 
Summary: A Totally Real Folding of the Regular Heptagon
Roger C. Alperin
There are several origami constructions for the heptagon; see [4] for one exam
ple. However, the construction is a totally real construction [3], so we can achieve it
with bisections and trisections of angles and constructions of perpendicular through
a point not on a line. We modify the heptagon construction in [2]. The explantion
of the trisection which we use below is discussed there.
Take a square piece of paper say 6 units on a side with center V and OV of
length 1 on the horizontal midline OV A7 of the square.
Construct distance of BV = 3
3 on the vertical midline of the square. First
construct A with AV of length 5 parallel to the vertical mideline; bisect the angle
of AV and midline; reflect A across this bisector to A on the midline; A V has
length
26; move A to A1 and reflect back to B so that the hypotenuse BO of
BOV has length
28.
