$$
\Huge
\begin{align*}
x &= \text{erf atanh cos } t \\
y &= \text{erf atanh sin } t
\end{align*}
$$
flatter and smoother rounded corners · web components
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Derivatives exist at every point. Maybe want to show upper bound on derivatives.
$$
\Huge
\begin{align*}
\text{A function is flat at a point if} & \text{ every derivative goes to zero at that point:} \\
\forall\ {\rm n} \in \mathbb{N}\text{, } \lim_{t\to 0} f^ {\rm (n)}_ {t} &= 0 \\
\\
x(t) &= \text{erf atanh cos } t \\
x'_ {t} &= e^ {-{\rm atanh}^ {2} \cos t}\ g(t) \\
x''_ {t} &= e^ {-{\rm atanh}^ {2} \cos t}\ (g'_ {t} + g^ {2}(t)) \\
&\dots \\
x^ {\rm (n)}_ {t} &\propto e^ {-{\rm atanh}^ {2} \cos t} \\
\\
\text{The function is flat wherever} & \text{ the exponential term is equal to zero.} \\
\forall\ m \in \mathbb{N}\text{, } \lim_{t\ \to\ m \pi} e^ {-{\rm atanh}^ {2} \cos t} &= 0 \\
\text{So the function} & \text{ is periodically flat.} \\
\therefore\ x^ {\rm (n)}_ {t} (m \pi) &= 0 \\
\end{align*}
$$