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ERIC Number: EJ1106688
Record Type: Journal
Publication Date: 2003
Pages: 4
Abstractor: ERIC
ISSN: ISSN-0228-0671
Three Worlds and the Imaginary Sphere
Inglis, Matthew
For the Learning of Mathematics, v23 n3 p24-27 2003
Gary and Tall (2001) recently suggested that mathematics can be split up into "three worlds": the embodied, the proceptual and the axiomatic. They claim that objects from each of these worlds are formed, and reasoned about, in significantly different ways. During the course of this article the author considers the three world's theory and present the view that, as currently described, it is not sufficient to characterise all mathematical objects. In doing this, the author discusses the investigations of Johann Heinrich Lambert into non-Euclidean geometry, and claim that, for Lambert, the so-called "imaginary sphere" does not fit comfortably into any of the three worlds. Through a discussion of an example from the classroom, the author suggests that, looking from the point of view of certain learners, many objects may not satisfactorily fit into Gray and Tall's worlds.
FLM Publishing Association. 382 Education South, University of Alberta, Edmonton, Alberta T6G 2G5, Canada. e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive; Opinion Papers
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A