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|Fold Judgement III (Posted on 2014-04-26)
A piece of paper has the precise shape of a triangle ABC with AB=2, AC=3, BC=4.
Show how you can construct a tetrahedron by folding three lines.
*** No geometric instrumental aid like straightedge, compass, ruler etc. is permissible.
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Submitted by K Sengupta
Rating: 4.0000 (1 votes)
Comment 1 of 1
only three folds are needed for the base edges of the tetrahedron,
Iím hoping that more folds are allowed in total. I seem to need three
extra folds, each applied to the original starting shape as follows.
a. Fold so that B coincides with
C. Use the fold to identify the
mid-point, M, of BC.
b. Fold so that the edges CA and
CB are collinear and call the
crease CD (D on AB).
c. Fold to form a crease through
M while aligning the two parts
of crease CD. Call this new
crease ME (E on AC).
d. Find the mid-point, N, of AE by
folding A on to E.
e. Fold along BN,
f. Fold along MN.
The folds along BN, MN and ME can now be used as the edges of the
required tetrahedron ABMN, with A, E and B, C being coincident pairs.
CM = BM = 2 (from a).
Triangle CEM isosceles (from b & c), so CE = CM =2 therefore CE = BA.
EN = AN (from d).
These three underlined statements prove that the edge segments match.
Posted by Harry
on 2014-05-06 17:40:26
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