Analysis of Mathematical Fiction with Geometric Themes

Title:

Analysis of Mathematical Fiction with Geometric Themes

Author(s):

Shloming, Jennifer Rebecca

Thesis Advisor(s):

Karp, Alexander P.

Date:

2012

Type:

Dissertations

Department:

Mathematics Education

Permanent URL:

http://hdl.handle.net/10022/AC:P:14870

Notes:

Ph.D., Columbia University.

Abstract:

Analysis of mathematical fiction with geometric themes is a study that connects the genre of mathematical fiction with informal learning. This study provides an analysis of 26 sources that include novels and short stories of mathematical fiction with regard to plot, geometric theme, cultural theme, and presentation. The authors' mathematical backgrounds are presented as they relate to both geometric and cultural themes. These backgrounds range from having little mathematical training to advance graduate work culminating in a Ph.D. in mathematics. This thesis demonstrated that regardless of background, the authors could write a mathematical fiction novel or short story with a dominant geometric theme. The authors' pedagogical approaches to delivering the geometric themes are also discussed. Applications from this study involve a pedagogical component that can be used in a classroom setting. All the sources analyzed in this study are fictional, but the geometric content is factual. Six categories of geometric topics were analyzed: plane geometry, solid geometry, projective geometry, axiomatics, topology, and the historical foundations of geometry. Geometry textbooks aligned with these categories were discussed with regard to mathematical fiction and formal learning. Cultural patterns were also analyzed for each source of mathematical fiction. There were also an analysis of the integration of cultural and geometric themes in the 26 sources of mathematical fiction; some of the cultural patterns discussed are gender bias, art, music, academia, mysticism, and social issues. On the basis of this discussion, recommendations for future studies involving the use of mathematical fiction were made.

Subject(s):

Mathematics education
Mathematics
 Item views:

329
 Metadata:

text  xml
 Suggested Citation:

Jennifer Rebecca Shloming,
2012,
Analysis of Mathematical Fiction with Geometric Themes, Columbia University Academic Commons,
http://hdl.handle.net/10022/AC:P:14870.