Press n or j to go to the next uncovered block, b, p or k for the previous block.
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import { BYRNE } from '../types'
import { deriveSteps } from '../engine/recipe/deriveSteps'
import { RECIPE_PROP_3, PROP_3_ANNOTATIONS } from '../engine/recipe/definitions/prop3'
function getProp3Tutorial(isTouch: boolean): TutorialSubStep[][] {
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'
return [
// ── Step 0: Place at A a line equal to CD (I.2 macro) ──
// Input order: segment start (C), segment end (D), target (A)
[
{
instruction: `${tap} point {pt:C}`,
speech: isTouch
? "We need to copy the length of line CD to point A. We'll use Proposition Two to do this. Tap point C first — the start of the line to copy."
: "We need to copy the length of line CD to point A. We'll use Proposition Two to do this. Click point C first — the start of the line to copy.",
hint: { type: 'point', pointId: 'pt-C' },
advanceOn: { kind: 'macro-select', index: 0 },
},
{
instruction: `${tap} point {pt:D}`,
speech: isTouch
? 'Now tap point D — the end of the shorter line. This tells Proposition Two which line to copy.'
: 'Now click point D — the end of the shorter line. This tells Proposition Two which line to copy.',
hint: { type: 'point', pointId: 'pt-D' },
advanceOn: { kind: 'macro-select', index: 1 },
},
{
instruction: `${tap} point {pt:A}`,
speech: isTouch
? "Now tap point A — that's where the copy goes."
: "Now click point A — that's where the copy goes.",
hint: { type: 'point', pointId: 'pt-A' },
advanceOn: null,
},
],
// ── Step 1: Draw circle centered at A through E ──
[
{
instruction: `${tapHold} point {pt:A}`,
speech: isTouch
? "Now we'll use the compass. The new point E is exactly as far from A as CD is long. Press and hold on A."
: "Now we'll use the compass. Point E is exactly as far from A as CD is long. Click and hold on A.",
hint: { type: 'point', pointId: 'pt-A' },
advanceOn: { kind: 'compass-phase', phase: 'center-set' },
},
{
instruction: `${drag} to point {pt:E}`,
speech: isTouch
? 'Drag to point E — this sets the compass to the length we copied.'
: 'Drag to point E — this sets the compass to the copied length.',
hint: { type: 'arrow', fromId: 'pt-A', toId: 'pt-E' },
advanceOn: { kind: 'compass-phase', phase: 'radius-set' },
},
{
instruction: `${sweep} around`,
speech: isTouch ? 'Sweep around to draw the circle!' : 'Move around to draw the circle!',
hint: { type: 'sweep', centerId: 'pt-A', radiusPointId: 'pt-E' },
advanceOn: null,
},
],
// ── Step 2: Mark where circle crosses AB → pt-F ──
[
{
instruction: `${tap} where the circle crosses line {seg:AB}`,
speech:
"See where the circle crosses line AB? Tap that intersection point. The line from A to that point is exactly the same length as CD — that's what we wanted to cut off!",
hint: {
type: 'candidates',
ofA: { kind: 'circle', centerId: 'pt-A', radiusPointId: 'pt-E' },
ofB: { kind: 'segment', fromId: 'pt-A', toId: 'pt-B' },
},
advanceOn: null,
},
],
]
}
/**
* Proposition I.3: Given two unequal straight lines, to cut off from
* the greater a straight line equal to the less.
*
* Given: Segment AB (longer, horizontal), segment CD (shorter, below-right)
*
* Construction:
* 0. Place at A a line equal to CD (I.2 macro) → pt-E, seg-AE
* 1. Draw circle centered at A through E (Post.3)
* 2. Mark where circle crosses AB (Def.15) → pt-F
*
* Result: AF = CD
*
* The proof chain:
* AE = CD (I.2, from macro)
* AF = AE (Def.15, F on circle(A,E))
* AF = CD (C.N.1, transitive via union-find)
*/
export const PROP_3: PropositionDef = {
id: 3,
title: 'Cut off from the greater a line equal to the less',
draggablePointIds: ['pt-A', 'pt-B', 'pt-C', 'pt-D'],
resultSegments: [{ fromId: 'pt-A', toId: 'pt-F' }],
givenElements: [
{
kind: 'point',
id: 'pt-A',
x: -2.5,
y: 0.5,
label: 'A',
color: BYRNE.given,
origin: 'given',
},
{
kind: 'point',
id: 'pt-B',
x: 1.5,
y: 0.5,
label: 'B',
color: BYRNE.given,
origin: 'given',
},
{
kind: 'point',
id: 'pt-C',
x: 0.5,
y: -1.5,
label: 'C',
color: BYRNE.given,
origin: 'given',
},
{
kind: 'point',
id: 'pt-D',
x: 2.0,
y: -1.5,
label: 'D',
color: BYRNE.given,
origin: 'given',
},
{
kind: 'segment',
id: 'seg-AB',
fromId: 'pt-A',
toId: 'pt-B',
color: BYRNE.given,
origin: 'given',
},
{
kind: 'segment',
id: 'seg-CD',
fromId: 'pt-C',
toId: 'pt-D',
color: BYRNE.given,
origin: 'given',
},
] as ConstructionElement[],
steps: deriveSteps(RECIPE_PROP_3, PROP_3_ANNOTATIONS),
getTutorial: getProp3Tutorial,
explorationNarration: {
introSpeech:
'You cut off an equal piece! Try dragging all four points to see how the construction adapts.',
pointTips: [
{
pointId: 'pt-A',
speech:
'See how the cut-off piece still matches the shorter segment? It works wherever A goes.',
},
{
pointId: 'pt-B',
speech: 'Watch what happens as AB changes length. What if it gets really short?',
},
{
pointId: 'pt-C',
speech: 'See the cut adjusting? It always matches the shorter line exactly.',
},
{
pointId: 'pt-D',
speech: 'Watch the circle adjust. The cut-off piece stays equal no matter what.',
},
],
breakdownTip:
'Oh! The shorter line became longer than the other one. Euclid said we need to cut from the greater — when that rule breaks, the construction falls apart!',
},
}
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