diff --git a/kugel.py b/kugel.py
index 931af68..70427bb 100644
--- a/kugel.py
+++ b/kugel.py
@@ -1,78 +1,64 @@
 import numpy as np
+from numpy import sqrt, arctan2, sin, cos, arcsin, arccos
+from numpy.typing import NDArray
+from typing import Tuple
+import winkelumrechnungen as wu
 
 
-def cart2sph(x, y, z):
-    r = np.sqrt(x**2 + y**2 + z**2)
-    phi = np.atan2(z, np.sqrt(x**2 + y**2))
-    lamb = np.atan2(y, x)
+def cart2sph(point: NDArray) -> Tuple[float, float, float]:
+    x, y, z = point
+    r = sqrt(x**2 + y**2 + z**2)
+    phi = arctan2(z, sqrt(x**2 + y**2))
+    lamb = arctan2(y, x)
 
-    return r, np.rad2deg(phi), np.rad2deg(lamb)
+    return r, phi, lamb
 
 
-def sph2cart(r, phi, lamb):
-    phi_rad = np.deg2rad(phi)
-    lamb_rad = np.deg2rad(lamb)
+def sph2cart(r: float, phi: float, lamb: float) -> NDArray:
+    x = r * cos(phi) * cos(lamb)
+    y = r * cos(phi) * sin(lamb)
+    z = r * sin(phi)
 
-    x = r * np.cos(phi_rad) * np.cos(lamb_rad)
-    y = r * np.cos(phi_rad) * np.sin(lamb_rad)
-    z = r * np.sin(phi_rad)
-
-    return x, y, z
+    return np.array([x, y, z])
 
 
-def kugel_erste_gha(R, phi_1, lamb_1, s_d, a_12):
+def gha1(R, phi0, lamb0, s, alpha0):
+    s_ = s / R
 
-    s = s_d / R
-    lamb_1_rad = np.deg2rad(lamb_1)
-    phi_1_rad = np.deg2rad(phi_1)
-    a_12_rad = np.deg2rad(a_12)
+    lamb1 = lamb0 + arctan2(sin(s_) * sin(alpha0),
+                            cos(phi0) * cos(s_) - sin(phi0) * sin(s_) * cos(alpha0))
 
-    sin_satz = np.sin(s) * np.sin(a_12_rad)
-    sin_kos = np.cos(phi_1_rad) * np.cos(s) - np.sin(phi_1_rad) * np.sin(s) * np.cos(a_12_rad)
-    delta_lam = np.atan2(sin_satz, sin_kos)
-    lamb_2_rad = lamb_1_rad + delta_lam
+    phi1 = arcsin(sin(phi0) * cos(s_) + cos(phi0) * sin(s_) * cos(alpha0))
 
-    phi_2_rad = np.asin(np.sin(phi_1_rad) * np.cos(s) + np.cos(phi_1_rad) * np.sin(s) * np.cos(a_12_rad))
-
-    sin_satz_2 = -np.cos(phi_1_rad) * np.sin(a_12_rad)
-    sin_kos_2 = np.sin(s) * np.sin(phi_1_rad) - np.cos(s) * np.cos(phi_1_rad) * np.cos(a_12_rad)
-    a_21_rad = np.atan2(sin_satz_2, sin_kos_2)
-    if a_21_rad < 0:
-        a_21_rad += 2 * np.pi
-
-    return np.rad2deg(phi_2_rad), np.rad2deg(lamb_2_rad), np.rad2deg(a_21_rad)
+    return phi1, lamb1
 
 
-def kugel_zweite_gha(R, phi_1, lamb_1, phi_2, lamb_2):
-    phi_1_rad = np.deg2rad(phi_1)
-    lamb_1_rad = np.deg2rad(lamb_1)
-    phi_2_rad = np.deg2rad(phi_2)
-    lamb_2_rad = np.deg2rad(lamb_2)
+def gha2(R, phi0, lamb0, phi1, lamb1):
+    s_ = arccos(sin(phi0) * sin(phi1) + cos(phi0) * cos(phi1) * cos(lamb1 - lamb0))
+    s = R * s_
 
-    sin_satz_1 = np.cos(phi_2_rad) * np.sin(lamb_2_rad - lamb_1_rad)
-    sin_kos_1 = np.cos(phi_1_rad) * np.sin(phi_2_rad) - np.sin(phi_1_rad) * np.cos(phi_2_rad) * np.cos(lamb_2_rad - lamb_1_rad)
-    a_12_rad = np.atan2(sin_satz_1, sin_kos_1)
+    alpha0 = arctan2(cos(phi1) * sin(lamb1 - lamb0),
+                     cos(phi0) * sin(phi1) - sin(phi0) * cos(phi1) * cos(lamb1 - lamb0))
 
-    kos = np.sin(phi_1_rad) * np.sin(phi_2_rad) + np.cos(phi_1_rad) * np.cos(phi_2_rad) * np.cos(lamb_2_rad - lamb_1_rad)
-    s = np.acos(kos)
-    s_d = R * s
+    alpha1 = arctan2(-cos(phi0) * sin(lamb1 - lamb0),
+                     cos(phi1) * sin(phi0) - sin(phi1) * cos(phi0) * cos(lamb1 - lamb0))
+    if alpha1 < 0:
+        alpha1 += 2 * np.pi
 
-    sin_satz_2 = -np.cos(phi_1_rad) * np.sin(lamb_2_rad - lamb_1_rad)
-    sin_kos_2 = np.cos(phi_2_rad) * np.sin(phi_1_rad) - np.sin(phi_2_rad) * np.cos(phi_1_rad) * np.cos(lamb_2_rad - lamb_1_rad)
-    a_21_rad = np.atan2(sin_satz_2, sin_kos_2)
-    if a_21_rad < 0:
-        a_21_rad += 2 * np.pi
-
-    return s_d, np.rad2deg(a_12_rad), np.rad2deg(a_21_rad)
+    return alpha0, alpha1, s
 
 
 if __name__ == "__main__":
     R = 6378815.904                                             # Bern
-    phi_1 = 10
-    lamb_1 = 40
-    a_12 = 100
+    phi0 = wu.deg2rad(10)
+    lamb0 = wu.deg2rad(40)
+    alpha0 = wu.deg2rad(100)
     s = 10000
-    phi_2, lamb_2, _ = kugel_erste_gha(R, phi_1, lamb_1, s, a_12)
+    phi1, lamb1 = gha1(R, phi0, lamb0, s, alpha0)
+    alpha0_g, alpha1, s_g = gha2(R, phi0, lamb0, phi1, lamb1)
+    phi1 = wu.rad2deg(phi1)
+    lamb1 = wu.rad2deg(lamb1)
+    alpha0_g = wu.rad2deg(alpha0_g)
+    alpha1 = wu.rad2deg(alpha1)
 
-    print(kugel_erste_gha(R, phi_1, lamb_1, s, a_12))
-    print(kugel_zweite_gha(R, phi_1, lamb_1, phi_2, lamb_2))
\ No newline at end of file
+    pass
\ No newline at end of file