forked from bai/curriculum-project-hub
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c17af60bb0
Single entry `display(info, target, parts)` over an ordered parts array, the frozen contract the generated typst driver calls. Per-kind dispatch for segment/example/lemma/sop; student/teacher matrix derived internally from `target` (student hides example solution + lemma proof; teacher shows all). Content-field values are consumed as already-evaluated content (driver `include`s them ⇒ module body, ADR-0006), never imported/stringified. Optional fields (lemma proof, example source) handled gracefully; unknown kind/target degrade without crashing. Zero @preview deps (CI-robust); CJK + math styled. Smoke compiles to non-empty student/teacher PDFs. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
71 lines
2.0 KiB
Typst
71 lines
2.0 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
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(
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kind: "segment",
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textbook: [
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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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],
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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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