Statements (15)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Wallace–Simson_line
|
| gptkbp:defines |
Given a triangle and a point on its circumcircle, the feet of the perpendiculars from the point to the sides of the triangle are collinear; this line is the Simson line.
|
| gptkbp:discoveredBy |
gptkb:William_Wallace
|
| gptkbp:field |
gptkb:geometry
gptkb:Euclidean_geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
Simson line
|
| gptkbp:namedAfter |
gptkb:Robert_Simson
|
| gptkbp:property |
If the point coincides with a vertex of the triangle, the Simson line coincides with the altitude from that vertex.
The envelope of the Simson lines as the point moves around the circumcircle is a deltoid curve. The Simson lines of two antipodal points on the circumcircle are perpendicular. The Simson line passes through the feet of the perpendiculars from a point on the circumcircle to the sides of the triangle. |
| gptkbp:relatedTo |
gptkb:train
|
| gptkbp:bfsParent |
gptkb:Robert_Simson
|
| gptkbp:bfsLayer |
5
|