Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 | import type { NumberLineState } from '../../types' import { numberToScreenX } from '../../numberLineTicks' /** * √2 Demo: "The Magic Shortcut" * * Visualises √2 ≈ 1.414 as the diagonal of a unit square. * * A 1×1 square sits on the number line with its base from 0 to 1. * The diagonal — the "shortcut" — is highlighted, then rotated down * (compass-arm style) to lie on the number line, landing at √2. * * The demo also shows why the shortcut is this length: the two * side-squares (area 1 each) combine to fill the diagonal-square * (area 2), planting the Pythagorean theorem seed visually. * * Finally we zoom in to show that √2's decimal expansion never * terminates, building intuition for irrational numbers. */ // ── Constants ──────────────────────────────────────────────────────── const SQRT2 = Math.SQRT2 // 1.4142135623730951 // ── Utilities ──────────────────────────────────────────────────────── function mapRange(v: number, s: number, e: number): number { if (v <= s) return 0 if (v >= e) return 1 return (v - s) / (e - s) } function smoothstep(t: number): number { const c = Math.max(0, Math.min(1, t)) return c * c * (3 - 2 * c) } function easeInOut(t: number): number { const c = Math.max(0, Math.min(1, t)) return c < 0.5 ? 2 * c * c : 1 - (-2 * c + 2) ** 2 / 2 } // ── Phase timing ───────────────────────────────────────────────────── // Must align with sqrt2DemoNarration.ts segment boundaries. const PHASE = { // Seg 1: journey starts startBegin: 0.0, startEnd: 0.1, // Seg 2: long path (draw square + highlight two sides) longPathBegin: 0.1, longPathEnd: 0.25, // Seg 3: shortcut diagonal appears shortcutBegin: 0.25, shortcutEnd: 0.35, // Seg 4: compass rotation rotateBegin: 0.35, rotateEnd: 0.5, // Seg 5: mystery spot mysteryBegin: 0.5, mysteryEnd: 0.6, // Seg 6: area proof (box squares) proofBegin: 0.6, proofEnd: 0.8, // Seg 7: zoom in on decimals zoomBegin: 0.8, zoomEnd: 0.92, // Seg 8: final reveal revealBegin: 0.92, revealEnd: 1.0, } as const // ── Colors ─────────────────────────────────────────────────────────── function squareCol(isDark: boolean) { return isDark ? '#60a5fa' : '#3b82f6' } // blue function pathCol(isDark: boolean) { return isDark ? '#fb923c' : '#ea580c' } // orange function diagCol(isDark: boolean) { return isDark ? '#34d399' : '#059669' } // green function diagColBright(isDark: boolean) { return isDark ? '#6ee7b7' : '#10b981' } function proofColA(isDark: boolean) { return isDark ? '#f87171' : '#dc2626' } // red function proofColB(isDark: boolean) { return isDark ? '#a78bfa' : '#7c3aed' } // purple function textCol(isDark: boolean) { return isDark ? 'rgba(255,255,255,0.9)' : 'rgba(0,0,0,0.8)' } function subtextCol(isDark: boolean) { return isDark ? 'rgba(255,255,255,0.6)' : 'rgba(0,0,0,0.5)' } // ── Viewport ───────────────────────────────────────────────────────── export function sqrt2DemoViewport(cssWidth: number, cssHeight: number) { // Center on [0, √2] with some padding; square is above axis up to height ~ppu const center = SQRT2 / 2 + 0.1 const ppu = Math.min((cssWidth * 0.65) / (SQRT2 + 0.8), cssHeight * 0.28) return { center, pixelsPerUnit: ppu } } // ── Drawing helpers ────────────────────────────────────────────────── /** Convert a number-line value to screen x */ type ToX = (v: number) => number /** Convert a height in NL units to screen pixels */ function hPx(val: number, ppu: number): number { return val * ppu } /** Draw the unit square outline above the axis */ function drawSquare( ctx: CanvasRenderingContext2D, toX: ToX, axisY: number, ppu: number, isDark: boolean, alpha: number, fillAlpha = 0.08 ) { const x0 = toX(0) const x1 = toX(1) const h = hPx(1, ppu) const y0 = axisY const y1 = axisY - h // Fill ctx.fillStyle = squareCol(isDark) ctx.globalAlpha = alpha * fillAlpha ctx.fillRect(x0, y1, x1 - x0, h) // Outline ctx.strokeStyle = squareCol(isDark) ctx.lineWidth = 2 ctx.globalAlpha = alpha * 0.7 ctx.strokeRect(x0, y1, x1 - x0, h) } /** Draw the "long path" — bottom + right edge of square, highlighted */ function drawLongPath( ctx: CanvasRenderingContext2D, toX: ToX, axisY: number, ppu: number, isDark: boolean, alpha: number, /** 0-1: how much of the path is drawn (0=none, 0.5=bottom done, 1=bottom+right) */ progress: number ) { if (progress <= 0 || alpha <= 0) return const x0 = toX(0) const x1 = toX(1) const h = hPx(1, ppu) ctx.strokeStyle = pathCol(isDark) ctx.lineWidth = 3.5 ctx.lineCap = 'round' ctx.globalAlpha = alpha ctx.beginPath() ctx.moveTo(x0, axisY) if (progress <= 0.5) { // Drawing the bottom edge const bp = progress / 0.5 ctx.lineTo(x0 + (x1 - x0) * bp, axisY) } else { // Bottom edge complete, drawing right edge ctx.lineTo(x1, axisY) const rp = (progress - 0.5) / 0.5 ctx.lineTo(x1, axisY - h * rp) } ctx.stroke() } /** Draw the diagonal line at a given rotation angle (0 = pointing up to (1,1), π/4 = flat on axis) */ function drawDiagonal( ctx: CanvasRenderingContext2D, toX: ToX, axisY: number, ppu: number, isDark: boolean, alpha: number, /** Angle from vertical: 0 = diagonal in square, π/4 = flat on number line */ angle: number, bright = false ) { if (alpha <= 0) return const ox = toX(0) const length = hPx(SQRT2, ppu) // The diagonal at angle=0 goes from (0,0) to (1,1) in NL coords. // Angle is measured from the original diagonal direction. // At angle=0: endpoint is at (1, 1) → screen (toX(1), axisY - hPx(1,ppu)) // At angle=π/4: endpoint is at (√2, 0) → screen (toX(√2), axisY) // // Original angle of the diagonal above horizontal = atan(1/1) = π/4 // Rotating from original position by `angle` radians clockwise const baseAngle = Math.PI / 4 // 45° above horizontal const currentAngle = baseAngle - angle // decreasing toward 0 (horizontal) const endX = ox + length * Math.cos(currentAngle) const endY = axisY - length * Math.sin(currentAngle) ctx.beginPath() ctx.moveTo(ox, axisY) ctx.lineTo(endX, endY) ctx.strokeStyle = bright ? diagColBright(isDark) : diagCol(isDark) ctx.lineWidth = 3.5 ctx.lineCap = 'round' ctx.globalAlpha = alpha ctx.stroke() // Endpoint dot ctx.beginPath() ctx.arc(endX, endY, 4, 0, Math.PI * 2) ctx.fillStyle = bright ? diagColBright(isDark) : diagCol(isDark) ctx.globalAlpha = alpha * 0.9 ctx.fill() } /** Draw the compass arc (trace of diagonal tip during rotation) */ function drawArc( ctx: CanvasRenderingContext2D, toX: ToX, axisY: number, ppu: number, isDark: boolean, alpha: number, /** 0-1: how much of the arc is drawn */ progress: number ) { if (progress <= 0 || alpha <= 0) return const ox = toX(0) const radius = hPx(SQRT2, ppu) // Arc from 45° above horizontal to 0° (horizontal) const startAngle = -Math.PI / 4 // canvas angles: negative = above x-axis const endAngle = 0 const arcEnd = startAngle + (endAngle - startAngle) * progress ctx.beginPath() ctx.arc(ox, axisY, radius, startAngle, arcEnd) ctx.strokeStyle = diagCol(isDark) ctx.lineWidth = 1.5 ctx.setLineDash([4, 3]) ctx.globalAlpha = alpha * 0.5 ctx.stroke() ctx.setLineDash([]) } /** Draw a side-square (for the Pythagorean proof) */ function drawProofSquare( ctx: CanvasRenderingContext2D, /** Top-left x, top-left y, width, height in screen coords */ sx: number, sy: number, sw: number, sh: number, color: string, alpha: number, fillAlpha = 0.35 ) { ctx.fillStyle = color ctx.globalAlpha = alpha * fillAlpha ctx.fillRect(sx, sy, sw, sh) ctx.strokeStyle = color ctx.lineWidth = 1.5 ctx.globalAlpha = alpha * 0.8 ctx.strokeRect(sx, sy, sw, sh) } /** Draw the tilted square on the diagonal (area = 2) */ function drawTiltedSquare( ctx: CanvasRenderingContext2D, toX: ToX, axisY: number, ppu: number, color: string, alpha: number, fillAlpha = 0.2 ) { // The tilted square has the diagonal as one side. // Vertices: (0,0), (1,1), (0,2), (-1,1) in NL coords // (rotated 45° square with side = √2, centered at (0,1)) const points = [ [0, 0], [1, 1], [0, 2], [-1, 1], ] ctx.beginPath() for (let i = 0; i < points.length; i++) { const sx = toX(points[i][0]) const sy = axisY - hPx(points[i][1], ppu) if (i === 0) ctx.moveTo(sx, sy) else ctx.lineTo(sx, sy) } ctx.closePath() ctx.fillStyle = color ctx.globalAlpha = alpha * fillAlpha ctx.fill() ctx.strokeStyle = color ctx.lineWidth = 1.5 ctx.globalAlpha = alpha * 0.7 ctx.stroke() } /** Draw a 5-pointed star */ function drawStar( ctx: CanvasRenderingContext2D, cx: number, cy: number, r: number, color: string, alpha: number ) { ctx.beginPath() for (let i = 0; i < 10; i++) { const angle = -Math.PI / 2 + (i * Math.PI) / 5 const rad = i % 2 === 0 ? r : r * 0.4 const px = cx + rad * Math.cos(angle) const py = cy + rad * Math.sin(angle) if (i === 0) ctx.moveTo(px, py) else ctx.lineTo(px, py) } ctx.closePath() ctx.fillStyle = color ctx.globalAlpha = alpha ctx.fill() } // ── Main render ────────────────────────────────────────────────────── export function renderSqrt2Overlay( ctx: CanvasRenderingContext2D, state: NumberLineState, cssWidth: number, cssHeight: number, isDark: boolean, revealProgress: number, opacity: number ): void { if (opacity <= 0) return const ppu = state.pixelsPerUnit const axisY = cssHeight / 2 const toX = (v: number) => numberToScreenX(v, state.center, ppu, cssWidth) ctx.save() // ── Seg 1: The journey starts — dot at zero ── if (revealProgress >= PHASE.startBegin) { const dotP = smoothstep(mapRange(revealProgress, PHASE.startBegin, PHASE.startBegin + 0.04)) if (dotP > 0) { const ox = toX(0) ctx.beginPath() ctx.arc(ox, axisY, 5 * dotP, 0, Math.PI * 2) ctx.fillStyle = diagCol(isDark) ctx.globalAlpha = opacity * dotP ctx.fill() } // "Start here!" label if (revealProgress < PHASE.longPathBegin) { const labelA = smoothstep(mapRange(revealProgress, 0.03, 0.06)) * (1 - smoothstep(mapRange(revealProgress, PHASE.startEnd - 0.02, PHASE.startEnd))) if (labelA > 0.01) { const fs = Math.max(11, Math.min(14, ppu * 0.12)) ctx.font = `${fs}px system-ui, sans-serif` ctx.fillStyle = textCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.globalAlpha = opacity * labelA ctx.fillText('Start here!', toX(0), axisY + 10) } } } // ── Seg 2: The long path — draw square + path ── const squareVisible = revealProgress >= PHASE.longPathBegin if (squareVisible) { const squareP = smoothstep( mapRange(revealProgress, PHASE.longPathBegin, PHASE.longPathBegin + 0.05) ) // Square should persist until the proof phase and then during reveal const squareFade = revealProgress >= PHASE.zoomBegin && revealProgress < PHASE.revealBegin ? 1 - smoothstep(mapRange(revealProgress, PHASE.zoomBegin, PHASE.zoomBegin + 0.03)) : revealProgress >= PHASE.revealBegin ? smoothstep(mapRange(revealProgress, PHASE.revealBegin, PHASE.revealBegin + 0.03)) : 1 if (squareP > 0 && squareFade > 0) { drawSquare(ctx, toX, axisY, ppu, isDark, opacity * squareP * squareFade) } // Long path animation if (revealProgress < PHASE.shortcutEnd) { const pathP = easeInOut( mapRange(revealProgress, PHASE.longPathBegin + 0.03, PHASE.longPathEnd - 0.02) ) const pathFade = 1 - smoothstep(mapRange(revealProgress, PHASE.shortcutBegin + 0.03, PHASE.shortcutEnd)) drawLongPath(ctx, toX, axisY, ppu, isDark, opacity * pathFade, pathP) // "1 step over" label on bottom, "1 step up" label on right if (pathP > 0.3 && pathP < 0.55) { const la = smoothstep(mapRange(pathP, 0.3, 0.5)) const fs = Math.max(10, Math.min(13, ppu * 0.11)) ctx.font = `${fs}px system-ui, sans-serif` ctx.fillStyle = pathCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.globalAlpha = opacity * la * pathFade ctx.fillText('1 step →', (toX(0) + toX(1)) / 2, axisY + 8) } if (pathP > 0.7) { const la = smoothstep(mapRange(pathP, 0.7, 0.9)) const fadeOut = 1 - smoothstep(mapRange(revealProgress, PHASE.shortcutBegin, PHASE.shortcutBegin + 0.05)) const fs = Math.max(10, Math.min(13, ppu * 0.11)) ctx.font = `${fs}px system-ui, sans-serif` ctx.fillStyle = pathCol(isDark) ctx.textAlign = 'left' ctx.textBaseline = 'middle' ctx.globalAlpha = opacity * la * fadeOut ctx.fillText('1 step ↑', toX(1) + 8, axisY - hPx(0.5, ppu)) } } } // ── Seg 3: The shortcut — diagonal appears in the square ── const diagVisible = revealProgress >= PHASE.shortcutBegin if (diagVisible) { // Before rotation, diagonal is at angle=0 (pointing to (1,1)) // During rotation, angle goes from 0 to π/4 // After rotation, it stays at π/4 (flat on number line) const diagAppearP = smoothstep( mapRange(revealProgress, PHASE.shortcutBegin, PHASE.shortcutBegin + 0.05) ) const rotateP = easeInOut( mapRange(revealProgress, PHASE.rotateBegin + 0.02, PHASE.rotateEnd - 0.02) ) const angle = rotateP * (Math.PI / 4) // During zoom phase, fade out diagonal in square position; during reveal, show on number line const diagFade = revealProgress >= PHASE.zoomBegin && revealProgress < PHASE.revealBegin ? 1 - smoothstep(mapRange(revealProgress, PHASE.zoomBegin, PHASE.zoomBegin + 0.03)) : revealProgress >= PHASE.revealBegin ? smoothstep(mapRange(revealProgress, PHASE.revealBegin, PHASE.revealBegin + 0.03)) : 1 // Draw the arc during rotation if (revealProgress >= PHASE.rotateBegin && revealProgress < PHASE.mysteryEnd) { drawArc(ctx, toX, axisY, ppu, isDark, opacity * diagFade, rotateP) } // Draw the diagonal itself drawDiagonal( ctx, toX, axisY, ppu, isDark, opacity * diagAppearP * diagFade, angle, rotateP >= 1 ) // "The shortcut!" label if (revealProgress >= PHASE.shortcutBegin && revealProgress < PHASE.rotateBegin) { const la = smoothstep( mapRange(revealProgress, PHASE.shortcutBegin + 0.02, PHASE.shortcutBegin + 0.05) ) * (1 - smoothstep(mapRange(revealProgress, PHASE.shortcutEnd - 0.02, PHASE.shortcutEnd))) if (la > 0.01) { const fs = Math.max(11, Math.min(14, ppu * 0.12)) ctx.font = `${fs}px system-ui, sans-serif` ctx.fillStyle = diagCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'bottom' ctx.globalAlpha = opacity * la // Position label near middle of diagonal const midX = (toX(0) + toX(1)) / 2 - 10 const midY = axisY - hPx(0.5, ppu) - 6 ctx.fillText('The shortcut!', midX, midY) } } } // ── Seg 5: Mystery spot — question mark ── if (revealProgress >= PHASE.mysteryBegin && revealProgress < PHASE.proofBegin) { const qP = smoothstep( mapRange(revealProgress, PHASE.mysteryBegin + 0.02, PHASE.mysteryBegin + 0.06) ) const qFade = 1 - smoothstep(mapRange(revealProgress, PHASE.mysteryEnd - 0.02, PHASE.mysteryEnd)) const qAlpha = qP * qFade if (qAlpha > 0.01) { const sqrt2X = toX(SQRT2) // Question mark const fs = Math.max(16, Math.min(24, ppu * 0.2)) ctx.font = `bold ${fs}px system-ui, sans-serif` ctx.fillStyle = diagCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'bottom' ctx.globalAlpha = opacity * qAlpha ctx.fillText('?', sqrt2X, axisY - 14) // "Between 1 and 2" label const lfs = Math.max(10, Math.min(13, ppu * 0.11)) ctx.font = `${lfs}px system-ui, sans-serif` ctx.fillStyle = textCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.globalAlpha = opacity * qAlpha * 0.8 ctx.fillText('More than 1, less than 2...', (toX(1) + toX(SQRT2)) / 2 + 10, axisY + 10) } } // ── Seg 6: Area proof — side squares + diagonal square ── if (revealProgress >= PHASE.proofBegin && revealProgress < PHASE.zoomBegin) { const proofP = mapRange(revealProgress, PHASE.proofBegin, PHASE.proofEnd) const proofFade = 1 - smoothstep(mapRange(revealProgress, PHASE.proofEnd - 0.02, PHASE.proofEnd)) // Phase 1: Side squares appear (0-0.35 of proof) const sideP = smoothstep(mapRange(proofP, 0, 0.35)) // Side square A: below the base (from x=0 to x=1, below axis) if (sideP > 0) { const x0 = toX(0) const x1 = toX(1) const h = hPx(1, ppu) drawProofSquare(ctx, x0, axisY, x1 - x0, h, proofColA(isDark), opacity * sideP * proofFade) // "Area = 1" label const fs = Math.max(10, Math.min(12, ppu * 0.1)) ctx.font = `bold ${fs}px system-ui, sans-serif` ctx.fillStyle = proofColA(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'middle' ctx.globalAlpha = opacity * sideP * proofFade * 0.9 ctx.fillText('Area = 1', (x0 + x1) / 2, axisY + h / 2) } // Side square B: to the left of the left edge if (sideP > 0) { const x0 = toX(-1) const x1 = toX(0) const h = hPx(1, ppu) const y1 = axisY - h drawProofSquare(ctx, x0, y1, x1 - x0, h, proofColB(isDark), opacity * sideP * proofFade) const fs = Math.max(10, Math.min(12, ppu * 0.1)) ctx.font = `bold ${fs}px system-ui, sans-serif` ctx.fillStyle = proofColB(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'middle' ctx.globalAlpha = opacity * sideP * proofFade * 0.9 ctx.fillText('Area = 1', (x0 + x1) / 2, y1 + h / 2) } // Phase 2: Tilted diagonal square appears (0.35-0.65 of proof) const tiltP = smoothstep(mapRange(proofP, 0.35, 0.65)) if (tiltP > 0) { drawTiltedSquare(ctx, toX, axisY, ppu, diagCol(isDark), opacity * tiltP * proofFade, 0.25) // "Area = 2" label const fs = Math.max(11, Math.min(14, ppu * 0.12)) ctx.font = `bold ${fs}px system-ui, sans-serif` ctx.fillStyle = diagCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'middle' ctx.globalAlpha = opacity * tiltP * proofFade ctx.fillText('Area = 2', toX(0), axisY - hPx(1, ppu)) } // Phase 3: "1 + 1 = 2" equation (0.65-1.0 of proof) const eqP = smoothstep(mapRange(proofP, 0.65, 0.85)) if (eqP > 0) { const fs = Math.max(12, Math.min(16, ppu * 0.14)) ctx.font = `bold ${fs}px system-ui, sans-serif` ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.globalAlpha = opacity * eqP * proofFade // Color-coded equation const eqX = toX(0.5) const eqY = axisY + hPx(1, ppu) + 12 // "1" in red ctx.fillStyle = proofColA(isDark) ctx.textAlign = 'right' ctx.fillText('1', eqX - 16, eqY) // "+" in text color ctx.fillStyle = textCol(isDark) ctx.textAlign = 'center' ctx.fillText('+', eqX - 8, eqY) // "1" in purple ctx.fillStyle = proofColB(isDark) ctx.textAlign = 'left' ctx.fillText('1', eqX, eqY) // "=" in text color ctx.fillStyle = textCol(isDark) ctx.textAlign = 'center' ctx.fillText('=', eqX + 16, eqY) // "2" in green ctx.fillStyle = diagCol(isDark) ctx.textAlign = 'left' ctx.fillText('2', eqX + 24, eqY) } } // ── Seg 7: Zoom in on decimals ── // The actual number-line viewport zoom is driven by useConstantDemo. // Here we just overlay a floating decimal expansion at the top of the screen. if (revealProgress >= PHASE.zoomBegin && revealProgress < PHASE.revealBegin) { const zoomP = mapRange(revealProgress, PHASE.zoomBegin, PHASE.zoomEnd) const fadeIn = smoothstep(Math.min(1, zoomP * 4)) // Decimal expansion typing out const decimalStr = '1.4142135623\u2026' const charsToShow = Math.min(decimalStr.length, Math.floor(1 + zoomP * (decimalStr.length - 1))) const displayText = '\u221A2 = ' + decimalStr.substring(0, charsToShow) const fs = Math.max(16, Math.min(24, cssWidth * 0.03)) ctx.font = `bold ${fs}px system-ui, monospace` ctx.fillStyle = diagCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.globalAlpha = opacity * fadeIn ctx.fillText(displayText, cssWidth / 2, 20) // Subtitle if (zoomP > 0.7) { const neverP = smoothstep(mapRange(zoomP, 0.7, 0.9)) const subFs = Math.max(11, Math.min(15, cssWidth * 0.02)) ctx.font = `italic ${subFs}px system-ui, sans-serif` ctx.fillStyle = subtextCol(isDark) ctx.textAlign = 'center' ctx.globalAlpha = opacity * neverP * 0.8 ctx.fillText('The digits never stop!', cssWidth / 2, 20 + fs + 6) } } // ── Seg 8: Final reveal ── if (revealProgress >= PHASE.revealBegin) { const revealP = smoothstep(mapRange(revealProgress, PHASE.revealBegin, PHASE.revealEnd)) // Diagonal on the number line drawDiagonal(ctx, toX, axisY, ppu, isDark, opacity * revealP, Math.PI / 4, true) // Star at √2 const sqrt2X = toX(SQRT2) const starY = axisY - 20 const starR = Math.max(6, Math.min(10, ppu * 0.06)) const starPulse = 1 + 0.1 * Math.sin(revealProgress * Math.PI * 8) drawStar(ctx, sqrt2X, starY, starR * starPulse * revealP, diagCol(isDark), opacity * revealP) // "√2" label if (revealP > 0.3) { const labelP = smoothstep(mapRange(revealP, 0.3, 0.7)) const fs = Math.max(18, Math.min(26, ppu * 0.22)) ctx.font = `bold ${fs}px system-ui, sans-serif` ctx.fillStyle = diagCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'bottom' ctx.globalAlpha = opacity * labelP ctx.fillText('√2', sqrt2X, starY - starR - 4) } // "≈ 1.414" value if (revealP > 0.5) { const valP = smoothstep(mapRange(revealP, 0.5, 0.85)) const fs = Math.max(14, Math.min(18, ppu * 0.16)) ctx.font = `bold ${fs}px system-ui, sans-serif` ctx.fillStyle = diagCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.globalAlpha = opacity * valP ctx.fillText('≈ 1.414', sqrt2X, axisY + 6) } // Subtitle if (revealP > 0.7) { const subP = smoothstep(mapRange(revealP, 0.7, 1.0)) const fs = Math.max(10, Math.min(13, ppu * 0.11)) ctx.font = `${fs}px system-ui, sans-serif` ctx.fillStyle = subtextCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.globalAlpha = opacity * subP * 0.7 ctx.fillText('The magic shortcut', sqrt2X, axisY + 26) } // Formula for curious kids if (revealP > 0.85) { const formulaP = smoothstep(mapRange(revealP, 0.85, 1.0)) const fs = Math.max(9, Math.min(11, ppu * 0.09)) ctx.font = `${fs}px system-ui, sans-serif` ctx.fillStyle = subtextCol(isDark) ctx.textAlign = 'center' ctx.textBaseline = 'bottom' ctx.globalAlpha = opacity * formulaP * 0.5 ctx.fillText('1² + 1² = (√2)²', sqrt2X, starY - starR - fs - 10) } } ctx.globalAlpha = 1 ctx.setLineDash([]) ctx.restore() } |