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Refine math content layout and enhance readability: Update math-chapter-patterns.md to emphasize the use of aligned multi-line KaTeX for chained calculations. Revise Pythagorean theorem examples in _index.md and core.html to follow the new formatting guidelines. Update SKILL.md to reinforce the preference for aligned equations across all subjects. Modify feed.xml and sitemap.xml to reflect recent updates and new chapter additions for improved navigation.

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Hananoshika Yomaru 2026-05-21 22:22:44 -07:00
parent 2ca490ff81
commit 945bcddde0
6 changed files with 73 additions and 45 deletions
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34
content/math/pythagoras-theorem/_index.md
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@ -54,31 +54,37 @@ strand = "Measures, Shape & Space"
<h3 id="find-hypotenuse" class="book-prose__heading">Find the hypotenuse</h3>
<p><strong>Example.</strong> If \(a=9\) and \(b=12\), find \(c\).</p>
<p class="book-formula">\[
c = \sqrt{9^2 + 12^2}
= \sqrt{81 + 144}
= \sqrt{225}
= 15
\begin{aligned}
c &= \sqrt{9^2 + 12^2} \\
&= \sqrt{81 + 144} \\
&= \sqrt{225} \\
&= 15
\end{aligned}
\]</p>
<p>The third side is 15 ft.</p>
<h3 id="find-leg" class="book-prose__heading">Find a missing leg</h3>
<p><strong>Example.</strong> If \(c=13\) and \(a=5\), find \(b\).</p>
<p class="book-formula">\[
b = \sqrt{c^2 - a^2}
= \sqrt{13^2 - 5^2}
= \sqrt{169 - 25}
= \sqrt{144}
= 12
\begin{aligned}
b &= \sqrt{c^2 - a^2} \\
&= \sqrt{13^2 - 5^2} \\
&= \sqrt{169 - 25} \\
&= \sqrt{144} \\
&= 12
\end{aligned}
\]</p>
<h3 id="radical-form" class="book-prose__heading">Leave answers in simplest radical form</h3>
<p><strong>Example.</strong> If \(c=10\) and \(a=2\), find \(b\).</p>
<p class="book-formula">\[
b = \sqrt{10^2 - 2^2}
= \sqrt{100 - 4}
= \sqrt{96}
= \sqrt{16 \cdot 6}
= 4\sqrt{6}
\begin{aligned}
b &= \sqrt{10^2 - 2^2} \\
&= \sqrt{100 - 4} \\
&= \sqrt{96} \\
&= \sqrt{16 \cdot 6} \\
&= 4\sqrt{6}
\end{aligned}
\]</p>
<h2 id="common-pitfall" class="book-prose__heading">Common pitfall</h2>

34
content/math/pythagoras-theorem/core.html
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@ -43,31 +43,37 @@
<h3 id="find-hypotenuse" class="book-prose__heading">Find the hypotenuse</h3>
<p><strong>Example.</strong> If \(a=9\) and \(b=12\), find \(c\).</p>
<p class="book-formula">\[
c = \sqrt{9^2 + 12^2}
= \sqrt{81 + 144}
= \sqrt{225}
= 15
\begin{aligned}
c &= \sqrt{9^2 + 12^2} \\
&= \sqrt{81 + 144} \\
&= \sqrt{225} \\
&= 15
\end{aligned}
\]</p>
<p>The third side is 15 ft.</p>
<h3 id="find-leg" class="book-prose__heading">Find a missing leg</h3>
<p><strong>Example.</strong> If \(c=13\) and \(a=5\), find \(b\).</p>
<p class="book-formula">\[
b = \sqrt{c^2 - a^2}
= \sqrt{13^2 - 5^2}
= \sqrt{169 - 25}
= \sqrt{144}
= 12
\begin{aligned}
b &= \sqrt{c^2 - a^2} \\
&= \sqrt{13^2 - 5^2} \\
&= \sqrt{169 - 25} \\
&= \sqrt{144} \\
&= 12
\end{aligned}
\]</p>
<h3 id="radical-form" class="book-prose__heading">Leave answers in simplest radical form</h3>
<p><strong>Example.</strong> If \(c=10\) and \(a=2\), find \(b\).</p>
<p class="book-formula">\[
b = \sqrt{10^2 - 2^2}
= \sqrt{100 - 4}
= \sqrt{96}
= \sqrt{16 \cdot 6}
= 4\sqrt{6}
\begin{aligned}
b &= \sqrt{10^2 - 2^2} \\
&= \sqrt{100 - 4} \\
&= \sqrt{96} \\
&= \sqrt{16 \cdot 6} \\
&= 4\sqrt{6}
\end{aligned}
\]</p>
<h2 id="common-pitfall" class="book-prose__heading">Common pitfall</h2>