diff --git a/src/python/test/test_geometry_math.py b/src/python/test/test_geometry_math.py
new file mode 100644
index 0000000..e4f4bb2
--- /dev/null
+++ b/src/python/test/test_geometry_math.py
@@ -0,0 +1,22 @@
+import numpy as np
+
+from pffdtd.geometry.math import find_third_vertex, transform_point
+
+
+def test_find_third_vertex():
+    v = find_third_vertex([0, 0, 0], [2, 0, 0])
+    assert np.allclose(v, ([1, +1.73205081, 0], [1, -1.73205081, 0]))
+
+    v = find_third_vertex([0, 0, 1.2], [3, 0, 1.2])
+    assert np.allclose(v, ([1.5, +2.59807621, 1.2], [1.5, -2.59807621, 1.2]))
+
+
+def test_transform_point():
+    p = transform_point([0, 0, 0], [1, 1, 1], [0, 0, 0], [0, 0, 0])
+    assert np.allclose(p, [0, 0, 0])
+
+    p = transform_point([1, 2, 3], [1, 1, 1], [0, 0, 0], [0, 0, 0])
+    assert np.allclose(p, [1, 2, 3])
+
+    p = transform_point([1, 2, 3], [1, 1, 1], [0, 0, 0], [-1, -2, -4])
+    assert np.allclose(p, [0, 0, -1])