How can students search for counterexamples? The mathematician seems aware that the patterns that hold for at least two examples might give her some idea about what a more general argument might entail, suggesting process pattern generalization.
Quillen and A. Arc Length Conjecture : Formula to calculate the length of an arc on a circle.
While confirming examples may help to provide insight into why a conjecture is true, we must also actively search for counterexamples. The conjectures were responses to an assignment to choose a class of quadrilaterals and to identify any properties of the angle bisectors or perpendicular bisectors of the sides of those figures.
Leonard displays knowledge of elementary number theory as he carefully selects four numbers that are not prime and that all have a composite number as a greatest common divisor. If I still fail, then I may look at my conditions and try and weaken them so as to bypass the troublesome part more easily.
But what if I try to write it as a sum of eight consecutive integers as well? Interviewer: Right.