# Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 11

## Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 11

Published $\text {1968}$

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## $11 \quad$ Special Plane Curves

### Lemniscate

$11.1$: Lemniscate of Bernoulli: Polar Definition
$11.2$: Lemniscate of Bernoulli: Cartesian Definition
$11.3$: Slope of Tangent to Lemniscate at Origin
$11.4$: Area of Lobe of Lemniscate of Bernoulli

### Cycloid

$11.5$: Equation of Cycloid
$11.6$: Area under Arc of Cycloid
$11.7$: Length of Arc of Cycloid
Cycloid

### Hypocycloid with Four Cusps

$11.8$: Equation of Astroid: Cartesian Form
$11.9$: Equation of Astroid: Parametric Form
$11.10$: Area inside Astroid
$11.11$: Length of Arc of Astroid
Astroid

### Cardioid

$11.12$: Equation of Cardioid: Polar
$11.13$: Area inside Cardioid
$11.14$: Length of Perimeter of Cardioid
Cardioid

### Catenary

$11.15$: Equation of Catenary
Catenary

### Three-Leaved Rose

$11.16$: Trifolium: Cosine Form
Trifolium: Sine Form
Number of Petals of Odd Index Rhodonea Curve

### Four-Leaved Rose

$11.17$: Quadrifolium: Cosine Form
Number of Petals of Even Index Rhodonea Curve

### Epicycloid

$11.18$: Equation of Epicycloid
Epicycloid
Cardioid

### General Hypocycloid

$11.19$: Equation of Hypocycloid
Hypocycloid

### Trochoid

$11.20$: Equation of Trochoid
Trochoid
Curtate Trochoid
Prolate Trochoid
Cycloid

### Tractrix

$11.21$: Equation of Tractrix: Parametric Form
Tractrix

### Witch of Agnesi

$11.22$: Equation of Witch of Agnesi: Cartesian
$11.23$: Equation of Witch of Agnesi: Parametric Form
Witch of Agnesi

### Folium of Descartes

$11.24$: Folium of Descartes: Cartesian Form
$11.25$: Folium of Descartes: Parametric Form
$11.26$: Area of Loop of Folium of Descartes
$11.27$: Asymptote to Folium of Descartes

### Involute of a Circle

$11.28$: Parametric Equation of Involute of Circle
Involute

### Evolute of an Ellipse

$11.29$: Evolute of Ellipse: Cartesian Form
$11.30$: Evolute of Ellipse: Parametric Form

### Ovals of Cassini

$11.31$: Equation of Ovals of Cassini: Polar Form
Ovals of Cassini
Ovals of Cassini: Shape
Lemniscate of Bernoulli is Special Case of Ovals of Cassini

### Limacon of Pascal

$11.32$: Equation of Limaçon of Pascal: Polar Form
Limaçon of Pascal
Limaçon of Pascal:Shape

### Cissoid of Diocles

$11.33$: Equation of Cissoid of Diocles: Cartesian Form
$11.34$: Equation of Cissoid of Diocles: Parametric Form
Cissoid of Diocles

### Spiral of Archimedes

$11.35$: Archimedean Spiral

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