Ortsbogen theorem
Encyclopedia
In geometry
, for any line segment AB and angle θ < π, the locus
of points C on one side of line AB such that angle ACB equals θ is an arc of a circle. Points outside this arc form sharper angles than θ, while points within this arc form wider angles.
In the Swiss school curriculum this arc is known as an "Ortsbogen" and the theorem that the locus has this shape is known as the Ortsbogen theorem.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, for any line segment AB and angle θ < π, the locus
Locus (mathematics)
In geometry, a locus is a collection of points which share a property. For example a circle may be defined as the locus of points in a plane at a fixed distance from a given point....
of points C on one side of line AB such that angle ACB equals θ is an arc of a circle. Points outside this arc form sharper angles than θ, while points within this arc form wider angles.
In the Swiss school curriculum this arc is known as an "Ortsbogen" and the theorem that the locus has this shape is known as the Ortsbogen theorem.