12 files changed, 0 insertions, 521 deletions
diff --git a/math/cylindrical_coordinates.org b/math/cylindrical_coordinates.org
deleted file mode 100644
index fab185b..0000000
--- a/math/cylindrical_coordinates.org
+++ /dev/null
@@ -1,37 +0,0 @@
-#+TITLE:Cylindrical Coordinates
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-#+LATEX_HEADER: \newcommand{\deriv}[2]{\frac{\text{d}#1}{\text{d}#2}}
-#+LATEX_HEADER: \newcommand{\unitv}[1]{\bm{\hat{e}}_#1}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-* Coordinate transformations
-\begin{align*}
-x &= r \cos\varphi\\
-y &= r \sin\varphi\\
-z &= z
-\end{align*}
-
-* Local unit vectors
-\begin{align*}
-\unitv{r} &= \cos\theta \unitv{x} + \sin\theta \unitv{y}\\
-\unitv{\theta} &= -\sin\theta \unitv{x} + \cos\theta \unitv{y}\\
-\unitv{z} &= \unitv{z}
-\end{align*}
-* Kinematic in cylindrical coordinates
-** Time derivatives of the local unit vectors
-\begin{align*}
-\deriv{\unitv{r}}{t} &= \dot{\theta}\unitv{\theta}\\
-\deriv{\unitv{\theta}}{t} &= -\dot{\theta}\unitv{r}\\
-\deriv{\unitv{z}}{t} &= 0
-\end{align*}
-** Position vector and its time derivatives
-\begin{align*}
-\bm{r} &= r\unitv{r} + z\unitv{z}\\
-\bm{v} &= \dot{r}\unitv{r} + r\dot\theta\unitv{\theta} + \dot{z}\unitv{z}\\
-\bm{a} &= \left(\ddot{r}-r\dot{\theta}^2\right)\unitv{r} + \left(2\dot{r}\dot{\theta}+r\ddot{\theta}\right)\unitv{\theta} + \ddot{z}\unitv{z}
-\end{align*}
diff --git a/math/derivatives.org b/math/derivatives.org
deleted file mode 100644
index 4d5d4be..0000000
--- a/math/derivatives.org
+++ /dev/null
@@ -1,31 +0,0 @@
-#+TITLE:Table of Derivatives
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-#+LATEX_HEADER: \newcommand{\dcoff}[1]{\frac{\text{d}}{\text{d}x} #1}
-#+LATEX_HEADER: \newcommand{\sdcoff}[1]{\frac{\text{d}#1}{\text{d}x}}
-#+LATEX_HEADER: \newcommand{\deriv}[2]{\frac{\text{d}}{\text{d}x} #1 &= #2}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-
-* General Properties of the Derivative
-Let $f$ and $g$ be real valued functions and $c$ some real constant:
-\begin{align*}
-\dcoff{(cf)} &= c\sdcoff{f}\\
-\dcoff{(f \pm g)} &= \sdcoff{f} \pm \sdcoff{g}\\
-\dcoff{(fg)} &= \sdcoff{f}g + f\sdcoff{g}\\
-\dcoff{\left(\frac{f}{g}\right)} &= \frac{\sdcoff{f}g - f\sdcoff{g}}{g^2}
-\end{align*}
-
-* Trigonometric Funtions
-\begin{align*}
-\deriv{\sin(x)}{\cos(x)}\\
-\deriv{\cos(x)}{-\sin(x)}\\
-\deriv{\tan(x)}{\sec^2(x)}\\
-\deriv{\sec(x)}{\sec(x)\tan(x)}\\
-\deriv{\csc(x)}{\csc(x)\cot(x)}\\
-\deriv{\csc(x)}{-\csc^2(x)}
-\end{align*}
diff --git a/math/index.org b/math/index.org
deleted file mode 100644
index 069c4b6..0000000
--- a/math/index.org
+++ /dev/null
@@ -1,13 +0,0 @@
-#+TITLE: Math and Physics articles
-#+SETUPFILE: ../math_options.org
-
-- [[file:vectors.org][Cross Product]]
-- [[file:cylindrical_coordinates.org][Cylindrical Coordinates]]
-- [[file:matrices.org][Matrix Properties]]
-- [[file:orbit.org][Orbit]]
-- [[file:polar_coordinates.org][Polar Coordinates]]
-- [[file:spherical_coordinates.org][Spherical Coordinates]]
-- [[file:derivatives.org][Table of Derivatives]]
-- [[file:integrals.org][Table of Integrals]]
-- [[file:levi_cevita.org][The Levi Cevita Symbol]]
-- [[file:trigonometry.org][Trigonometric identities]]
-\ No newline at end of file
diff --git a/math/integrals.org b/math/integrals.org
deleted file mode 100644
index 6a32903..0000000
--- a/math/integrals.org
+++ /dev/null
@@ -1,20 +0,0 @@
-#+TITLE:Table of Integrals
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-#+LATEX_HEADER: \newcommand{\intg}[2]{\int #1 \text{d}x &= #2 + C}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-
-* Trigonometric Funtions
-\begin{align*}
-\intg{\sin(x)}{-\cos(x)}\\
-\intg{\cos(x)}{\sin(x)}\\
-\intg{\tan(x)}{-\ln(\cos(x))}\\
-\intg{\sec(x)}{\ln(\sec(x) + \tan(x))}\\
-\intg{\csc(x)}{-\ln(\csc(x) + \cot(x))}\\
-\intg{\cot(x)}{\ln(\sin(x))}
-\end{align*}
diff --git a/math/levi_cevita.org b/math/levi_cevita.org
deleted file mode 100644
index aaa2074..0000000
--- a/math/levi_cevita.org
+++ /dev/null
@@ -1,26 +0,0 @@
-#+TITLE: The Levi Cevita Symbol
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-* Levi Cevita symbol
-\begin{equation*}
-\varepsilon_{ijk} = \left\{\begin{array}{rl}
-1,&(i,j,k) \in \{(1,2,3), (2,3,1), (3,1,2)\}\\
--1,&(i,j,k) \in \{(3,2,1), (2,1,3), (1,3,2)\}\\
-0,&\text{otherwise}
-\right{}
-\end{array}
-\end{equation*}
-
-\begin{equation*}
-\varepsilon_{ijk} = \varepsilon_{jki} = \varepsilon_{kij} = - \varepsilon_{ikj} = - \varepsilon_{jik} = - \varepsilon_{kji} = 1
-\end{equation*}
-
-\begin{align*}
-\sum_{k=1}^3 \varepsilon_{ijk}\varepsilon_{kmn} = \delta_{im} \delta_{jn} - \delta_{in} \delta_{jm}
-\end{align*}
diff --git a/math/math.css b/math/math.css
deleted file mode 100644
index d4e1054..0000000
--- a/math/math.css
+++ /dev/null
@@ -1,85 +0,0 @@
-/*
-p.author
-p.date
-p.creator
-.title
-.subtitle
-.todo
-.done
-.WAITING
-.timestamp
-.timestamp-kwd
-.timestamp-wrapper
-.tag
-._HOME
-.target
-.linenr
-.code-highlighted
-div.outline-N
-div.outline-text-N
-.section-number-N
-.figure-number
-.table-number
-.listing-number
-div.figure
-pre.src
-pre.example
-p.verse
-div.footnotes
-p.footnote
-.footref
-.footnum
-.org-svg
-*/
-
-html {
-    height: 100%;
-    color: #cccccc;
-    background-color: hsl(240, 30%, 10%);
-}
-
-body {
-    margin: auto;
-    max-width: 64em;
-    min-height: 100%;
-    display: flex;
-    flex-direction: column;
-    background-color: hsl(240, 30%, 15%);
-}
-
-main {
-    padding: 2em 2em 2em 2em;
-    flex-grow: 1;
-}
-
-h1 {
-    text-align: center;
-}
-
-#content {
-    max-width: 50em;
-    margin: auto;
-}
-
-div.outline-2:first-of-type {
-    padding: 0.25em 1em;
-    background-color: hsl(60,30%,30%);
-}
-
-.equation-container {
-    display: block;
-    padding: 1em 2em;
-    background-color: hsl(240, 30%, 20%);
-    overflow: auto;
-    border: 1px solid hsl(240, 30%, 50%)
-}
-
-img {
-    max-width: unset;
-}
-
-.equation-container img {
-    object-fit: contain;
-    display: block;
-    margin: auto;
-}
diff --git a/math/matrices.org b/math/matrices.org
deleted file mode 100644
index a7ba58b..0000000
--- a/math/matrices.org
+++ /dev/null
@@ -1,32 +0,0 @@
-#+TITLE:Matrix Properties
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-* Basic properties
-\begin{align*}
-A + B = B + A
-\end{align*}
-* Dot product
-\begin{align*}
-(A^\text{T})^\text{T} &= A\\
-(A + B)^\text{T} &= A^\text{T} + B^\text{T}\\
-(AB)^\text{T} &= B^\text{T}A^\text{T}
-\end{align*}
-* Transpose
-\begin{align*}
-\bm{a} \cdot \bm{b} &= \overline{\bm{b}} \cdot \bm{a}\\
-\bm{a} \cdot \bm{b} &= \bm{a}^\text{T} \bm{b}
-\end{align*}
-
-* Hermitian transpose
-\begin{align*}
-A^\ast &= \left[\overline{a_{ij}}\right]\\
-(\lambda A)^\ast &= \left[\overline{\lambda a_{ij}}\right] = \overline{\lambda} \left[a_{ij}\right]^\ast = \overline{\lambda}\,\overline{A}\\
-A^\dag &= (A^\ast)^\text{T}\\
-A^{\dag\dag} &= A
-\end{align*}
diff --git a/math/orbit.org b/math/orbit.org
deleted file mode 100644
index 88079a6..0000000
--- a/math/orbit.org
+++ /dev/null
@@ -1,93 +0,0 @@
-#+TITLE:Orbit
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-#+LATEX_HEADER: \usepackage{amssymb}
-#+LATEX_HEADER: \newcommand{\deriv}[2]{\frac{\text{d}#1}{\text{d}#2}}
-#+LATEX_HEADER: \newcommand{\unitv}[1]{\bm{\hat{e}}_#1}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-* Deriving Kepler's first law from Newton's law of universal gravitation
-
-The movement of an object with mass $m$ orbiting another body with mass $M$ is
-given by Newton's law of gravitation. If $m \ll M$ it is possible to consider
-the position of the larger object constant and use it as the origin of our
-coordinate system. Then the following equation applies for movement of the
-smaller object:
-
-\begin{equation*}
-m\ddot{\bm{r}} = - \frac{GMm}{r^3}\bm{r} \Leftrightarrow \ddot{\bm{r}} = - \frac{GM}{r^3}\bm{r}
-\end{equation*}
-
-In order to solve this differential equation we first consider the angular
-momentum of or object around its orbit.
-
-\begin{equation*}
-\bm{L} = \bm{r} \times m \dot{\bm{r}}
-\end{equation*}
-
-In the abscense of external toques, because the only force acting on the object
-is parallel to its position, the angular momentum is conserved.
-
-\begin{equation*}
-\deriv{\bm{L}}{t} = \dot{\bm{r}} \times m \dot{\bm{r}} + \bm{r} \times m \ddot{\bm{r}} = 0
-\end{equation*}
-
-We now multiply both sides of our equation from the right by the angular
-momentum and develop the right side of the equation using vector identities.
-
-\begin{align*}
-\ddot{\bm{r}} \times \bm{L} &= -GM\frac{\bm{r} \times \left(\bm{r} \times m \dot{\bm{r}}\right)}{r^3}\\
-&= - \frac{GMm}{r^3} \left(\left(\bm{r} \cdot \dot{\bm{r}}\right)\bm{r} - \left(\bm{r} \cdot \bm{r}\right)\dot{\bm{r}}\right)\\
-&= GMm\left(\frac{\left(\bm{r} \cdot \bm{r}\right)\dot{\bm{r}}}{r^3} - \frac{\left(\bm{r} \cdot \dot{\bm{r}}\right)\bm{r}}{r^3}\right)\\
-&= GMm\left(\frac{\dot{\bm{r}}}{r} - \frac{\left(\bm{r} \cdot \dot{\bm{r}}\right)\bm{r}}{r^3}\right)\\
-&= GMm\left(\frac{1}{r} \deriv{\bm{r}}{t} + \deriv{}{t}\left(\frac{1}{r}\right)\bm{r}\right)\\
-&= GMm\deriv{}{t}\left(\frac{\bm{r}}{r}\right)
-\end{align*}
-
-We observe that each side of our equation is a derivative of a quantity. We know
-integrate both sides and take the integrations constant into account.
-
-\begin{align*}
-& \deriv{}{t} \left(\dot{\bm{r}} \times \bm{L}\right) = GM \deriv{}{t}\left(\frac{\bm{r}}{r}\right)\\
-\Leftrightarrow \quad & \dot{\bm{r}} \times \bm{L} = GM \frac{\bm{r}}{r} + \bm{a}
-\end{align*}
-
-Our objective is now to solve the equation for $r$, so we multiply both sides by $\bm{r}$:
-
-\begin{align*}
-\dot{\bm{r}} \times \left(\bm{r} \times \dot{\bm{r}}\right) &= GM \frac{\bm{r}}{r} + \bm{a}\\
-\bm{r} \cdot \left(\dot{\bm{r}} \times \left(\bm{r} \times \dot{\bm{r}}\right)\right) &= GMr + \bm{r} \cdot \bm{a}
-\end{align*}
-
-By applying a cyclic permutation of the resulting triple product and using the
-known property of the scalar product we now express the equation only in terms
-of the magnitudes of the vectors.
-
-\begin{align*}
-\left(\bm{r} \times \dot{\bm{r}}\right) \cdot \left(\bm{r} \times \dot{\bm{r}}\right) &= GMr + \bm{r} \cdot \bm{a}\\
-\left(\frac{L}{m}\right)^2 &= GMr + \bm{r} \cdot \bm{a}\\
-\left(\frac{L}{m}\right)^2 &= GMr + r a \cos\theta
-\end{align*}
-
-The last steps are to solve for $r$
-
-\begin{align*}
-r &= \left(\frac{L}{m}\right)^2 \frac{1}{GM + a \cos\theta}\\
-&= \left(\frac{L}{m}\right)^2 \frac{1}{GM} \frac{1}{1 + \frac{a}{GM} \cos\theta}\\
-&= \left(\frac{L}{m}\right)^2 \frac{1}{GM} \frac{1}{1 + e\cos\theta}
-\end{align*}
-
-Finally we reach our result. Objects orbiting according to Newton's Law of
-Gravitation follow paths that correspond to the conic sections. Here is Kepler's
-first Law a special case, where our object has a stable orbit around the larger
-body.
-
-\begin{equation*}
-r &= \frac{L^2}{GM m^2} \frac{1}{1 + e\cos\theta}
-\end{equation*}
-
-* Deriving a physical interpretation of the excentricity of the orbit
diff --git a/math/polar_coordinates.org b/math/polar_coordinates.org
deleted file mode 100644
index ff07be3..0000000
--- a/math/polar_coordinates.org
+++ /dev/null
@@ -1,36 +0,0 @@
-#+TITLE:Polar Coordinates
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-#+LATEX_HEADER: \newcommand{\deriv}[2]{\frac{\text{d}#1}{\text{d}#2}}
-#+LATEX_HEADER: \newcommand{\unitv}[1]{\bm{\hat{e}}_#1}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-* Coordinate transformations
-\begin{align*}
-x &= r \cos\theta\\
-y &= r \sin\theta
-\end{align*}
-
-* Local unit vectors
-\begin{align*}
-\unitv{r} &= \cos\theta \unitv{x} + \sin\theta \unitv{y}\\
-\unitv{\theta} &= -\sin\theta \unitv{x} + \cos\theta \unitv{y}
-\end{align*}
-
-* Kinematic in polar coordinates
-** Time derivatives of the local unit vectors
-\begin{align*}
-\deriv{\unitv{r}}{t} &= \dot{\theta}\unitv{\theta}\\
-\deriv{\unitv{\theta}}{t} &= -\dot{\theta}\unitv{r}
-\end{align*}
-** Position vector and its time derivatives
-\begin{align*}
-\bm{r} &= r\unitv{r}\\
-\bm{v} &= \dot{r}\unitv{r} + r\dot\theta\unitv{\theta}\\
-\bm{a} &= \left(\ddot{r} - r\dot\theta^2\right)\unitv{r}
-+ \left(2\dot{r}\dot\theta + r\ddot\theta\right)\unitv{\theta}
-\end{align*}
diff --git a/math/spherical_coordinates.org b/math/spherical_coordinates.org
deleted file mode 100644
index 1c7fd9c..0000000
--- a/math/spherical_coordinates.org
+++ /dev/null
@@ -1,39 +0,0 @@
-#+TITLE:Spherical Coordinates
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-#+LATEX_HEADER: \newcommand{\deriv}[2]{\frac{\text{d}#1}{\text{d}#2}}
-#+LATEX_HEADER: \newcommand{\unitv}[1]{\bm{\hat{e}}_#1}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-* Coordinate transformations
-\begin{align*}
-x &= r \sin\theta \cos\varphi\\
-y &= r \sin\theta \sin\varphi\\
-z &= r \cos\theta
-\end{align*}
-
-* Local unit vectors
-\begin{align*}
-\bm{\hat{e}}_r &= \sin\theta \cos\varphi \bm{\hat{e}}_x + \sin\theta \sin\varphi \bm{\hat{e}}_y + \cos\theta \bm{\hat{e}}_z\\
-\bm{\hat{e}}_\theta &= \cos\theta \cos\varphi \bm{\hat{e}}_x + \cos\theta \sin\varphi \bm{\hat{e}}_y - \sin\theta \bm{\hat{e}}_z\\
-\bm{\hat{e}}_\varphi &= - \sin\theta \sin\varphi \bm{\hat{e}}_x + \sin\theta \cos\varphi \bm{\hat{e}}_y
-\end{align*}
-* Kinematic in spherical coordinates
-** Time derivatives of the local unit vectors
-\begin{align*}
-\deriv{\unitv{r}}{t} &= \dot{\theta}\unitv{\theta} + \dot{\varphi}\sin\theta \unitv{\varphi}\\
-\deriv{\unitv{\theta}}{t} &= -\dot{\theta}\unitv{r} + \dot{\varphi}\cos\theta \unitv{\varphi}\\
-\deriv{\unitv{\varphi}}{t} &= -\dot{\varphi} \left(\sin\theta\unitv{r} + \cos\theta\unitv{\theta}\right)
-\end{align*}
-** Position vector and its time derivatives
-\begin{align*}
-\bm{r} &= r\unitv{r}\\
-\bm{v} &= \dot{r}\unitv{r} + r\dot\theta\unitv{\theta} + r\dot\varphi\sin\theta\unitv{\varphi}\\
-\bm{a} &= \left(\ddot{r} - r\dot\theta^2 - r\dot\varphi^2\sin^2\theta\right)\unitv{r}
-+ \left(2\dot{r}\dot\theta + r\ddot\theta - r\dot\varphi^2\sin\theta\cos\theta\right)\unitv{\theta}
-+ \left(2\dot{r}\dot\varphi\sin\theta + 2r\dot\theta\dot\varphi\cos\theta + r\ddot\varphi\sin\theta\right)\unitv{\varphi}
-\end{align*}
diff --git a/math/trigonometry.org b/math/trigonometry.org
deleted file mode 100644
index 3e81eeb..0000000
--- a/math/trigonometry.org
+++ /dev/null
@@ -1,51 +0,0 @@
-#+TITLE:Trigonometric identities
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-
-* Pythagorean identities
-\begin{align*}
-&\cos^2\left(x\right) + \sin^2\left(x\right) = 1\\
-&\tan^2\left(x\right) + 1                    = \sec^2\left(x\right)\\
-&1                    + \cot^2\left(x\right) = \csc^2\left(x\right)
-\end{align*}
-* Sum of angles
-\begin{align*}
-&\sin\left(a \pm b\right) = \sin\left(a\right)\cos\left(b\right) \pm \cos\left(a\right)\sin\left(b\right)\\
-&\cos\left(a \pm b\right) = \cos\left(a\right)\cos\left(b\right) \mp \sin\left(a\right)\sin\left(b\right)\\
-&\tan(a \pm b) = \frac{\tan(a) \pm \tan(b)}{1 \mp \tan(a) \tan(b)}
-\end{align*}
-* Multiple angles
-\begin{align*}
-&\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\
-&\cos(2\theta) = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta
-\end{align*}
-* Half-angle formulae
-\begin{align*}
-&\sin \frac{\theta}{2} = \pm \sqrt{\frac{1-\cos\theta}{2}}\\
-&\cos \frac{\theta}{2} = \pm \sqrt{\frac{1+\cos\theta}{2}}
-\end{align*}
-* Power-reduction formulae
-\begin{align*}
-&\sin^2\theta = \frac{1 - \cos(2\theta)}{2}\\
-&\cos^2\theta = \frac{1 + \cos(2\theta)}{2}
-\end{align*}
-* Product-to-sum formulae
-\begin{align*}
-&2 \cos\theta \cos\varphi = \cos(\theta-\varphi) + \cos(\theta+\varphi)\\
-&2 \sin\theta \sin\varphi = \cos(\theta-\varphi) - \cos(\theta+\varphi)\\
-&2 \sin\theta \cos\varphi = \sin(\theta+\varphi) + \sin(\theta-\varphi)\\
-&2\cos\theta\sin\varphi = \sin(\theta+\varphi) - \sin(\theta-\varphi)
-\end{align*}
-* Sum-to-product formulae
-\begin{align*}
-&\sin\theta \pm \sin\varphi = 2 \sin\left(\frac{\theta\pm\varphi}{2}\right) \cos\left(\frac{\theta\mp\varphi}{2}\right)\\
-&\cos\theta + \cos\varphi = 2 \cos\left(\frac{\theta+\varphi}{2}\right) \cos\left(\frac{\theta-\varphi}{2}\right)\\
-&\tan\theta \pm \tan\varphi = \frac{\sin(\theta\pm\varphi)}{\cos\theta \cos\varphi}\\
-&\cos\theta - \cos\varphi = - 2 \sin\left(\frac{\theta+\varphi}{2}\right) \sin\left(\frac{\theta-\varphi}{2}\right)
-\end{align*}
diff --git a/math/vectors.org b/math/vectors.org
deleted file mode 100644
index 49d8132..0000000
--- a/math/vectors.org
+++ /dev/null
@@ -1,58 +0,0 @@
-#+TITLE:Cross Product
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-
-* Definition
-We shall define the cross product in terms of two properties we are
-interested in:
-
-- Distributive: $\bm{a} \times \left(\bm{b} + \bm{c}\right) = \bm{a} \times \bm{b} + \bm{a} \times \bm{c}$
-- Orthogonal: $\bm{a} \times \bm{b} = \bm{c} \implies \bm{c} \cdot \bm{a} = \bm{0} \land \bm{c} \cdot \bm{b} = \bm{0}$
-
-It is worth mentioning that given a pair of vectors in $\mathbb{R}^3$
-there exist an infinite amount of vectors that satisfy these
-properties, so it is also necessary to introduce the following
-relations between the basis vectors to properly define the cross
-product.
-
-\begin{align*}
-\bm{e}_1 &= \bm{e}_2 \times \bm{e}_3\\
-\bm{e}_2 &= \bm{e}_3 \times \bm{e}_1\\
-\bm{e}_3 &= \bm{e}_1 \times \bm{e}_2\\
-\bm{e}_i \times \bm{e}_i &= \bm{0},\qquad\text{For}\quad i = 1,2,3
-\end{align*}
-
-We introduce the Levi-Civita symbol to condense our calculations.
-
-\begin{equation*}
-\epsilon_{ijk} \coloneqq \bm{e}_i \cdot \left(\bm{e}_j \times \bm{e}_k\right)
-\end{equation*}
-
-Based on this we may now derive a way to compute the cross product of
-two vectors
-
-\begin{align*}
-\left[\bm{a} \times \bm{b}\right]_i &= \left[\left(\sum_j a_j \bm{e}_j\right) \times \left(\sum_k b_k \bm{e_k}\right)\right]_i\\
-&= \left[\sum_{jk} a_j b_k \left(\bm{e}_j \times \bm{e}_k\right)\right]_i\\
-&= \sum_{jk} a_j b_k \bm{e}_i \cdot \left(\bm{e}_j \times \bm{e}_k\right)\\
-&= \sum_{jk} \epsilon_{ijk} a_j b_k\\
-\bm{a} \times \bm{b} &= \sum_{ijk} \epsilon_{ijk} a_i b_j \bm{e}_k
-\end{align*}
-
-* Properties
-\begin{align*}
-&\bm{a} \times \bm{b} = - \bm{b} \times \bm{a}\\
-&\bm{a} \cdot \left(\bm{b} \times \bm{c}\right)
-= \bm{b} \cdot \left(\bm{c} \times \bm{a}\right)
-= \bm{c} \cdot \left(\bm{a} \times \bm{b}\right)\\
-&\bm{a} \times \left(\bm{b} \times \bm{c}\right)
-= \left(\bm{a} \cdot \bm{c}\right)\bm{b} - \left(\bm{a} \cdot \bm{b}\right)\bm{c}\\
-&\left(\bm{a} \times \bm{b}\right) \times \left(\bm{c} \times \bm{d}\right)
-= \left(\bm{a}\cdot\bm{c}\right) \left(\bm{b}\cdot\bm{d}\right) - \left(\bm{a}\cdot\bm{d}\right) \left(\bm{b}\cdot\bm{c}\right)
-\end{align*}