to have come from the gamma distribution. The critical values of the proposed statistic are evaluated through extensive simulations of the unit-scaled gamma distributions and computations. The empirical powers of the statistic are obtained and compared with some well-known tests for the gamma distribution, and the results show that the proposed statistic can be recommended as a test for the gamma distribution.

Incorporating history of mathematics in open-ended problem solving: An empirical study

“…Hundred fowls problem and similar recasts also appear in the works of Christoff Rudolff (Germany, 1525 AD) Coss, Seki Takakazu (Japan, 1683 AD) and Leonhard Euler's Elements of algebra, along with formal methods and rigorous rules for finding solutions (Campbell & Higgins, 2019;Euler, 1828). A complete historical overview of the hundred fowls problem can be found in Rizos and Gkrekas (2022b).…”