LATENT REFERENCES / TAG1
Coplanarity
Original title: 共立性平面
This reference note belongs to Tag1 in Latent References, an archive curated by Keigo Yoshida. Its archive region is Theoria. The note preserves its source text and links so that readers can trace the material behind the 3D map.
- Collection
- Tag1
- Archive region
- Theoria
Archived reference note
English translation of the archived note. JP shows the original text. Source links and literal code are retained; the translation does not update or independently verify the source claims.
A coplanar plane (Coplanar Plane/coplanarity) refers in mathematics and geometry to a state where multiple points or lines all exist “on the same plane.”
The main characteristics and conditions are as follows.
1. Coplanarity of points (coplanarity condition)
• 3 points: Any 3 points in space always determine 1 plane, so they are necessarily coplanar.
• 4 or more points: Vectors are used to determine whether 4 points (A, B, C, D) lie on the same plane. If the scalar triple product of vectors \(\vec{AB}\), \(\vec{AC}\), and \(\vec{AD}\) is 0, these 4 points are coplanar.
共立性平面（Coplanar Plane / 共面）とは、数学や幾何学において、複数の点や直線がすべて「同一の平面上」に存在している状態を指します。
主な特徴と条件は以下の通りです。
1. 点の共立性（共面条件）
• 3つの点：空間内の任意の3点は、常に1つの平面を決定するため、必ず共立（共面）します。
• 4つ以上の点：4点（A, B, C, D）が同じ平面上にあるかどうかは、ベクトルを用いて判定します。ベクトル \(\vec{AB}\), \(\vec{AC}\), \(\vec{AD}\) のスカラー三重積が 0 になる場合、これらの4点は共立しています。
Source updated 2026-10-06 · Snapshot 2026-10-08
Source links and calculated neighbors
Cosine values measure shared lexical features, not truth, agreement or identical meaning. Original reference links are labeled separately.
- CompatibilityComputed lexical cosine similarity 0.274 · shared title, text, tags and references
- Section PlaneComputed lexical cosine similarity 0.163 · shared title, text, tags and references
- A Party in Full SwingComputed lexical cosine similarity 0.141 · shared title, text, tags and references