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In geometry, a nephroid (from Ancient Greek νεφρός (nephrós) 'kidney') is a specific plane curve. It is a type of epicycloid in which the smaller circle's radius differs from the larger one by a factor of one-half.
The analysis highlights Metric properties, Strict definition and The evolute and involute of a nephroid as prominent areas in the source structure around Nephroid.
Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.
Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.
High-confidence facts extracted from structured source data. Use them as anchors for further research.
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The extracted context around Nephroid shows recurring relationship patterns in the source. For example, Nephroid → envelope of the chords of the circle, envelope of the chords of the circle.Nephroid as caustic of one half of a circleThe considerations made in the previous section give a proof for the fact, epicycloid.Nephroid as envelope of a pencil of circlesLet be c 0 Another extracted example is Nephroid → Although, Proctor, Richard. Use these groups to spot repeated connection types before inspecting the individual relationships.
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displaystyle circle one varphi sin cos radius representation point curve parametric see diagram gets equation evolute envelope half cusps hence
TTTA extracted 10 structured relationships around Nephroid. Examples in this analysis include Nephroid → is a → epicycloid.Nephroid as envelope of a pencil of circlesLet be c 0 and Nephroid → is a → envelope of the chords of the circle.Nephroid as caustic of one half of a circleThe considerations made in the previous section give a proof for the fact. The table shows each extracted connection, where it came from and its confidence.
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Nephroid | is a | epicycloid.Nephroid as envelope of a pencil of circlesLet be c 0 | 0.90 | text |
| Nephroid | is a | envelope of the chords of the circle.Nephroid as caustic of one half of a circleThe considerations made in the previous section give a proof for the fact | 0.90 | text |
| Nephroid | is a | envelope of the chords of the circle | 0.90 | text |
| Nephroid | related to Construction | Hence | 0.60 | section |
| Nephroid | related to Name | Although | 0.60 | section |
| Nephroid | related to Name | Richard | 0.60 | section |
| Nephroid | related to Name | Proctor | 0.60 | section |
| Nephroid | related to Nephroid as envelope of a pencil of lines | Similar | 0.60 | section |
| Nephroid | related to Nephroid as envelope of a pencil of lines | Draw | 0.60 | section |
| Nephroid | related to Strict definition | Jordan | 0.60 | section |
The concept neighborhoods around Nephroid bring nearby vocabulary together. In this analysis, examples include One, Displaystyle and Hence. Use the clusters to find adjacent concepts and terminology that may deserve separate research.
For Nephroid, one of the stronger structural bridges in this analysis connects Nephroid with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.
TTTA analyzes the structure around Nephroid to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Metric properties, Strict definition & The evolute and involute of a nephroid, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.
Source: Wikipedia — Nephroid · EN edition · Analysis: TopicsToTalkAbout
