Maurya, Akash
(2023)
Connections between Paper Folding, Geometry and Proof.
At Right Angles.
pp. 1618.
ISSN 25821873
Abstract
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 onethird (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.
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