The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » geometry.puzzles

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Re: Two (I think) interesting Problems
Replies: 1   Last Post: Jan 14, 1993 2:39 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Havard Johnsbraten

Posts: 1
Registered: 12/6/04
Re: Two (I think) interesting Problems
Posted: Jan 14, 1993 2:37 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply (Yoav Ilan Haim Parish) poses the problem

How can I fold an approximate (regular) pentagon from a
quadratic sheet of paper easily ?

In addition to the nice constructions of G.J. McCaughan and Marvin Minsky
(the man with the finite automata?) I have the following contribution:

One of my students once showed me this beautiful paper folding procedure,
wondering whether or not it was exact:

Start with a square ABCD. Fold along the diagonal BD, folding C to A.
Find the midpoint E on AB (folding B to A and opening it again).
Then fold D to E.
By this last folding you get two new points: F on BD and G on AD.
The angle EFG is about twice the angle BFE.
Bisect angle EFG by folding such that G will be lying on FE, and fold
BFE to the backside.
Now you may use a scissor to cut out a regular pentagon (cut at right
or a nice star (cut more arbitrarily)!

The folding procedure above is not exact; the angle BFE being slightly
than 37 degrees, instead of the exact value of 36 degrees. But when you
folding, you are not able to see the inaccuracy. (The McCaughan folding
from an A4-sheet wasn't exact either, but also very close.)
But F divides BD in an exact rational ratio: DF:FB = 5:7 !

o o
Havard Johnsbraten, Telemark College of Education, Notodden, Norway
E-mail or
G=haavard;S=johnsbraaten;O=tmlh;P=uninett;A= ;C=no

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.