In ancient mathematics, one famous kind of puzzle was constructing certain geometric shapes using nothing but a straight edge and a compass.
These tools might seem very primitive, but they were easy to build with sufficient accuracy. They also avoided dealing with units, of which there wasn’t a standardised system like we have today.
The construction of some geometric shapes, like an equilateral triangle, is very simple:
Other constructions, like the regular 17-gon, are much more complicated and were not discovered until thousands of years later, by genius Carl Friedrich Gauss:
But there are some things that are seemingly impossible to construct using just straight edge and compass. Countless mathematicians have tried to find a solution, but they all were unsuccessful.
One of these constructions that was thought to be impossible is Trisecting the Angle. If you are given an arbitrary angle, it is very simple to bisect it into two equal halves. But no one was able to find a way to split the angle into three equal parts — until now!
Despite taking more that 2500 years to find, the solution, which was discovered by Dr Ekoj Lirpa from Medfield College, consists of just six steps:
The discovery has caused amazement from mathematicians all around the world, and means that many textbooks will need to be rewritten.
It also shows that mathematics is still an area of very active research: there is a lot we don’t yet know, left to discover by the next generations of mathematicians.
On Mathigon, you can lean more about Euclidean Geometry. Please contact us if you have any questions!
