What does trisection mean?
Trisection is the division of something into three parts, often three equal parts. Its best-known mathematical use is in geometry, where a line segment or angle can be divided into three equal sections; a triangle may also be divided into three smaller triangles. The word is precise and somewhat formal, so it suits mathematical, scientific, or analytical writing rather than casual conversation. Outside geometry, it can describe any process that divides a subject, plan, or institution into three distinct components. Trisection is especially memorable because angle trisection became a major problem in the history of geometry. Although some special angles can be trisected using established constructions, general angle trisection is impossible with only an unmarked straightedge and compass, a result that helped reveal the limits of classical geometric methods.
nounThe act of dividing something into three parts, especially the division of a line segment or angle into three equal parts. In geometry, the term also refers to the process of dividing a triangle into three smaller triangles.
- The act of dividing a quantity, line segment, angle, or geometric figure into three parts, especially three equal parts.
"The construction demonstrates a classic trisection of the angle into three equal measures."
"The trisection of the triangle produced three smaller triangles with equal areas."
"The lecture examined the historical difficulties surrounding angle trisection."
The plural is used when referring to multiple divisions into three parts or to multiple instances of the process.
"The guide includes practical trisections of several geometric shapes."
Angle trisection is one of geometry's most famous construction problems—and one that cannot be solved with only a straightedge and compass in the same way as angle bisection.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does trisection come from?
Trisection entered English in the early 17th century from the Latin trisectio, meaning a division into three. The word is associated with the Latin prefix tri-, meaning three, and the Latin root secare, meaning to cut. Related English words such as section, dissection, and trisect reflect this same cutting-based ancestry.
How trisection is actually used
The term is primarily formal and technical. It is especially common in mathematics and geometry, but it can be used more generally when discussing the division of a subject or organization into three parts.
Easily confused with trisection
Trisection is the noun naming the division into three parts, while trisect is the verb describing the act of dividing something that way.