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Nephroid

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.

Metric properties, Strict definition & The evolute and involute of a nephroid

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Metric properties

5 related topics

Strict definition

4 related topics

The evolute and involute of a nephroid

3 related topics

Overview

12 related topics

Topics to explore

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Overview

Name

Strict definition

Metric properties

Construction

The evolute and involute of a nephroid

Inversion of a nephroid

Advanced semantic analysis

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Map overview Semantic statistics

Nephroid

Nodes36
Edges35
Triples20
Avg. degree1.94
Density0.055556
Components1

How this topic connects Entity context

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Nephroid

Top relations

is a · 3
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
related to Name · 3
Nephroid → Although, Proctor, Richard
related to Nephroid as envelope of a pencil of lines · 3
Nephroid → Draw, Similar, The
related to Construction · 2
Nephroid → Hence, It
related to Involute · 2
Nephroid → Because, The
related to Nephroid as caustic of one half of a circle · 2
Nephroid → If, The
related to External links · 1
Nephroid → Mathworld
related to Inversion of a nephroid · 1
Nephroid → The
related to Metric properties · 1
Nephroid → For
related to Nephroid as envelope of a pencil of circles · 1
Nephroid → Let

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Important terminology

displaystyle circle one varphi sin cos radius representation point curve parametric see diagram gets equation evolute envelope half cusps hence

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Nephroidis aepicycloid.Nephroid as envelope of a pencil of circlesLet be c 00.90text
Nephroidis aenvelope 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 fact0.90text
Nephroidis aenvelope of the chords of the circle0.90text
Nephroidrelated to ConstructionIt0.60section
Nephroidrelated to ConstructionHence0.60section
Nephroidrelated to External linksMathworld0.60section
Nephroidrelated to Inversion of a nephroidThe0.60section
Nephroidrelated to InvoluteBecause0.60section
Nephroidrelated to InvoluteThe0.60section
Nephroidrelated to Metric propertiesFor0.60section
Nephroidrelated to NameAlthough0.60section
Nephroidrelated to NameRichard0.60section

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