000RM.dvi

332 Constructions with the golden section

Appendix: Another construction of regular pentagon^6

Given a circle, centerO, let
(i)AXY be an isosceles triangle whose height is^54 of the radius of the
circle,
(ii)B′,C′be points on the circumference such thatAX′=AY′= radius,
(iii)P=AX∩OB′andQ=AY∩OC′,
(iv) the linePQintersect the circumference atBandC.
ThenABandACare two sides of a regular pentagon inscribed in the
circle.

B′ C′

X Y

P Q

B C

O

A

(^6) D. Nelson, A regular pentagon construction,Math. Gazette, 61 (1977) 215–216.