Wacker Art Curves Wappen der Familie Wacker
Leuchtturm Hafeneinfahrt
Bild: "Leuchtturm Hafeneinfahrt"

Prolog

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Curves

x(t)=t2-1;   y(t)=t(t2-1);

Folium of Descartes

x(t)=3t/(1+t3);   y(t)=3t2)/(1+t3);

Curves

x=(1-cos(t))cos(t);   y=(1-cos(t))sin(t)

x=(1-cos(t))cos(2t);   y=(1-cos(t))sin(2t)

x=(1-cos(t))cos(3t);   y=(1-cos(t))sin(3t)

x=(1-cos(t))cos(4t);   y=(1-cos(t))sin(4t)

Curves

Astroide

Epitrochoid

Epitrochoid

x=(a+b)cos(t)-c⋅cos((a/b+1)t);
y=(a+b)sin(t)-c⋅sin((a/b+1)t);

a=3; b=2; c=5;

a=5; b=3; c=8;

Lissajous Curves

x = 2sin(t);   y=sin(2t);

x=cos(t);   y=sin(3t;)

x = sin(2t);   y=2sin(t);

x=sin(t);   y=sin(4t;)

Curves Drawn in Polar Coordinates

x = r(φ)cos(φ);   y = r(φ)sin(φ);   The radius r is a function of φ.

r(φ) = cos(φ);

r(φ) = sin(φ);

r(φ) = cos(2φ);

r(φ) = sin(2φ);

r(φ) = cos(3φ);

r(φ) = sin(3φ);

r(φ) = cos(4φ);

r(φ) = sin(4φ);

r(φ) = cos(2φ)sin(3φ);

r(φ) = cos(3φ)sin(5φ);

Spirals

Weg zum Leuchtturm
Bild: "Der Weg zum Leuchturm"

The next page is about Calculus.

24.August 2021 Version 1.0
Copyright: Hermann Wacker Uhlandstraße 10 D-85386 Eching bei Freising Germany Haftungsausschluß