Connections between Paper Folding, Geometry and Proof

Maurya, Akash (2023) Connections between Paper Folding, Geometry and Proof. At Right Angles. pp. 16-18. ISSN 2582-1873

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Let us consider a rectangle ABCD. We create another rectangle ABFE within it by joining the midpoints F and E of the breadths of the original rectangle ABCD. Then the diagonal AC of the original rectangle and the diagonal BE of the second rectangle (ABFE) intersect at a point O in such a way that if we draw a straight line through O parallel to DC, which intersects the breadths AD & BC of the original rectangle at G and H respectively, then we get a third rectangle ABHG whose breadth will be one-third (1/3) the breadth of the original rectangle.” In general, if we apply this same process to the newly obtained rectangle, then we will get a new rectangle whose breadth will be again one third of the previous rectangle i.e., this will be a continuous process. Further we will get the same result if we get the intersection point by involving other diagonals of rectangles i.e., BD and AF respectively. Note: This intriguing statement was made by my mentor. It happened as described below.

Item Type: Articles in APF Magazines
Authors: Maurya, Akash
Document Language:
Uncontrolled Keywords: Paper Folding, Geometry, Exploration, Verification, Reasoning, Proof.
Subjects: Natural Sciences > Mathematics
Divisions: Azim Premji University > University Publications > At Right Angles
Full Text Status: Public
Publisher URL:

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