Conformal Maps

​
square size
number of lines
a
α
0
α
1
α
2
β
0
β
1
β
2
Conformal map of a square under the map
z(1-a)
α
0
+
α
1
z+
α
2
2
z
+acos
β
0
+
β
1
z+
β
2
2
z

.

Details

square size — size of the original square
number of lines — number of lines in each direction in the original square
a
,
α
0
,
α
1
,
α
2
,
β
0
,
β
1
,
β
2
— parameters of the map
z(1-a)
α
0
+
α
1
z+
α
2
2
z
+acos
β
0
+
β
1
z+
β
2
2
z

Conformal maps of the complex plane onto itself play a central role in complex analysis. Locally, they preserve angles.

External Links

Conformal Mapping (Wolfram MathWorld)

Permanent Citation

Michael Trott
​
​"Conformal Maps"​
​http://demonstrations.wolfram.com/ConformalMaps/​
​Wolfram Demonstrations Project​
​Published: April 27, 2007