A Totally Real Folding of the Regular Heptagon Roger C. Alperin 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. Collections: Mathematics