Translation guide
The highest point or the point where lines or edges meet. In mathematics, it refers to a corner point of a geometric shape or graph. In anatomy, it's the top of the head. In everyday language, it can mean the peak or summit of something.
The point where two or more lines, edges, or curves meet in geometry or graph theory.
The standard term for 'vertex' in geometry and graph theory. Used for corners of polygons, polyhedra, and nodes in graphs.
三角形の頂点から底辺に垂線を引く。
Draw a perpendicular line from the vertex of the triangle to the base.
グラフ理論では、ノードを頂点と呼ぶ。
In graph theory, nodes are called vertices.
The crown or highest point of the skull.
Specifically refers to the top of the head, the vertex of the skull.
頭頂部に痛みを感じる。
I feel pain at the vertex of my head.
Refers to the hair whorl at the crown, often used colloquially for the top of the head.
つむじのあたりがかゆい。
The area around my vertex itches.
The highest point or summit of something, such as a career, mountain, or achievement.
Used metaphorically for the peak or apex of something, like a career or mountain.
彼はついに権力の頂点に立った。
He finally reached the vertex of power.
富士山の頂点に立つ。
Stand at the vertex of Mt. Fuji.
Often used for the climax or peak of an experience, career, or emotion. Can have a nuance of 'zenith'.
Literally 'highest point', a straightforward term for vertex in a non-technical sense.
The point on the celestial sphere directly overhead, or a point where the prime vertical meets the horizon.
The astronomical term for zenith, the point directly overhead. Sometimes used for vertex in celestial navigation.
太陽が天頂に達する。
The sun reaches the vertex.
Both mean 'peak' or 'vertex', but 頂点 is more general and can be used for physical points (geometry, mountains) and abstract peaks. 絶頂 is more often used for the climax of a state or emotion, like 'the height of fame' or 'the peak of pleasure'.
While 頂点 can mean 'top', in anatomy, the specific term for the vertex of the head is 頭頂 (とうちょう). Using 頂点 for the head might be understood but sounds odd.
放物線の頂点は(0,0)にある。
The vertex of the parabola is at (0,0).
彼は頭頂に禿げがある。
He has a bald spot on his vertex.
彼の人気は絶頂に達した。
His popularity reached its vertex.
この山の最高点は標高3000メートルだ。
The vertex of this mountain is 3000 meters above sea level.