Exploring the 'lunes' - Jan. 23-27: Christie was just starting lunch when Stevie sat down next to her, clutching a tattered book. "I was reading this book called 'Curious and Interesting Geometry', and I found this neat picture. It's about a thing called 'lunes'. Here's the picture: * * * B *+++++++* * * *++++++* *+| * * *++++++* *+++| * * *+++++* *+++++| * * *++++* *+++++++| * * *++* *+++++++++| * * * * *+++++++++++| * * A *_____________|_____________* C D ABC is half a square inscribed in a semi-circle (A->B->C). Then a semi-circle is constructed on AB. BD is then constructed, the perpendicular bisector of AC, and triangle ABD is shaded, as is the part of the outer semi-circle that's not part of the original semicircle. Rumor has it that Hippocrates of Chios proved something about these two regions, but the next page in the book is missing! So I have to figure it out, because it's driving me nuts!" "Don't stop thinking about it," said Christie. "Let's see if we can figure it out right now." Correct solutions to the problem were submitted by: Sean Nichols, Burnaby South Secondary School Susan Quan, Masterman High School Eric Wahl, Masterman High School Cecilia Merediz, Fairfield HS 9th Grade Geometry Class at Wheatland Junior High Next problem || Previous problem || Table of Contents || Forum Home Page

2 July 1995