Everything about Orthocenter
Intersection of triangle altitudes
The orthocenter of a triangle, usually denoted by H, is the point where the three altitudes intersect. The orthocenter lies inside the triangle if and only if the triangle is acute. For a right triangle, the orthocenter coincides with the vertex at the right angle. For an equilateral triangle, all triangle centers coincide at its centroid. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: OrthocenterA 5-minute orientation
- Skim a recent paper: On a property of the orthocenterInfluential work since 2022
- Pick up a classic book: Geometrical kaleidoscopeThe most-reprinted book on the subject
- Read the landmark paper: Some Information Measures Based on Centroid, Orthocenter, Circumcenter and Incenter Points of Transformed Triangular Fuzzy Numbers and their ApplicationsCited 10 times
- Go sideways: Euler lineA closely related topic
- Go sideways: CircumcircleA closely related topic
📖 Definitions
Noun One of the centers (UK:centres) of a triangle, defined as being the intersection of its three altitudes; in an acute triangle, it is inside the triangle; in an obtuse triangle, it is outside the triangle; in a right-angled triangle it is the vertex opposite the hypotenuse and so is on the triangle.
🏆 Landmark papers (most cited)
Some Information Measures Based on Centroid, Orthocenter, Circumcenter and Incenter Points of Transformed Triangular Fuzzy Numbers and their Applications
Hyperbolic is the only Hilbert geometry having circumcenter or orthocenter generally
Characterization of Euclidean geometry by existence of circumcenter or orthocenter
Fuzzy Risk Analysis based on a new approach of Ranking Fuzzy Numbers using Orthocenter of Centroids
Synthetic foundations of cevian geometry, III: the generalized orthocenter
A characterization by optimization of the orthocenter of a triangle
Design of Tactile Sensor for Measuring Orthocenter Deviation and Friction in Wafer Transmission Process
Random orthocenter strategy in interior search algorithm and its engineering application
🆕 Influential since 2022
📚 Books worth reading
- 📕Geometrical kaleidoscopeBoris Pritsker · 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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