Press n or j to go to the next uncovered block, b, p or k for the previous block.
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PropositionDef,
ConstructionElement,
ConstructionState,
TutorialSubStep,
EuclidNarrationOptions,
ExpectedAction,
} from '../types'
import { BYRNE } from '../types'
import type { KidLanguageStyle } from '@/db/schema/player-session-preferences'
import { deriveSteps } from '../engine/recipe/deriveSteps'
import { RECIPE_PROP_2, PROP_2_ANNOTATIONS } from '../engine/recipe/definitions/prop2'
import { RECIPE_REGISTRY } from '../engine/recipe/definitions/registry'
import { recipeToConclusion } from '../engine/recipe/adapters'
import { evaluateRecipe } from '../engine/recipe/evaluate'
import { getPoint } from '../engine/constructionState'
const DEFAULT_LANGUAGE_STYLE: KidLanguageStyle = 'standard'
const PROP_2_STEP_INSTRUCTIONS: Record<KidLanguageStyle, string[]> = {
simple: [
'Draw a line from {pt:A} to {pt:B}',
'Build an equilateral triangle on {seg:AB} ({prop:1|I.1})',
'Draw a circle with center {pt:B} through {pt:C}',
'From {pt:D}, extend past {pt:B} to meet the circle',
'Draw a circle with center {pt:D} through {pt:E}',
'From {pt:D}, extend past {pt:A} to meet the circle',
],
standard: [
'Join point {pt:A} to point {pt:B}',
'Construct equilateral triangle on {seg:AB} ({prop:1|I.1})',
'Draw a circle centered at {pt:B} through {pt:C}',
'From {pt:D}, extend through {pt:B} to meet the circle at {pt:E}',
'Draw a circle centered at {pt:D} through {pt:E}',
'From {pt:D}, extend through {pt:A} to meet the circle at {pt:F}',
],
classical: [
'Join {pt:A} to {pt:B}',
'Construct the equilateral triangle on {seg:AB} ({prop:1|I.1})',
'Describe the circle with center {pt:B} and radius {seg:BC}',
'From {pt:D}, produce past {pt:B} to meet the circle at {pt:E}',
'Describe the circle with center {pt:D} and radius {seg:DE}',
'From {pt:D}, produce past {pt:A} to meet the circle at {pt:F}',
],
}
function getProp2Tutorial(isTouch: boolean, options?: EuclidNarrationOptions): TutorialSubStep[][] {
const style = options?.languageStyle ?? DEFAULT_LANGUAGE_STYLE
const tap = isTouch ? 'Tap' : 'Click'
const tapHold = isTouch ? 'Tap and hold' : 'Click and hold'
const drag = isTouch ? 'Drag' : 'Drag'
const sweep = isTouch ? 'Sweep your finger' : 'Move your mouse'
const byStyle = (copy: Record<KidLanguageStyle, string>) => copy[style] ?? copy.standard
return [
// ── Step 0: Join A to B ──
[
{
instruction: `${drag} from {pt:A} to {pt:B}`,
speech: byStyle({
simple: 'Postulate 1 lets us draw a straight line from any point to any point. Draw AB.',
standard:
'Postulate 1 lets us draw a straight line from any point to any point. Draw AB.',
classical: 'By Postulate 1, join A to B.',
}),
hint: { type: 'arrow', fromId: 'pt-A', toId: 'pt-B' },
advanceOn: null,
},
],
// ── Step 1: Construct equilateral triangle (I.1 macro) ──
[
{
instruction: `${tap} point {pt:A}`,
speech: isTouch
? byStyle({
simple:
'Now use Proposition I.1 to build an equilateral triangle on AB. Tap A to start.',
standard:
'Now use Proposition I.1 to construct an equilateral triangle on AB. Tap A to start.',
classical:
'Use Proposition I.1 to construct the equilateral triangle on AB. Tap A to begin.',
})
: byStyle({
simple:
'Now use Proposition I.1 to build an equilateral triangle on AB. Click A to start.',
standard:
'Now use Proposition I.1 to construct an equilateral triangle on AB. Click A to start.',
classical:
'Use Proposition I.1 to construct the equilateral triangle on AB. Click A to begin.',
}),
hint: { type: 'point', pointId: 'pt-A' },
advanceOn: { kind: 'macro-select', index: 0 },
},
{
instruction: `${tap} point {pt:B}`,
speech: isTouch
? byStyle({
simple: 'Tap B to finish. In an equilateral triangle, DA equals DB.',
standard: 'Tap B to finish. Because the triangle is equilateral, DA equals DB.',
classical: 'Tap B to finish. Since the triangle is equilateral, DA equals DB.',
})
: byStyle({
simple: 'Click B to finish. In an equilateral triangle, DA equals DB.',
standard: 'Click B to finish. Because the triangle is equilateral, DA equals DB.',
classical: 'Click B to finish. Since the triangle is equilateral, DA equals DB.',
}),
hint: { type: 'point', pointId: 'pt-B' },
advanceOn: null,
},
],
// ── Step 2: Circle at B through C ──
[
{
instruction: `${tapHold} point {pt:B}`,
speech: isTouch
? byStyle({
simple:
'Now draw a circle with center B and radius BC (Postulate 3). Press and hold on B.',
standard:
'Now describe a circle with center B and radius BC (Postulate 3). Press and hold on B.',
classical: 'By Postulate 3, describe the circle with center B and radius BC.',
})
: byStyle({
simple:
'Now draw a circle with center B and radius BC (Postulate 3). Click and hold on B.',
standard:
'Now describe a circle with center B and radius BC (Postulate 3). Click and hold on B.',
classical: 'By Postulate 3, describe the circle with center B and radius BC.',
}),
hint: { type: 'point', pointId: 'pt-B' },
advanceOn: { kind: 'compass-phase', phase: 'center-set' },
},
{
instruction: `${drag} to point {pt:C}`,
speech: byStyle({
simple: 'Drag to C to set the radius. Every point on this circle is BC away from B.',
standard: 'Drag to C to set the radius. Every point on this circle is BC away from B.',
classical:
'Drag to C to set the radius. Every point on this circle is at distance BC from B.',
}),
hint: { type: 'arrow', fromId: 'pt-B', toId: 'pt-C' },
advanceOn: { kind: 'compass-phase', phase: 'radius-set' },
},
{
instruction: `${sweep} around`,
speech: isTouch
? byStyle({
simple: 'Sweep around to draw the circle centered at B.',
standard: 'Sweep around to draw the circle centered at B.',
classical: 'Carry the circle around.',
})
: byStyle({
simple: 'Move around to draw the circle centered at B.',
standard: 'Move around to draw the circle centered at B.',
classical: 'Carry the circle around.',
}),
hint: { type: 'sweep', centerId: 'pt-B', radiusPointId: 'pt-C' },
advanceOn: null,
},
],
// ── Step 3: Extend DB past B to E (Postulate 2) ──
[
{
instruction: `${drag} from {pt:D} toward {pt:B}`,
speech: byStyle({
simple: 'Now extend line DB past B using Postulate 2. Drag from D toward B.',
standard: 'Now extend line DB past B using Postulate 2. Drag from point D toward B.',
classical: 'By Postulate 2, produce DB beyond B. Drag from D toward B.',
}),
hint: { type: 'point', pointId: 'pt-D' },
advanceOn: { kind: 'extend-phase' as const, phase: 'extending' as const },
},
{
instruction: `Extend through the circle to place {pt:E} where the line meets it`,
speech: byStyle({
simple:
'Keep going past B and release to place point E where the line meets the circle. Then BE equals BC.',
standard:
'Continue past B and release to place E where the line meets the circle. Because E is on the circle centered at B, BE equals BC.',
classical:
'Continue past B and release at E, where it meets the circle. Since E is on the circle with center B, BE equals BC.',
}),
hint: { type: 'none' as const },
advanceOn: null,
},
],
// ── Step 4: Circle at D through E ──
[
{
instruction: `${tapHold} point {pt:D}`,
speech: isTouch
? byStyle({
simple: 'Now draw a circle with center D and radius DE. Press and hold on D.',
standard: 'Now describe a circle with center D and radius DE. Press and hold on D.',
classical: 'Describe the circle with center D and radius DE.',
})
: byStyle({
simple: 'Now draw a circle with center D and radius DE. Click and hold on D.',
standard: 'Now describe a circle with center D and radius DE. Click and hold on D.',
classical: 'Describe the circle with center D and radius DE.',
}),
hint: { type: 'point', pointId: 'pt-D' },
advanceOn: { kind: 'compass-phase', phase: 'center-set' },
},
{
instruction: `${drag} to point {pt:E}`,
speech: byStyle({
simple: 'Drag to E to set the radius. Every point on this circle is DE away from D.',
standard: 'Drag to E to set the radius. Every point on this circle is DE away from D.',
classical:
'Drag to E to set the radius. Every point on this circle is at distance DE from D.',
}),
hint: { type: 'arrow', fromId: 'pt-D', toId: 'pt-E' },
advanceOn: { kind: 'compass-phase', phase: 'radius-set' },
},
{
instruction: `${sweep} around`,
speech: isTouch
? byStyle({
simple: 'Sweep around to draw the circle centered at D.',
standard: 'Sweep all the way around to draw the circle centered at D.',
classical: 'Carry the circle around.',
})
: byStyle({
simple: 'Move around to draw the circle centered at D.',
standard: 'Move all the way around to draw the circle centered at D.',
classical: 'Carry the circle around.',
}),
hint: { type: 'sweep', centerId: 'pt-D', radiusPointId: 'pt-E' },
advanceOn: null,
},
],
// ── Step 5: Extend DA past A to F (Postulate 2) ──
[
{
instruction: `${drag} from {pt:D} toward {pt:A}`,
speech: byStyle({
simple: 'Now extend line DA past A. Drag from D toward A.',
standard: 'Now extend line DA past A using Postulate 2. Drag from point D toward A.',
classical: 'By Postulate 2, produce DA beyond A. Drag from D toward A.',
}),
hint: { type: 'point', pointId: 'pt-D' },
advanceOn: { kind: 'extend-phase' as const, phase: 'extending' as const },
},
{
instruction: `Extend through the circle to place {pt:F} where the line meets it`,
speech: byStyle({
simple:
'Keep going past A and release to place point F. Then DF equals DE. Subtract equals from equals to get AF = BE, and since BE = BC, AF = BC.',
standard:
'Continue past A and release to place F where the line meets the circle. DF equals DE, and since DA equals DB, subtract equals from equals to get AF = BE. Because BE = BC, AF = BC.',
classical:
'Continue past A and release at F. Then DF equals DE. Subtract equals from equals: AF = BE. And since BE = BC, AF = BC.',
}),
hint: { type: 'none' as const },
advanceOn: null,
},
],
]
}
/**
* Proposition I.2: To place at a given point a straight line equal
* to a given straight line.
*
* Given: Point A (the point), segment BC (the line to copy)
*
* Construction (using I.1 as a macro):
* 1. Join A to B (Post.1)
* 2. Construct equilateral △ ABD on AB (I.1 macro)
* 3. Circle at B through C (Post.3) — meets extension of DB at E
* 4. Mark E (Euclid's G)
* 5. Circle at D through E (Post.3) — meets extension of DA at F
* 6. Mark F (Euclid's L)
*
* Result: AF = BC
*
* Element IDs at each step (given: pt-A, pt-B, pt-C, seg-BC):
* Step 1 → seg-2 (AB) [seg-BC is seg count 1]
* Step 2 (macro I.1):
* pt-D (apex — circles are internal to the proven tool)
* seg-3 (DA)
* seg-4 (DB)
* Step 3 → cir-1 (circle B,C)
* Step 4 → pt-E (on extension of DB beyond B)
* Step 5 → cir-2 (circle D,E)
* Step 6 → pt-F (on extension of DA beyond A)
*/
export const PROP_2: PropositionDef = {
id: 2,
title: 'Place a line equal to a given line at a given point',
draggablePointIds: ['pt-A', 'pt-B', 'pt-C'],
// completionMessage derived from proof engine at runtime
resultSegments: [{ fromId: 'pt-A', toId: 'pt-F' }],
givenElements: [
{
kind: 'point',
id: 'pt-A',
x: -1.5,
y: 1.5,
label: 'A',
color: BYRNE.given,
origin: 'given',
},
{
kind: 'point',
id: 'pt-B',
x: 0,
y: 0,
label: 'B',
color: BYRNE.given,
origin: 'given',
},
{
kind: 'point',
id: 'pt-C',
x: 1.5,
y: 0,
label: 'C',
color: BYRNE.given,
origin: 'given',
},
{
kind: 'segment',
id: 'seg-BC',
fromId: 'pt-B',
toId: 'pt-C',
color: BYRNE.given,
origin: 'given',
},
] as ConstructionElement[],
steps: deriveSteps(RECIPE_PROP_2, PROP_2_ANNOTATIONS),
stepInstructionsByStyle: PROP_2_STEP_INSTRUCTIONS,
getTutorial: getProp2Tutorial,
explorationNarration: {
introSpeech:
'You copied a distance using only postulates, definitions, and common notions. Drag points A, B, or C to see the equalities still follow by logic.',
pointTips: [
{
pointId: 'pt-A',
speech:
'AF always equals BC because the circles and subtractions enforce it, not because of measurement.',
},
{
pointId: 'pt-B',
speech: 'The construction moves, but DA = DB and BE = BC still hold, so AF = BC.',
},
{
pointId: 'pt-C',
speech: 'BC sets the circle radius at B, so the copied length always matches BC.',
},
],
},
explorationNarrationByStyle: {
simple: {
introSpeech:
'You copied the length using circles and straight lines. Drag A, B, or C to see AF stay equal to BC.',
pointTips: [
{
pointId: 'pt-A',
speech: 'AF stays equal to BC because the construction forces it.',
},
{
pointId: 'pt-B',
speech: 'DA = DB and BE = BC still hold, so AF = BC.',
},
{
pointId: 'pt-C',
speech: 'BC sets the circle radius at B, so the copy always matches BC.',
},
],
},
standard: {
introSpeech:
'You copied a distance using only postulates, definitions, and common notions. Drag points A, B, or C to see the equalities still follow by logic.',
pointTips: [
{
pointId: 'pt-A',
speech:
'AF always equals BC because the circles and subtractions enforce it, not because of measurement.',
},
{
pointId: 'pt-B',
speech: 'The construction moves, but DA = DB and BE = BC still hold, so AF = BC.',
},
{
pointId: 'pt-C',
speech: 'BC sets the circle radius at B, so the copied length always matches BC.',
},
],
},
classical: {
introSpeech:
'You placed a line equal to the given line by postulates and common notions. Drag A, B, or C to see the equalities persist.',
pointTips: [
{
pointId: 'pt-A',
speech: 'Because DF = DE and DA = DB, the subtraction gives AF = BE.',
},
{
pointId: 'pt-B',
speech: 'Since BE = BC, and AF = BE, we have AF = BC.',
},
{
pointId: 'pt-C',
speech: 'BC fixes the radius, so the copied length always equals BC.',
},
],
},
},
deriveConclusion: recipeToConclusion(RECIPE_PROP_2),
resolveStep(
stepIndex: number,
state: ConstructionState,
_stepData: Map<number, Record<string, unknown>>
): { expected?: ExpectedAction; instruction?: string; highlightIds?: string[] } | null {
if (stepIndex !== 3 && stepIndex !== 5) return null
// Evaluate the full recipe using the geometry engine to get authoritative positions
const ptB = getPoint(state, 'pt-B')
const ptC = getPoint(state, 'pt-C')
const ptA = getPoint(state, 'pt-A')
if (!ptB || !ptC || !ptA) return null
const trace = evaluateRecipe(RECIPE_PROP_2, [ptB, ptC, ptA], RECIPE_REGISTRY)
if (!trace) return null
// Step 3: extend DB past B → E at circle(B, BC) intersection
if (stepIndex === 3) {
const ptE = trace.pointMap.get('E')
const through = getPoint(state, 'pt-B')
if (!ptE || !through) return null
const dist = Math.sqrt((ptE.x - through.x) ** 2 + (ptE.y - through.y) ** 2)
return {
expected: { type: 'extend', baseId: 'pt-D', throughId: 'pt-B', distance: dist, label: 'E' },
}
}
// Step 5: extend DA past A → F at circle(D, DE) intersection
if (stepIndex === 5) {
const ptF = trace.pointMap.get('F')
const through = getPoint(state, 'pt-A')
if (!ptF || !through) return null
const dist = Math.sqrt((ptF.x - through.x) ** 2 + (ptF.y - through.y) ** 2)
return {
expected: { type: 'extend', baseId: 'pt-D', throughId: 'pt-A', distance: dist, label: 'F' },
}
}
return null
},
}
|