From 945bcddde0b081c41953c7445b995ed659ffc1a6 Mon Sep 17 00:00:00 2001 From: Hananoshika Yomaru Date: Thu, 21 May 2026 22:22:44 -0700 Subject: [PATCH] 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. --- .agents/skills/ofb/SKILL.md | 2 ++ .agents/skills/ofb/math-chapter-patterns.md | 14 +++++++++ content/math/pythagoras-theorem/_index.md | 34 ++++++++++++--------- content/math/pythagoras-theorem/core.html | 34 ++++++++++++--------- static/feed.xml | 30 +++++++++--------- static/sitemap.xml | 4 +-- 6 files changed, 73 insertions(+), 45 deletions(-) diff --git a/.agents/skills/ofb/SKILL.md b/.agents/skills/ofb/SKILL.md index f839c61..4ea0f34 100644 --- a/.agents/skills/ofb/SKILL.md +++ b/.agents/skills/ofb/SKILL.md @@ -135,6 +135,8 @@ Live chapters live under `content/{subject}/{slug}/`: **Math checkpoints / dots:** follow [math-chapter-patterns.md](math-chapter-patterns.md); shared dot classes in `content/math/subject.scss`. +**Math equation layout (all subjects):** for chained calculations, **always prefer multi-line KaTeX** and **always align at the equal sign** using `aligned` (e.g. `\begin{aligned} ... &= ... \\ ... \end{aligned}`). Do not write long one-line chains; aligned multi-line steps are the default for readability and mobile layout. + ### Interactive demo technology choices Interactive demos can use different technologies based on the learning goal and interaction type: diff --git a/.agents/skills/ofb/math-chapter-patterns.md b/.agents/skills/ofb/math-chapter-patterns.md index 4bb40a1..f77b3f0 100644 --- a/.agents/skills/ofb/math-chapter-patterns.md +++ b/.agents/skills/ofb/math-chapter-patterns.md @@ -7,6 +7,20 @@ Use these conventions in `core.html` and `supplement.html` so every math chapter - Wrapper: `
` - Section titles: `

` - In-chapter links: plain `` inside `.book-prose` (theme styles them) +- For chained calculations, prefer aligned multi-line KaTeX: + +```html +

\[ + \begin{aligned} + b &= \sqrt{c^2-a^2} \\ + &= \sqrt{13^2-5^2} \\ + &= \sqrt{144} \\ + &= 12 + \end{aligned} +\]

+``` + +This keeps equal signs aligned and avoids long single-line equations on mobile. ## Checkpoints (required shape) diff --git a/content/math/pythagoras-theorem/_index.md b/content/math/pythagoras-theorem/_index.md index d59f9f2..ae3410e 100644 --- a/content/math/pythagoras-theorem/_index.md +++ b/content/math/pythagoras-theorem/_index.md @@ -54,31 +54,37 @@ strand = "Measures, Shape & Space"

Find the hypotenuse

Example. If \(a=9\) and \(b=12\), find \(c\).

\[ - c = \sqrt{9^2 + 12^2} - = \sqrt{81 + 144} - = \sqrt{225} - = 15 + \begin{aligned} + c &= \sqrt{9^2 + 12^2} \\ + &= \sqrt{81 + 144} \\ + &= \sqrt{225} \\ + &= 15 + \end{aligned} \]

The third side is 15 ft.

Find a missing leg

Example. If \(c=13\) and \(a=5\), find \(b\).

\[ - b = \sqrt{c^2 - a^2} - = \sqrt{13^2 - 5^2} - = \sqrt{169 - 25} - = \sqrt{144} - = 12 + \begin{aligned} + b &= \sqrt{c^2 - a^2} \\ + &= \sqrt{13^2 - 5^2} \\ + &= \sqrt{169 - 25} \\ + &= \sqrt{144} \\ + &= 12 + \end{aligned} \]

Leave answers in simplest radical form

Example. If \(c=10\) and \(a=2\), find \(b\).

\[ - b = \sqrt{10^2 - 2^2} - = \sqrt{100 - 4} - = \sqrt{96} - = \sqrt{16 \cdot 6} - = 4\sqrt{6} + \begin{aligned} + b &= \sqrt{10^2 - 2^2} \\ + &= \sqrt{100 - 4} \\ + &= \sqrt{96} \\ + &= \sqrt{16 \cdot 6} \\ + &= 4\sqrt{6} + \end{aligned} \]

Common pitfall

diff --git a/content/math/pythagoras-theorem/core.html b/content/math/pythagoras-theorem/core.html index e9975f2..9101256 100644 --- a/content/math/pythagoras-theorem/core.html +++ b/content/math/pythagoras-theorem/core.html @@ -43,31 +43,37 @@

Find the hypotenuse

Example. If \(a=9\) and \(b=12\), find \(c\).

\[ - c = \sqrt{9^2 + 12^2} - = \sqrt{81 + 144} - = \sqrt{225} - = 15 + \begin{aligned} + c &= \sqrt{9^2 + 12^2} \\ + &= \sqrt{81 + 144} \\ + &= \sqrt{225} \\ + &= 15 + \end{aligned} \]

The third side is 15 ft.

Find a missing leg

Example. If \(c=13\) and \(a=5\), find \(b\).

\[ - b = \sqrt{c^2 - a^2} - = \sqrt{13^2 - 5^2} - = \sqrt{169 - 25} - = \sqrt{144} - = 12 + \begin{aligned} + b &= \sqrt{c^2 - a^2} \\ + &= \sqrt{13^2 - 5^2} \\ + &= \sqrt{169 - 25} \\ + &= \sqrt{144} \\ + &= 12 + \end{aligned} \]

Leave answers in simplest radical form

Example. If \(c=10\) and \(a=2\), find \(b\).

\[ - b = \sqrt{10^2 - 2^2} - = \sqrt{100 - 4} - = \sqrt{96} - = \sqrt{16 \cdot 6} - = 4\sqrt{6} + \begin{aligned} + b &= \sqrt{10^2 - 2^2} \\ + &= \sqrt{100 - 4} \\ + &= \sqrt{96} \\ + &= \sqrt{16 \cdot 6} \\ + &= 4\sqrt{6} + \end{aligned} \]

Common pitfall

diff --git a/static/feed.xml b/static/feed.xml index b918d7b..1537bde 100644 --- a/static/feed.xml +++ b/static/feed.xml @@ -4,7 +4,21 @@ Open Free Books https://openfreebooks.org/ Recent updates to Open Free Books pages and live chapters. - Thu, 21 May 2026 23:42:19 GMT + Fri, 22 May 2026 05:18:34 GMT + + Coordinate geometry foundations + https://openfreebooks.org/math/coordinate-geometry-foundations/ + https://openfreebooks.org/math/coordinate-geometry-foundations/ + Fri, 22 May 2026 05:18:34 GMT + Plot points, find distances and midpoints, and work with slopes of lines in the Cartesian plane. + + + Pythagoras' theorem + https://openfreebooks.org/math/pythagoras-theorem/ + https://openfreebooks.org/math/pythagoras-theorem/ + Fri, 22 May 2026 05:18:34 GMT + Use Pythagoras' theorem and its converse in 2D problems and coordinate settings. + Basic math notation https://openfreebooks.org/math/basic-math-notation/ @@ -89,13 +103,6 @@ Thu, 21 May 2026 16:54:30 GMT Find equations of circles, tangents, and intersections using coordinate methods and distance. - - Coordinate geometry foundations - https://openfreebooks.org/math/coordinate-geometry-foundations/ - https://openfreebooks.org/math/coordinate-geometry-foundations/ - Thu, 21 May 2026 16:54:30 GMT - Plot points, find distances and midpoints, and work with slopes of lines in the Cartesian plane. - Deductive geometry https://openfreebooks.org/math/deductive-geometry/ @@ -145,13 +152,6 @@ Thu, 21 May 2026 16:54:30 GMT Count outcomes with permutations and combinations, then compute probabilities in finite sample spaces. - - Pythagoras' theorem - https://openfreebooks.org/math/pythagoras-theorem/ - https://openfreebooks.org/math/pythagoras-theorem/ - Thu, 21 May 2026 16:54:30 GMT - Use Pythagoras' theorem and its converse in 2D problems and coordinate settings. - Charts & averages https://openfreebooks.org/math/statistical-charts-averages/ diff --git a/static/sitemap.xml b/static/sitemap.xml index 40fa4f5..23533f0 100644 --- a/static/sitemap.xml +++ b/static/sitemap.xml @@ -62,7 +62,7 @@ https://openfreebooks.org/math/coordinate-geometry-foundations/ - 2026-05-21T16:54:30.000Z + 2026-05-22T05:18:34.000Z https://openfreebooks.org/math/counting-and-numbers/ @@ -146,7 +146,7 @@ https://openfreebooks.org/math/pythagoras-theorem/ - 2026-05-21T16:54:30.000Z + 2026-05-22T05:18:34.000Z https://openfreebooks.org/math/quadratic-equations/