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

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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