Triangle Centres
Euclidean geometry
Date of Birth:
Ancient Greek
A Bit About Triangle Centres
The study of triangle centers dates back to ancient Greece, where mathematicians such as Euclid, Archimedes, and Apollonius explored the properties of triangles and their centers. Although the concept of triangle centers has evolved over time, it remains a fundamental area of study in geometry
One of the earliest known triangle centers is the circumcenter, which was studied by the ancient Greeks and is mentioned in Euclid's Elements. Later, in the 19th century, mathematicians such as Karl von Staudt and Jakob Steiner developed new methods for studying triangle centers, and introduced new concepts such as the symmedian point and the Brocard points.
Today, the study of triangle centers remains an active area of research in mathematics, with new centers being discovered and explored all the time.
Developmental Stage
Around 300 BCE
Around 200 BCE
Around 200 CE
19th century
20th century
Present day
Euclid's Elements contains the first known mention of the circumcentre of a triangle, which is the point where the perpendicular bisectors of the sides intersect.
So as the centroid of a triangle, which is the point where the three medians of the triangle intersect
The concept of the orthocenter of a triangle was also studied by Apollonius, the first mathematicians to explore the properties of orthocentric triangles and their centers.
Archimedes studies the properties of the circumcentre and its relationship to the incircle and excircles of a triangle.
Ptolemy introduces the concept of the incentre of a triangle, which is the point where the angle bisectors of the triangle intersect.
Mathematicians such as Karl von Staudt and Jakob Steiner develop new methods for studying triangle centers, and introduce new concepts such as the symmedian point and the Brocard points.
Mathematicians continue to explore the properties of triangle centers, and develop new analytical and computational methods for studying them.
The study of triangle centers remains an active area of research in mathematics, with new centers being discovered and explored all the time. The concepts of centroid, orthocenter, incenter, and circumcenter continue to play an important role in geometry education and research, and have led to many important discoveries and advancements in mathematics and related fields.
