Abbott Dimension, Mathematics Inspired by Flatland

Jeremy Siegert

Research output: Contribution to journalArticlepeer-review


What is the “right way” to define dimension? Mathematicians working in the early and middle 20th-century formalized three intuitive definitions of dimension that all turned out to be equivalent on separable metric spaces. But were these definitions the “right” ones? What would it mean to have the “right” definition of dimension? In this paper we attempt to inspire thought about these questions by introducing Abbott dimension, a geometrically intuitive definition of dimension based on Edwin Abbott’s 1884 novella Flatland. We show that while Abbott dimension has intuitive appeal, it does not always agree with the classical definitions of dimension on separable metric spaces.

Original languageEnglish
JournalAmerican Mathematical Monthly
StateAccepted/In press - 1 Jan 2023


  • 54F45

ASJC Scopus subject areas

  • General Mathematics


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