60 



Kansas Academy of Science. 



THE CIRCLE THAT IS NOT A CIRCLE. 



By C. E. Warfel, Wamegro, Kan. 



A GOOD many years ago, while teaching in a college in Illinoie, 

 a proposition one day suggested itself to me, and after several 

 futile efforts the figure herein presented was evolved and some ex- 

 periments made in its practical application to machinery and to 

 determine whether or not it was mechanically correct. 



Little attention was further given it for several years, until one 

 evening about a year ago, in a casual conversation with the learned 

 secretary of this Society, it was presented to him, and his curiosity 

 was thereby aroused and he requested that it be submitted to the 

 Academy. 



THE PROPOSITION. 



Construct a plane figure which is not a circle such that passing 

 in a straight line through a certain point within from perimeter to 

 perimeter it will be same distance across in every direction. 



CONSTRUCTION. 



First. — With any point A as a center, and with any radius 

 X, construct a quadrant of any circle BC. 



Second. — With the same point A as a center, and with any 

 greater (or less) radius D, construct a quadrant of another circle 

 EF directly opposite the quadrant BC. 



77^2?y/.— Construct a line GH perpendicular to the bisector of 

 the two arcs BC and EF. 



