All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Fold Judgement III (Posted on 2014-04-26) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Possible solution Comment 1 of 1
Although 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.

Proof:
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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information