diff --git a/report/subsections/circles.tex b/report/subsections/circles.tex
index b9365f8..c0430e9 100644
--- a/report/subsections/circles.tex
+++ b/report/subsections/circles.tex
@@ -4,11 +4,13 @@
 
 \paragraph{Characteristic circles computation}
 
-	We take a point sampled on the spline. It gives us information about the sphere located on this point : C(t) the sphere center coordinates and r(t) its radius. We also have their derivatives : C'(t) and r'(t). The idea is to find the intersection between this sphere and the characteristic plane, which would give us the characteristic circle.
-	If a point P is on the circle, then we can write this formula : 
-	$<C'(t),PC(t)> - r'(t)r(t) = 0$
+	We take a point sampled on the spline. It gives us information about the sphere located on this point : $\overrightarrow{C}(t)$ the sphere center coordinates and r(t) its radius. We also have their derivatives : $\overrightarrow{C'}(t)$ and r'(t). The idea is to find the intersection between this sphere and the characteristic plane, which would give us the characteristic circle.
+	If a point P is on the circle, then we can write this formula : \\
+	$<\overrightarrow{C'}(t),\overrightarrow{PC}(t)> -r'(t)r(t) = 0$
+	
 and then we calculate the center of the characteristic circle with this formula :
-	$Cp(t) = C(t) – r'(t)r(t)/norm(C'(t))² * C'(t)$
+
+	$\overrightarrow{Cp}(t) = \overrightarrow{C}(t) - r'(t)r(t)/ /| \overrightarrow{C'}(t)/| ^{2} * \overrightarrow{C'}(t)$
 
 \begin{figure}[H]
    \begin{center}