Wacker Art Curves
Bild: "Leuchtturm Hafeneinfahrt"

## Prolog

### Attention

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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

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