Use mathematical notation in README.md

Author: alandefreitas

README.md

@@ -493,7 +493,7 @@ More examples:
 [![example_pareto_2](docs/examples/discrete_data/pareto/pareto_2_thumb.png)](examples/discrete_data/pareto/pareto_2.cpp)  [![example_pareto_3](docs/examples/discrete_data/pareto/pareto_3_thumb.png)](examples/discrete_data/pareto/pareto_3.cpp) [![example_pareto_4](docs/examples/discrete_data/pareto/pareto_4_thumb.png)](examples/discrete_data/pareto/pareto_4.cpp)
 </details>
 
-Pareto Charts are a type of chart that uses both $y$ axes. The $y_1$ axis is used to represent bars with the data values in descending order. The $y_2$ axis is used to represent the cumulative distribution function of the data in the $y_1$ axis. By default, a Pareto Chart includes up to 10 items or as many items as needed to represent 95% of the cumulative distribution.
+Pareto Charts are a type of chart that uses both <img src="https://render.githubusercontent.com/render/math?math=y"> axes. The <img src="https://render.githubusercontent.com/render/math?math=y_1"> axis is used to represent bars with the data values in descending order. The <img src="https://render.githubusercontent.com/render/math?math=y_2"> axis is used to represent the cumulative distribution function of the data in the <img src="https://render.githubusercontent.com/render/math?math=y_1"> axis. By default, a Pareto Chart includes up to 10 items or as many items as needed to represent 95% of the cumulative distribution.
 
 If you need Pareto *fronts* rather than Pareto *charts*, we refer to [Scatter Plots](#scatter-plot) for two-dimensional fronts, [Plot matrices](#plot-matrix) for three-dimensional fronts, or [Parallel Coordinate Plots](#parallel-coordinates) for many-objective fronts. These plot subcategories are described in Section [Data Distribution](#data-distribution). If you also need a tool to calculate these fronts efficiently, we refer to the [Pareto Front Library](https://github.com/alandefreitas/pareto-front).
 
@@ -551,15 +551,15 @@ More examples:
 
 For the first geography plot, **Matplot++** calls `geoplot()`, which creates a filled polygon with the world map. This first plot receives the tag `"map"` so that subsequent geography plots recognize there is no need to recreate this world map.
 
-The data for the world map comes from Natural Earth. They provide data at 1:10m, 1:50m, and 1:110m scales. The `geoplot` function will initially use the data at the 1:110m scales. The `geolimits` function can be used to update the axis limits for geography plots. The difference between the usual functions for adjusting axis limits (`xlim` and `ylim`) and `geolimits` is that the latter will also update the map resolution according to the new limits for the $x$ and $y$ axis.
+The data for the world map comes from Natural Earth. They provide data at 1:10m, 1:50m, and 1:110m scales. The `geoplot` function will initially use the data at the 1:110m scales. The `geolimits` function can be used to update the axis limits for geography plots. The difference between the usual functions for adjusting axis limits (`xlim` and `ylim`) and `geolimits` is that the latter will also update the map resolution according to the new limits for the <img src="https://render.githubusercontent.com/render/math?math=x"> and <img src="https://render.githubusercontent.com/render/math?math=y"> axis.
 
 The `geolimits` function will query the `figure` size and, depending on the new limits for the axes, update the map to the 1:10m, or 1:50m scales if needed. Because it would be very inefficient to render the whole world map at a 1:10m or 1:50m scale only to display a region of this map, the `geolimits` function also crops the data pertinent to the new region being displayed.
 
 Note that this does not only involve removing data points outside the new limits but it also needs to create new data points on the correct borders to create new polygons coherent with the map entry points in the region. For this reason, the algorithm needs to track all submaps represented as closed polygons in the original world map. If submaps are completely inside or outside the new ranges, we can respectively include or dismiss the data points. However, if the submap is only partially inside the new limits, to generate the correct borders for the polygons, we need to track all points outside the limits to classify the directions of these points outside the limits. We do that by only including points that change quadrants around the new limits so that the map entry points create polygons that look like they would if the complete world map were still being rendered outside these new limits.
 
 If the you are not interested in geographic plots, the build script includes an option to remove the high-resolution maps at 1:10m and 1:50m scales from the library. In this case, the library will always use the map at a 1:110m scale no matter the axis limits.
 
-The function `world_cities` returns a list of major world cities. Its parameters define the minimum distances between cities in the $x$ and $y$ axes. The `greedy_tsp` function is a naive greedy algorithm to find a route between these cities as a Traveling Salesman Problem (TSP). We use the `geoplot` function to draw this route. Note that we use method chaining to define some further plot properties. Finally, the `text` function includes the city names in the map.
+The function `world_cities` returns a list of major world cities. Its parameters define the minimum distances between cities in the <img src="https://render.githubusercontent.com/render/math?math=x"> and <img src="https://render.githubusercontent.com/render/math?math=y"> axes. The `greedy_tsp` function is a naive greedy algorithm to find a route between these cities as a Traveling Salesman Problem (TSP). We use the `geoplot` function to draw this route. Note that we use method chaining to define some further plot properties. Finally, the `text` function includes the city names in the map.
 
 #### Geoscatter Plot
 
@@ -625,9 +625,9 @@ More examples:
 [![example_polarplot_2](docs/examples/polar_plots/polarplot/polarplot_2_thumb.png)](examples/polar_plots/polarplot/polarplot_2.cpp)  [![example_polarplot_3](docs/examples/polar_plots/polarplot/polarplot_3_thumb.png)](examples/polar_plots/polarplot/polarplot_3.cpp)  [![example_polarplot_4](docs/examples/polar_plots/polarplot/polarplot_4_thumb.png)](examples/polar_plots/polarplot/polarplot_4.cpp)  [![example_polarplot_5](docs/examples/polar_plots/polarplot/polarplot_5_thumb.png)](examples/polar_plots/polarplot/polarplot_5.cpp)  [![example_polarplot_6](docs/examples/polar_plots/polarplot/polarplot_6_thumb.png)](examples/polar_plots/polarplot/polarplot_6.cpp)  [![example_polarplot_7](docs/examples/polar_plots/polarplot/polarplot_7_thumb.png)](examples/polar_plots/polarplot/polarplot_7.cpp)  [![example_polarplot_8](docs/examples/polar_plots/polarplot/polarplot_8_thumb.png)](examples/polar_plots/polarplot/polarplot_8.cpp)
 </details>
 
-By emplacing a polar plot in the `axes`, the `axes` move to a polar mode, where we use the $r$ and $t$ axis instead of the $x$ and $y$ axis.
+By emplacing a polar plot in the `axes`, the `axes` move to a polar mode, where we use the <img src="https://render.githubusercontent.com/render/math?math=r"> and <img src="https://render.githubusercontent.com/render/math?math=t"> axis instead of the <img src="https://render.githubusercontent.com/render/math?math=x"> and <img src="https://render.githubusercontent.com/render/math?math=y"> axis.
 
-From the backend point of view, these axes are an abstraction to the user. The data points in the $r$ and $t$ axis are drawn by converting the positions from the polar coordinates $r$ and $t$ to the Cartesian coordinates $x$ and $y$ with the relationships $x=r \cos{t}$ and $y=r \sin{t}$.
+From the backend point of view, these axes are an abstraction to the user. The data points in the <img src="https://render.githubusercontent.com/render/math?math=r"> and <img src="https://render.githubusercontent.com/render/math?math=t"> axis are drawn by converting the positions from the polar coordinates <img src="https://render.githubusercontent.com/render/math?math=r"> and <img src="https://render.githubusercontent.com/render/math?math=t"> to the Cartesian coordinates <img src="https://render.githubusercontent.com/render/math?math=x"> and <img src="https://render.githubusercontent.com/render/math?math=y"> with the relationships <img src="https://render.githubusercontent.com/render/math?math=x=r\cos{t}"> and <img src="https://render.githubusercontent.com/render/math?math=y=r\sin{t}">.
 
 Aside from this conversion, these plot subcategories are analogous to line plots, scatter plots, histograms, quiver plots, and line functions. 
 
@@ -719,13 +719,13 @@ More examples:
   
 All these subcategories depend on the `contours` type. They also depend on lazy evaluation for generating the contour lines. When the function `draw` is called in the `contours` class, it preprocesses all contour lines for a three-dimensional function.
 
-Although it is relatively simple to show a heatmap with the values for the $z$-axis, calculating contour lines relative to the $z$-axis is more complex than it might seem at first. We provide the function `contourc` for calculating contour lines. This function uses an adaptation of the algorithm adopted by Matplotlib.
+Although it is relatively simple to show a heatmap with the values for the <img src="https://render.githubusercontent.com/render/math?math=z">-axis, calculating contour lines relative to the <img src="https://render.githubusercontent.com/render/math?math=yz">-axis is more complex than it might seem at first. We provide the function `contourc` for calculating contour lines. This function uses an adaptation of the algorithm adopted by Matplotlib.
 
-The algorithm creates a quad grid defined by the $x$ and $y$ values. It uses this grid to infer a contour line passing through positions with the same $z$ value. The algorithm sweeps through the grid twice to generate these lines. The first sweep looks for lines that start on the boundaries. The second sweep looks for interior closed loops.
+The algorithm creates a quad grid defined by the <img src="https://render.githubusercontent.com/render/math?math=x"> and <img src="https://render.githubusercontent.com/render/math?math=y"> values. It uses this grid to infer a contour line passing through positions with the same <img src="https://render.githubusercontent.com/render/math?math=z"> value. The algorithm sweeps through the grid twice to generate these lines. The first sweep looks for lines that start on the boundaries. The second sweep looks for interior closed loops.
 
 Filled contours are closed polygons for pairs of contour levels. Some polygons for filled contours might be holes inside other polygons. The algorithm needs to keep track of these relationships so that we can render the polygons in their accurate order. To avoid an extra step that identifies this relationship between the polygons, the sweeping algorithm already identifies which polygons are holes for each level.
 
-Once we find the quads with the contour line, the line is generated by interpolating the $z$ values around that quad.
+Once we find the quads with the contour line, the line is generated by interpolating the <img src="https://render.githubusercontent.com/render/math?math=z"> values around that quad.
   
 #### Filled Contour
 
@@ -759,7 +759,7 @@ More examples:
 [![example_fcontour_2](docs/examples/contour_plots/fcontour/fcontour_2_thumb.png)](examples/contour_plots/fcontour/fcontour_2.cpp)  [![example_fcontour_3](docs/examples/contour_plots/fcontour/fcontour_3_thumb.png)](examples/contour_plots/fcontour/fcontour_3.cpp)  [![example_fcontour_4](docs/examples/contour_plots/fcontour/fcontour_4_thumb.png)](examples/contour_plots/fcontour/fcontour_4.cpp)  [![example_fcontour_5](docs/examples/contour_plots/fcontour/fcontour_5_thumb.png)](examples/contour_plots/fcontour/fcontour_5.cpp)  [![example_fcontour_6](docs/examples/contour_plots/fcontour/fcontour_6_thumb.png)](examples/contour_plots/fcontour/fcontour_6.cpp)  [![example_fcontour_7](docs/examples/contour_plots/fcontour/fcontour_7_thumb.png)](examples/contour_plots/fcontour/fcontour_7.cpp)  [![example_fcontour_8](docs/examples/contour_plots/fcontour/fcontour_8_thumb.png)](examples/contour_plots/fcontour/fcontour_8.cpp)  [![example_fcontour_9](docs/examples/contour_plots/fcontour/fcontour_9_thumb.png)](examples/contour_plots/fcontour/fcontour_9.cpp)  [![example_fcontour_10](docs/examples/contour_plots/fcontour/fcontour_10_thumb.png)](examples/contour_plots/fcontour/fcontour_10.cpp)  [![example_fcontour_11](docs/examples/contour_plots/fcontour/fcontour_11_thumb.png)](examples/contour_plots/fcontour/fcontour_11.cpp)
 </details>  
 
-By default, the function `fcontour` will generate 9 contour lines from a lambda function. The functions `contour` and `contourf`, on the other hand, plot contour lines and filled contour lines from a grid of data points for $x$, $y$, and $z$.
+By default, the function `fcontour` will generate 9 contour lines from a lambda function. The functions `contour` and `contourf`, on the other hand, plot contour lines and filled contour lines from a grid of data points for <img src="https://render.githubusercontent.com/render/math?math=x">, <img src="https://render.githubusercontent.com/render/math?math=y">, and <img src="https://render.githubusercontent.com/render/math?math=z">.
 
 ### Vector Fields
 
@@ -781,7 +781,7 @@ More examples:
 [![example_quiver_2](docs/examples/vector_fields/quiver/quiver_2_thumb.png)](examples/vector_fields/quiver/quiver_2.cpp)  [![example_quiver_3](docs/examples/vector_fields/quiver/quiver_3_thumb.png)](examples/vector_fields/quiver/quiver_3.cpp)  [![example_quiver_4](docs/examples/vector_fields/quiver/quiver_4_thumb.png)](examples/vector_fields/quiver/quiver_4.cpp)
 </details>
 
-All these subcategories depend on the `vectors` object type. In a two-dimensional plot, for each value of $x$ and $y$ with the position of a vector, it also requires the value of $u$ and $v$ indicating its direction and magnitude. In a three-dimensional plot, the direction and magnitude are defined by $u$, $v$, and $w$.
+All these subcategories depend on the `vectors` object type. In a two-dimensional plot, for each value of <img src="https://render.githubusercontent.com/render/math?math=x"> and <img src="https://render.githubusercontent.com/render/math?math=y"> with the position of a vector, it also requires the value of <img src="https://render.githubusercontent.com/render/math?math=u"> and <img src="https://render.githubusercontent.com/render/math?math=v"> indicating its direction and magnitude. In a three-dimensional plot, the direction and magnitude are defined by <img src="https://render.githubusercontent.com/render/math?math=u">, <img src="https://render.githubusercontent.com/render/math?math=v">, and <img src="https://render.githubusercontent.com/render/math?math=w">.
 
 
 A quiver plot (or velocity plot) shows a grid of vectors whose direction and magnitude are scaled to prevent the overlap between vectors in subsequent quads. 
@@ -1128,7 +1128,7 @@ More examples:
 [![example_rectangle_2](docs/examples/annotations/rectangle/rectangle_2_thumb.png)](examples/annotations/rectangle/rectangle_2.cpp)  [![example_rectangle_3](docs/examples/annotations/rectangle/rectangle_3_thumb.png)](examples/annotations/rectangle/rectangle_3.cpp)  [![example_rectangle_4](docs/examples/annotations/rectangle/rectangle_4_thumb.png)](examples/annotations/rectangle/rectangle_4.cpp)  [![example_rectangle_5](docs/examples/annotations/rectangle/rectangle_5_thumb.png)](examples/annotations/rectangle/rectangle_5.cpp)
 </details>  
 
-The rectangle object can have a border curvature from $0$ to $1$. We can also annotate with text, arrows, polygons, and lines.
+The rectangle object can have a border curvature from <img src="https://render.githubusercontent.com/render/math?math=0"> to <img src="https://render.githubusercontent.com/render/math?math=1">. We can also annotate with text, arrows, polygons, and lines.
 
 #### Filled Polygon