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fixed drawer navs and updated geometry contents
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@justinkx
justinkx committed Aug 13, 2020
1 parent e47c186 commit 27d7e97
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3 changes: 2 additions & 1 deletion App/Navigation/DrawerItem.js
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Expand Up @@ -33,7 +33,8 @@ const DrawerItem = ({ category, themeValues, navigation }) => {
<TouchableOpacity
onPress={() => {
navigation.navigate('ContentPage', {
subCategory: item,
title: item.topic,
url: item.url,
});
}}
style={[
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290 changes: 290 additions & 0 deletions HTML/Geometry/3 Dimensional Euclidean Geometry.html
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>3 Dimensional Euclidean Geometry</title>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
processEscapes: true
}
});
</script>
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script
type="text/javascript"
id="MathJax-script"
async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"
></script>
</head>

<body>
<p class="paragraph">
In physics and mathematics, a sequence of n numbers can be understood as a
location in n-dimensional space. When n = 3, the set of all such locations
is called <b>Three-dimensional Euclidean</b> space
</p>
<figure>
<img
style="width: 320px; height: 350px;"
src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/83/Coord_planes_color.svg/600px-Coord_planes_color.svg.png"
/>
<figcaption>
A representation of a three-dimensional Cartesian coordinate system with
the x-axis pointing towards the observer.
</figcaption>
</figure>
<h2 class="subHeader">
Coordinate systems
</h2>
<p class="paragraph">
Cartesian geometry describes every point in three-dimensional space by
means of three coordinates.Three coordinate axes are given, each
perpendicular to the other two at the origin, the point at which they
cross.They are usually labeled x, y, and z. Relative to these axes, the
position of any point in three-dimensional space is given by an ordered
triple of real numbers, each number giving the distance of that point from
the origin measured along the given axis, which is equal to the distance
of that point from the plane determined by the other two axes
</p>
<div
style="
display: flex;
flex-direction: row;
justify-content: space-between;
flex-wrap: wrap;
width: 100%;
"
>
<figure style="width: 45%;">
<img
src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/64/Coord_XYZ.svg/240px-Coord_XYZ.svg.png"
/>
<figcaption>
Cartesian coordinate system
</figcaption>
</figure>
<figure style="width: 45%;">
<img
src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Cylindrical_Coordinates.svg/240px-Cylindrical_Coordinates.svg.png"
/>
<figcaption>
Cylindrical coordinate system
</figcaption>
</figure>
<figure style="width: 45%;">
<img
src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Spherical_Coordinates_%28Colatitude%2C_Longitude%29.svg/240px-Spherical_Coordinates_%28Colatitude%2C_Longitude%29.svg.png"
/>
<figcaption>
Spherical coordinate system
</figcaption>
</figure>
</div>
<h2 class="subHeader">
Lines and planes
</h2>
<p class="paragraph">
Two distinct points always determine a (straight) line. Three distinct
points are either collinear or determine a unique plane. On the other
hand, four distinct points can either be collinear, coplanar, or determine
the entire space.
</p>
<p class="paragraph">
Two distinct lines can either intersect, be parallel or be skew. Two
parallel lines, or two intersecting lines, lie in a unique plane, so skew
lines are lines that do not meet and do not lie in a common plane.
</p>
<div class="theorem">
<p class="paragraph">
Two distinct planes can either meet in a common line or are parallel
(i.e., do not meet). Three distinct planes, no pair of which are
parallel, can either meet in a common line, meet in a unique common
point, or have no point in common.<br /><br />
In the last case, the three lines of intersection of each pair of planes
are mutually parallel. A line can lie in a given plane, intersect that
plane in a unique point, or be parallel to the plane. In the last case,
there will be lines in the plane that are parallel to the given line.
</p>
<p class="paragraph">
A hyperplane is a subspace of one dimension less than the dimension of
the full space. The hyperplanes of a three-dimensional space are the
two-dimensional subspaces, that is, the planes.<br /><br />
In terms of Cartesian coordinates, the points of a hyperplane satisfy a
single linear equation, so planes in this 3-space are described by
linear equations. A line can be described by a pair of independent
linear equations—each representing a plane having this line as a common
intersection.
</p>
</div>
<h2 class="subHeader">
Spheres and balls
</h2>
<p class="paragraph">
A sphere in 3-space (also called a 2-sphere because it is a 2-dimensional
object) consists of the set of all points in 3-space at a fixed distance r
from a central point P. The solid enclosed by the sphere is called a ball
(or, more precisely a 3-ball). The volume of the ball is given by:
<br /><br />
\(V = \frac{4}{3}\pi r^{3}.\)
</p>
<figure style="height: 320px;">
<img
style="width: 320px; height: 320px;"
src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/440px-Sphere_wireframe_10deg_6r.svg.png"
/>
</figure>
<div class="summary">
<h3>Dot product, angle, and length</h3>
<p class="paragraph">
The dot product of two vectors \(A = [A1, A2, A3]\) and \(B = [B1, B2,
B3]\) is defined as : <br /><br />
\({\displaystyle \mathbf {A} \cdot \mathbf {B} }\)
\(=A_{1}B_{1}+A_{2}B_{2}+A_{3}B_{3}.\)
</p>
<p class="paragraph">
The magnitude of a vector \(A\) is denoted by \(||A||\). The dot product
of a vector \(A = [A1, A2, A3]\) with itself is <br /><br />
\({\displaystyle \mathbf {A} \cdot \mathbf {A} =}\) \(\|\mathbf {A}
\|^{2}=A_{1}^{2}+A_{2}^{2}+A_{3}^{2},\) <br />
which gives \({\displaystyle \|\mathbf {A} \|={\sqrt {\mathbf {A} \cdot
\mathbf {A} }}=}\) \({\sqrt {A_{1}^{2}+A_{2}^{2}+A_{3}^{2}}}\)
</p>
<p class="paragraph">
Without reference to the components of the vectors, the dot product of
two non-zero Euclidean vectors \(A \) and \( B\) is given by
<br /><br />
\(\mathbf {A} \cdot \mathbf {B} =\|\mathbf {A} \|\,\|\mathbf {B} \|\cos
\theta ,\) <br /><br />where \(θ\) is the angle between \(A\) and \(B\).
</p>
</div>
</body>
<style>
body {
padding: 20px;
background-color: white;
margin: 0px;
font-family: sans-serif;
}

figcaption {
color: black;
}

h1,
h2,
h3,
h4 {
color: black;
}

.ul {
color: black;
}

.ul > li {
margin-bottom: 10px;
}

.header {
text-align: center;
color: rgb(180, 9, 152);
margin-bottom: 20px;
}

.subHeader {
font-size: 20px;
font-weight: bold;
text-align: left;
color: indigo;
}

.paragraph {
color: black;
margin-bottom: 10px;
}

.logGraph {
height: 250px;
width: 100%;
max-width: 450px;
}

figure {
margin: 30px 0px;
}

figcaption {
color: gray;
font-size: 13px;
text-align: center;
}

.note {
width: 90%;
max-height: 30vh;
border: 0.5px solid rgb(224, 224, 224);
overflow: scroll;
border-radius: 5px;
background: #fff;
flex-direction: column;
justify-content: flex-start;
align-items: flex-start;
box-shadow: 0 1px 1px rgba(0, 0, 0, 0.15), 0 10px 0 -5px #eee,
0 10px 1px -4px rgba(0, 0, 0, 0.15), 0 20px 0 -10px #eee,
0 20px 1px -9px rgba(0, 0, 0, 0.15);

padding: 10px;
}

.note-list {
width: 100%;
}

.notes {
margin: 0px;
padding-bottom: 8px;
color: rgb(17, 17, 248);
}

::-webkit-scrollbar {
width: 6px;
height: 6px;
}

.summary {
background-color: #58427c;
background-image: linear-gradient(316deg, #58427c 0%, #746cc0 74%);
padding: 15px;
margin: 25px 0px;
border-radius: 6px;
border-left: 6px solid #fd02be;
}

::-webkit-scrollbar-thumb {
border-radius: 4px;
-webkit-box-shadow: inset 0 0 3px rgba(0, 0, 0, 0.5);
}

.theorem {
width: 90%;
display: block;
border: 1px solid rgb(245, 214, 131);
background-color: rgb(245, 214, 131);
padding: 10px;
border-radius: 5px;
margin: 20px 0px;
color: black;
border-left: 5px solid red;
}

.result {
font-size: 16px;
font-weight: bold;
color: rgb(32, 0, 75);
}
</style>
</html>
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