deletions | additions       diff --git a/kinematics_angle.tex b/kinematics_angle.tex  index dac97e1..c0b6d5b 100644  --- a/kinematics_angle.tex  +++ b/kinematics_angle.tex 
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\end{split}  \end{equation}  According to \cite{McDonald_2001} since the pion is a spin zero particle, the decay is isotropic in the pion rest frame. Therefore, the volume elements can be seen as concentric cylinders to integrate over. In order to calculate the neutrino flux to be measured at a given angle, we need to know $\frac{\partial E_{\pi}}{\partial \cos \theta}$ to get $\frac{d^2 N}{d E_{\nu} d \cos \theta}$ to calculate the total number per $\cos \theta$ per beam energy.