NotesFAQContact Us
Search Tips
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ862756
Record Type: Journal
Publication Date: 2009-Nov
Pages: 5
Abstractor: ERIC
Reference Count: 4
ISSN: ISSN-0025-5769
Delving Deeper: One Cut, Two Halves, Three Questions
Ren, Guanshen
Mathematics Teacher, v103 n4 p305-309 Nov 2009
A square can be divided into two equal parts with any cut through the center. The first question that arises is, Would any cut through the center of a regular polygon divide it into two equal parts? If not, the second question is, What kind of lines through the center of the polygon would cut it into two halves? However, many objects are not regular polygons, and an arbitrary convex polygon does not have a center. Thus, it is natural to ask a third and more challenging question: How can an arbitrary convex quadrilateral, pentagon, or hexagon be divided into two halves by using one line? This article answers these questions by using methods of elementary geometry. (Contains 14 figures.)
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A