mirror of
https://github.com/HananoshikaYomaru/openfreebooks.git
synced 2026-11-13 13:05:51 +00:00
Refactor math notation and integer foundations content: Update basic math notation to replace half-bar representation with a dot-based notation for clarity. Enhance integer foundations by revising definitions, adding historical context, and improving explanations of operations, absolute value, and percentages. Include new examples and applications to better illustrate concepts and their relevance in real-world scenarios.
This commit is contained in:
Hananoshika Yomaru
parent
057f2bebf2
commit
f74867fe4c
9 changed files with 1073 additions and 80 deletions
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@ -0,0 +1,403 @@
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import { onCleanup, onMount } from "solid-js";
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const MIN_VALUE = -10;
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const MAX_VALUE = 10;
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const STEP = 0.5;
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function clampToStep(value: number) {
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const clamped = Math.max(MIN_VALUE, Math.min(MAX_VALUE, value));
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return Math.round(clamped / STEP) * STEP;
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}
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function relationSymbol(a: number, b: number) {
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if (a > b) return ">";
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if (a < b) return "<";
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return "=";
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}
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type DemoPalette = {
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canvasFill: string;
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distanceBand: string;
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positiveRay: string;
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negativeRay: string;
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axisLine: string;
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arrow: string;
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majorTick: string;
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minorTick: string;
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tickLabel: string;
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axisLabel: string;
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guideLine: string;
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absoluteLabelBg: string;
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absoluteLabelText: string;
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pointValueText: string;
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pointRing: string;
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pointA: string;
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pointB: string;
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};
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function resolvePalette(): DemoPalette {
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const explicitTheme = document.documentElement.getAttribute("data-theme");
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const isDark =
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explicitTheme === "dark" ||
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(explicitTheme !== "light" && window.matchMedia("(prefers-color-scheme: dark)").matches);
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if (isDark) {
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return {
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canvasFill: "#0f172a",
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distanceBand: "rgba(56, 189, 248, 0.8)",
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positiveRay: "#22d3ee",
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negativeRay: "#fda4af",
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axisLine: "#e2e8f0",
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arrow: "#f1f5f9",
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majorTick: "#e2e8f0",
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minorTick: "#94a3b8",
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tickLabel: "#f8fafc",
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axisLabel: "#cbd5e1",
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guideLine: "rgba(226, 232, 240, 0.65)",
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absoluteLabelBg: "rgba(15, 23, 42, 0.82)",
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absoluteLabelText: "#f8fafc",
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pointValueText: "#f8fafc",
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pointRing: "#0f172a",
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pointA: "#2dd4bf",
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pointB: "#f59e0b",
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};
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}
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return {
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canvasFill: "rgba(148, 163, 184, 0.08)",
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distanceBand: "rgba(14, 116, 144, 0.75)",
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positiveRay: "#0f766e",
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negativeRay: "#b91c1c",
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axisLine: "#334155",
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arrow: "#64748b",
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majorTick: "#475569",
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minorTick: "#94a3b8",
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tickLabel: "#475569",
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axisLabel: "#64748b",
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guideLine: "rgba(15, 23, 42, 0.25)",
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absoluteLabelBg: "rgba(255, 255, 255, 0.92)",
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absoluteLabelText: "#0f172a",
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pointValueText: "#0f172a",
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pointRing: "#ffffff",
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pointA: "#0f766e",
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pointB: "#b45309",
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};
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}
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function IntegerCompareDemo() {
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let rootRef: HTMLDivElement | undefined;
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let canvasRef: HTMLCanvasElement | undefined;
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let valueARef: HTMLSpanElement | undefined;
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let valueBRef: HTMLSpanElement | undefined;
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let relationRef: HTMLSpanElement | undefined;
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let distanceRef: HTMLSpanElement | undefined;
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onMount(() => {
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const canvas = canvasRef;
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if (!canvas) return;
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const ctxCandidate = canvas.getContext("2d");
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if (!(ctxCandidate instanceof CanvasRenderingContext2D)) return;
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const ctx: CanvasRenderingContext2D = ctxCandidate;
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const canvasEl: HTMLCanvasElement = canvas;
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let valueA = -2;
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let valueB = -5;
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let dragging: "a" | "b" | null = null;
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let dpr = window.devicePixelRatio || 1;
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let logicalWidth = 760;
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let logicalHeight = 260;
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const marginX = 40;
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const axisY = 164;
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const handleY = 98;
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const pxPerUnit = () => (logicalWidth - marginX * 2) / (MAX_VALUE - MIN_VALUE);
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const toScreenX = (value: number) => marginX + (value - MIN_VALUE) * pxPerUnit();
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const fromScreenX = (screenX: number) => MIN_VALUE + (screenX - marginX) / pxPerUnit();
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function drawArrowHead(x: number, y: number, direction: 1 | -1, color: string) {
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const size = 7;
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ctx.fillStyle = color;
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ctx.beginPath();
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ctx.moveTo(x, y);
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ctx.lineTo(x - direction * size, y - size * 0.75);
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ctx.lineTo(x - direction * size, y + size * 0.75);
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ctx.closePath();
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ctx.fill();
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}
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function drawPoint(x: number, y: number, color: string, ringColor: string) {
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ctx.beginPath();
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ctx.arc(x, y, 10, 0, Math.PI * 2);
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ctx.fillStyle = color;
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ctx.fill();
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ctx.lineWidth = 2;
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ctx.strokeStyle = ringColor;
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ctx.stroke();
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}
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function updateText() {
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if (valueARef) valueARef.textContent = valueA.toFixed(1);
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if (valueBRef) valueBRef.textContent = valueB.toFixed(1);
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if (relationRef) relationRef.textContent = relationSymbol(valueA, valueB);
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if (distanceRef) distanceRef.textContent = Math.abs(valueA - valueB).toFixed(1);
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}
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function draw() {
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const palette = resolvePalette();
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ctx.clearRect(0, 0, logicalWidth, logicalHeight);
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ctx.fillStyle = palette.canvasFill;
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ctx.fillRect(0, 0, logicalWidth, logicalHeight);
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const xA = toScreenX(valueA);
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const xB = toScreenX(valueB);
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const xZero = toScreenX(0);
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const minX = Math.min(xA, xB);
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const maxX = Math.max(xA, xB);
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ctx.strokeStyle = palette.distanceBand;
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ctx.lineWidth = 9;
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ctx.lineCap = "round";
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ctx.beginPath();
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ctx.moveTo(minX, axisY);
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ctx.lineTo(maxX, axisY);
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ctx.stroke();
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const drawZeroRay = (value: number, x: number, y: number) => {
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if (value === 0) return;
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ctx.strokeStyle = value > 0 ? palette.positiveRay : palette.negativeRay;
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ctx.lineWidth = 5;
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ctx.lineCap = "round";
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ctx.beginPath();
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ctx.moveTo(xZero, y);
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ctx.lineTo(x, y);
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ctx.stroke();
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};
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drawZeroRay(valueA, xA, axisY - 12);
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drawZeroRay(valueB, xB, axisY + 12);
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ctx.strokeStyle = palette.axisLine;
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ctx.lineWidth = 2;
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ctx.lineCap = "round";
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ctx.beginPath();
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ctx.moveTo(marginX - 12, axisY);
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ctx.lineTo(logicalWidth - marginX + 12, axisY);
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ctx.stroke();
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drawArrowHead(logicalWidth - marginX + 12, axisY, 1, palette.arrow);
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drawArrowHead(marginX - 12, axisY, -1, palette.arrow);
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for (let tick = MIN_VALUE; tick <= MAX_VALUE; tick += 1) {
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const x = toScreenX(tick);
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const major = tick % 2 === 0;
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ctx.strokeStyle = major ? palette.majorTick : palette.minorTick;
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ctx.lineWidth = major ? 1.5 : 1;
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ctx.beginPath();
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ctx.moveTo(x, axisY - (major ? 9 : 6));
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ctx.lineTo(x, axisY + (major ? 9 : 6));
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ctx.stroke();
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if (major) {
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ctx.font = "12px var(--mono, ui-monospace, monospace)";
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ctx.textAlign = "center";
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ctx.textBaseline = "top";
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ctx.fillStyle = palette.tickLabel;
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ctx.fillText(String(tick), x, axisY + 11);
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}
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}
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ctx.font = "600 12px var(--font-sans, system-ui, sans-serif)";
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ctx.textAlign = "right";
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ctx.textBaseline = "bottom";
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ctx.fillStyle = palette.axisLabel;
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ctx.fillText("Number line", logicalWidth - marginX + 12, axisY - 12);
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ctx.strokeStyle = palette.guideLine;
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ctx.lineWidth = 1.5;
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ctx.setLineDash([5, 4]);
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ctx.beginPath();
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ctx.moveTo(xA, handleY + 12);
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ctx.lineTo(xA, axisY - 12);
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ctx.moveTo(xB, handleY + 12);
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ctx.lineTo(xB, axisY - 12);
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ctx.stroke();
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ctx.setLineDash([]);
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drawPoint(xA, handleY, palette.pointA, palette.pointRing);
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drawPoint(xB, handleY, palette.pointB, palette.pointRing);
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const drawPointValue = (x: number, value: number) => {
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const text = value.toFixed(1);
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const y = handleY - 20;
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ctx.font = "700 12px var(--mono, ui-monospace, monospace)";
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ctx.textAlign = "center";
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ctx.textBaseline = "middle";
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ctx.fillStyle = palette.pointValueText;
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ctx.fillText(text, x, y);
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};
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drawPointValue(xA, valueA);
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drawPointValue(xB, valueB);
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const absText = `|A - B| = ${Math.abs(valueA - valueB).toFixed(1)}`;
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const absX = (xA + xB) / 2;
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const absY = axisY - 30;
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ctx.font = "700 12px var(--mono, ui-monospace, monospace)";
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const absTextWidth = ctx.measureText(absText).width;
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ctx.fillStyle = palette.absoluteLabelBg;
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ctx.fillRect(absX - absTextWidth / 2 - 6, absY - 9, absTextWidth + 12, 18);
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ctx.fillStyle = palette.absoluteLabelText;
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ctx.textAlign = "center";
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ctx.textBaseline = "middle";
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ctx.fillText(absText, absX, absY);
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updateText();
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}
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function resize() {
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dpr = window.devicePixelRatio || 1;
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const rect = canvasEl.getBoundingClientRect();
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logicalWidth = Math.max(320, rect.width);
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logicalHeight = 260;
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canvasEl.width = Math.round(logicalWidth * dpr);
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canvasEl.height = Math.round(logicalHeight * dpr);
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canvasEl.style.height = `${logicalHeight}px`;
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ctx.setTransform(1, 0, 0, 1, 0, 0);
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ctx.scale(dpr, dpr);
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draw();
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}
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function pickHandle(pointerX: number, pointerY: number) {
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const xA = toScreenX(valueA);
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const xB = toScreenX(valueB);
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const distA = Math.hypot(pointerX - xA, pointerY - handleY);
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const distB = Math.hypot(pointerX - xB, pointerY - handleY);
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if (distA <= 18 && distA <= distB) return "a";
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if (distB <= 18) return "b";
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return null;
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}
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function onPointerDown(event: PointerEvent) {
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const rect = canvasEl.getBoundingClientRect();
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const x = event.clientX - rect.left;
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const y = event.clientY - rect.top;
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dragging = pickHandle(x, y);
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if (!dragging) return;
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canvasEl.setPointerCapture(event.pointerId);
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canvasEl.style.cursor = "grabbing";
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event.preventDefault();
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}
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function onPointerMove(event: PointerEvent) {
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if (!dragging) {
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const rect = canvasEl.getBoundingClientRect();
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const x = event.clientX - rect.left;
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const y = event.clientY - rect.top;
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canvasEl.style.cursor = pickHandle(x, y) ? "grab" : "default";
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return;
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}
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const rect = canvasEl.getBoundingClientRect();
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const x = event.clientX - rect.left;
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const next = clampToStep(fromScreenX(x));
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if (dragging === "a") {
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valueA = next;
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} else {
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valueB = next;
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}
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draw();
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event.preventDefault();
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}
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function onPointerEnd(event: PointerEvent) {
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if (dragging) {
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canvasEl.releasePointerCapture(event.pointerId);
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}
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dragging = null;
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canvasEl.style.cursor = "default";
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}
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function onResetClick() {
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valueA = -2;
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valueB = -5;
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draw();
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}
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const resetBtn = rootRef?.querySelector<HTMLButtonElement>("[data-compare-reset]");
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resetBtn?.addEventListener("click", onResetClick);
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canvasEl.addEventListener("pointerdown", onPointerDown);
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canvasEl.addEventListener("pointermove", onPointerMove);
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canvasEl.addEventListener("pointerup", onPointerEnd);
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canvasEl.addEventListener("pointercancel", onPointerEnd);
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window.addEventListener("resize", resize);
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const themeObserver = new MutationObserver(() => {
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draw();
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});
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themeObserver.observe(document.documentElement, {
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attributes: true,
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attributeFilter: ["data-theme"],
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});
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const darkQuery = window.matchMedia("(prefers-color-scheme: dark)");
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const onSystemThemeChange = () => draw();
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darkQuery.addEventListener("change", onSystemThemeChange);
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resize();
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onCleanup(() => {
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resetBtn?.removeEventListener("click", onResetClick);
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canvasEl.removeEventListener("pointerdown", onPointerDown);
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canvasEl.removeEventListener("pointermove", onPointerMove);
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canvasEl.removeEventListener("pointerup", onPointerEnd);
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canvasEl.removeEventListener("pointercancel", onPointerEnd);
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window.removeEventListener("resize", resize);
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themeObserver.disconnect();
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darkQuery.removeEventListener("change", onSystemThemeChange);
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});
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});
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return (
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<section class="math-widget integer-compare-demo" aria-labelledby="integer-compare-demo-title">
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<h3 id="integer-compare-demo-title" class="math-widget__title">
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Comparison demo: drag A and B on the number line
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</h3>
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<div class="math-widget__body" ref={rootRef}>
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<p class="math-widget__caption">
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Drag each point horizontally. The point farther right is greater. The highlighted segment
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shows absolute distance.
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</p>
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<canvas
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ref={canvasRef}
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class="integer-compare-demo__canvas"
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aria-label="Interactive number line for comparing integers"
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/>
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<p class="integer-compare-demo__readout" aria-live="polite">
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A = <span ref={valueARef}>-2.0</span>, B = <span ref={valueBRef}>-5.0</span>, so A{" "}
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<span ref={relationRef}>{">"}</span> B and |A - B| ={" "}
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<span ref={distanceRef}>3.0</span>
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</p>
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<div class="integer-compare-demo__actions">
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<button
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type="button"
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class="scenario-demo__btn integer-compare-demo__reset-btn"
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data-compare-reset
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aria-label="Reset example"
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title="Reset example"
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>
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<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.5" stroke-linecap="round" stroke-linejoin="round" class="icon icon-tabler icons-tabler-outline icon-tabler-reload">
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<path stroke="none" d="M0 0h24v24H0z" fill="none" />
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<path d="M19.933 13.041a8 8 0 1 1 -9.925 -8.788c3.899 -1 7.935 1.007 9.425 4.747" />
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<path d="M20 4v5h-5" />
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</svg>
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</button>
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</div>
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</div>
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</section>
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);
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}
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export default IntegerCompareDemo;
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