In this bicentenary year of 2021, let's revisit a result that bears his name. The emperor is said to have had a keen interest in geometry; according to one story, he once discussed the subject with two mathematicians of his day, Joseph Lagrange (1763–1813) and Pierre-Simon Laplace (1749–1827).
Articles recommended for you.
A symmetry appearing out of nowhere, an equilateral triangle emerging amid the trisectors of a completely arbitrary triangle: that is the whole "miracle" of Morley and his theorem. The many proofs of this beautiful property are marvels of geometry and trigonometry.
Talking about the "power of a point with respect to a circle" may seem old-fashioned nowadays. Yet this elegant geometric notion had its heyday and its uses. Its applications to various mathematical questions are highly fruitful.
Three sides completely determine a triangle, up to orientation. With four sides, infinitely many polygons can be constructed. Nevertheless, many general properties can be established for arbitrary convex quadrilaterals.
The midpoint of two points and the center of gravity of a triangle are familiar concepts from middle school onward. What do they have in common? How can they be generalized? In the early 19th century, a new approach to geometry put them on a firm mathematical footing through the concept of the barycenter.
Discussion
Sign in to post a comment and talk with other readers.
No comments yet. Be the first to respond.
