From a Doodle to a Theorem: A Case Study in Mathematical Discovery

Journal of Humanistic Mathematics

article

Juan Fernández González¹  Dirk Schlimm² 

[1] Harvard University;McGill University

关键词: compass and straightedge constructions;    diagrams;    geometry;    mathematical discovery;    philosophy of mathematical practice;   

DOI  :  10.5642/jhummath.RUJI8696

学科分类：社会科学、人文和艺术（综合）

来源: Claremont Center for the Mathematical Sciences

【 摘 要 】

We present some aspects of the genesis of a geometric construction, which can be carried out with compass and straightedge, from the original idea to the published version (Fernández González 2016). The Midpoint Path Construction makes it possible to multiply the length of a line segment by a rational number between 0 and 1 by constructing only midpoints and a straight line. In the form of an interview, we explore the context and narrative behind the discovery, with first-hand insights by its author. Finally, we discuss some general aspects of this case study in the context of philosophy of mathematical practice.

【 授权许可】

CC BY-NC-ND