Can You Solve “Unsolvable” Mathematical Problems? (Nov, 1931)
Can You Solve “Unsolvable” Mathematical Problems?
PROBLEMS of mathematics, long considered unsolvable, may soon give up their secrets to inquiring mathematicians. The problem of trisecting an angle by plane geometry, for example, is one which has puzzled mathematicians for 2500 years, and which has come to be regarded as insolvable as the squaring of a circle. Rev. Joseph J. Callahan, president of Duquesne University, recently announced that he had solved the trisection problem by the Euclidean method of geometry.
The diagram herewith was not made by Father Callahan, who has not made public his solution, but it shows a well-known way of trisecting an angle. Angle DOA is trisected and angles BOC and BCO each is one-third of the original angle DOA. Angles OAB and OBA each is twice angles BOC and BCO. The unsolvable problem is the angle’s trisection by ruler and compass, which is the method by which mathematicians assume Father Callahan has solved the puzzle.
“Squaring the circle”, or obtaining the exact area of a circle by mathematical formulae, is a familiar geometric problem which has defied solution for years, and which has probably caused as many headaches among mathematicians as the perpetual motion problem has been responsible for among inventors. With the development of mechanical methods of solving such problems as angle trisection and circle squaring, however, the geometric solution of the problems is mostly of academic interest. Surveyors and engineers have long been accustomed to trisecting angles by rule of thumb methods which prove entirely adequate for their purposes.