minor edit

Author: ShenCiao

docs/Proportional-Interval-Stamp/Proportional-Interval-Stamp.mdx

@@ -122,7 +122,7 @@ Meanwhile, the interval is always proportional to the radius.
 
 You might be confused by the statement "always proportional to the radius."
 Though it's intuitively correct as the animation below shows.
-I'll soon explain it with precise mathematical formulas, so don't worry about it too much for now.
+I'll soon explain it mathematically, so don't worry about it too much for now.
 
 ![interval animation](./interval-ratio-animation.gif)
 <figcaption>
@@ -193,7 +193,7 @@ $$
 \tag{1} n(x) = -\frac{1}{\eta \cos\theta} \ln(r_0 - \cos\theta x) \bigg|_0^x = -\frac{1}{\eta \cos\theta} \ln (1 - \frac{\cos\theta x}{r_0})
 $$
 
-Exchange the dependent and independent variable in formula (1) and get:
+Exchange the dependent and independent variable in equation (1) and get:
 
 $$
 \tag{2} x(n) = \frac{r_0}{\cos\theta}(1 - e^{-\eta\cos\theta n})
@@ -205,7 +205,7 @@ $$
 \tag{3} n_L = \frac{L}{\eta (r_0-r_1)}\ln \frac{r_0}{r_1}
 $$
 
-We will soon use the formula (1)(2)(3) in our code.
+We will soon use the equation (1)(2)(3) in our code.
 
 How do we place footprints?
 Imagine a point starts from the first vertex and moves along the polyline.
@@ -220,7 +220,7 @@ Label the two roots with $x_1$ and $x_2$.
 
 To calculate the nearest stamp point (the black dot in the figure) between $x_1$ and $x_2$,
 we need to compute the number of stamps from $x_1$ to the polyline's first vertex, which is also called stamp index (or stamp count) at $x_1$.
-According to formula (1), on the current edge, the number of stamps from vertex0 to $x_1$ is $n(x_1)$.
+According to equation (1), on the current edge, the number of stamps from vertex0 to $x_1$ is $n(x_1)$.
 Label the stamp index of vertex0 as $n_{s_0}$, and label vertex1's as $n_{s_1}$.
 (The symbol $s$ represents the arc from the first to current vertex).
 
@@ -230,10 +230,10 @@ Therefore, the stamp index of $x_1$ is $n_{s_0} + n(x_1)$.
 Because we place footprints at the points with integer stamp index,
 the ceiling of $n_{s_0} + n(x_1)$ is the nearest stamp's index,
 denoted as $n_\mathrm{nearest} = \lceil n_{s_0} + n(x_1) \rceil$.
-Replace it into the formula (2) to get its position $x_{\mathrm{nearest}} = x(\lceil n_{s_0} + n(x_1) \rceil)$,
+Replace it into the equation (2) to get its position $x_{\mathrm{nearest}} = x(\lceil n_{s_0} + n(x_1) \rceil)$,
 and all other positions $x(n_\mathrm{nearest} + 1)$, $x(n_\mathrm{nearest} + 2) \dots$
 
-Additionally, to determine $n_{s_0}$ and $n_{s_1}$, we can compute the prefix sum of the $n_L$ in formula (3) over all edges.
+Additionally, to determine $n_{s_0}$ and $n_{s_1}$, we can compute the prefix sum of the $n_L$ in equation (3) over all edges.
 Put them into vertex data and pass them into fragment shader, exactly same as the value `length` in the Stamp section.
 
 ## Implementation
@@ -245,7 +245,7 @@ import Stroke from "./ProportionalStampStroke";
 
 **Zero division:**
 It's common for a stroke to have zero radii at their starting or ending vertices.
-When either $r_0$ or $r_1$ is zero, the value in formula (3) can approach infinity.
+When either $r_0$ or $r_1$ is zero, the value in equation (3) can approach infinity.
 This will bring numeric errors, which we surely want to avoid.
 A simple solution is to add a small number to the radii, as demoed in the code above.
 For a more rigorous approach, you can implement checks to prevent $r_0/r_1$ in the logarithm from becoming zero or excessively large.
@@ -277,7 +277,7 @@ $$
 $$
 
 **Proof:**
-Substitute formula (3) into $r(x) = r_0 - \cos\theta x$ to obtain $r(n) = r_0e^{-\eta\cos\theta n}$.
+Substitute equation (3) into $r(x) = r_0 - \cos\theta x$ to obtain $r(n) = r_0e^{-\eta\cos\theta n}$.
 The remainder of proof is straightforward.
 
 Note that these ratios are independent of $n$ or $x$,
@@ -320,7 +320,7 @@ This suggests that at any point in a given edge, the number of stamps that can c
 If we connect the points with the same $\lambda$, they form an isocolor line.
 
 **Proof:**
-With the formula (1), we can derive:
+With the equation (1), we can derive:
 
 $$
 n(x_2) - n(x_1) = \frac{1}{\eta \cos\theta}\ln \frac{r(x_1)}{r(x_2)}
@@ -376,5 +376,5 @@ If you are interested in more details about the solving process, check the drop-
 
   You verify the result after substituting $a, b, c$.
   Note that when $\lambda = 0$ or $\lambda = 1$, the $\triangle PQX_{1}$ and $\triangle PQX_{2}$ don't exist,
-  but the formula still works.
+  but the equations still works.
 </details>