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

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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
Quadrifolium: Sine 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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