forked from EduCraft/curriculum-project-hub
sjfhsjfh
6f46aa708a
Fixes the numbering bug (single pattern "一、" reused across levels → level-2
rendered "二、一、…"). display now takes a `config` dict; heading numbering uses
numbly per level — framework default ("{1:一}、","{1:1}.{2:1}","{1:1}.{2:1}.{3:1}")
→ 一、 / 1.1 / 1.1.1 — overridable via config.numbering.heading from the
engineering file (ADR-0009's file-resident override path, the layer whose absence
caused the bug). Verified: grep "二、一" = 0 across all smoke PDFs.
Adds @preview/numbly:0.1.0 (pure typst, zero transitive deps), VENDORED in-repo
at render/vendor/typst-packages/preview/numbly/0.1.0/ for network-free CI;
resolve via --package-cache-path render/vendor/typst-packages. parts contract +
student/teacher field visibility unchanged.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
84 lines
2.5 KiB
Typst
84 lines
2.5 KiB
Typst
// Shared hand-written sample lesson exercising all 4 kinds.
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// Content field values are plain content blocks — exactly what the Rust driver
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// would hand us via `include`.
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#let info = (
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title: "向量与几何 · 示例讲义",
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author: ("张老师", "李老师"),
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)
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#let parts = (
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// segment — with NESTED headings so per-level numbering is visible:
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// level-1 `=` should render `一、`, level-2 `==` should render `1.1`
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// (NOT the old buggy `二、一、`).
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(
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kind: "segment",
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textbook: [
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= 平面向量的数量积
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本节研究平面向量的基本运算。设 $arrow(a)$、$arrow(b)$ 为平面内两个向量，
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其数量积定义为 $arrow(a) dot arrow(b) = |arrow(a)| |arrow(b)| cos theta$，
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其中 $theta$ 为两向量的夹角。
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== 坐标表示
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在直角坐标系下，若 $arrow(a) = (x_1, y_1)$、$arrow(b) = (x_2, y_2)$，则
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$arrow(a) dot arrow(b) = x_1 x_2 + y_1 y_2$。
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== 几何意义
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数量积等于一个向量的模与另一向量在其方向上投影之积。
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],
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),
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// example WITH source
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(
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kind: "example",
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source: "2024 高考甲卷",
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problem: [
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已知 $arrow(a) = (1, 2)$，$arrow(b) = (3, -1)$，求 $arrow(a) dot arrow(b)$。
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],
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solution: [
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由坐标公式，$arrow(a) dot arrow(b) = 1 times 3 + 2 times (-1) = 3 - 2 = 1$。
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],
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),
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// example WITHOUT source
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(
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kind: "example",
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problem: [
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求向量 $arrow(a) = (3, 4)$ 的模长 $|arrow(a)|$。
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],
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solution: [
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$|arrow(a)| = sqrt(3^2 + 4^2) = sqrt(25) = 5$。
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],
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),
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// lemma WITH proof
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(
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kind: "lemma",
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stmt: [
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对任意向量 $arrow(a)$、$arrow(b)$，有 $|arrow(a) dot arrow(b)| <= |arrow(a)| |arrow(b)|$。
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],
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proof: [
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由数量积定义 $arrow(a) dot arrow(b) = |arrow(a)| |arrow(b)| cos theta$，
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又 $|cos theta| <= 1$，故 $|arrow(a) dot arrow(b)| = |arrow(a)| |arrow(b)| |cos theta| <= |arrow(a)| |arrow(b)|$。
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$qed$
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],
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),
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// lemma WITHOUT proof (proof key omitted entirely)
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(
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kind: "lemma",
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stmt: [
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两个非零向量垂直当且仅当其数量积为零，即 $arrow(a) perp arrow(b) <==> arrow(a) dot arrow(b) = 0$。
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],
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),
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// sop
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(
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kind: "sop",
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sop: [
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求两向量夹角的标准步骤：
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+ 计算数量积 $arrow(a) dot arrow(b)$；
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+ 分别计算模长 $|arrow(a)|$、$|arrow(b)|$；
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+ 代入 $cos theta = (arrow(a) dot arrow(b)) / (|arrow(a)| |arrow(b)|)$ 求出 $theta$。
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],
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),
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)
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