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,
TutorialSubStep,
EuclidNarrationOptions,
} from '../types'
import type { KidLanguageStyle } from '@/db/schema/player-session-preferences'
import { BYRNE } from '../types'
import { deriveSteps } from '../engine/recipe/deriveSteps'
import { RECIPE_PROP_1, PROP_1_ANNOTATIONS } from '../engine/recipe/definitions/prop1'
const DEFAULT_LANGUAGE_STYLE: KidLanguageStyle = 'standard'
const PROP_1_STEP_INSTRUCTIONS: Record<KidLanguageStyle, string[]> = {
simple: [
'Draw a circle with center {pt:A} through {pt:B}',
'Draw a circle with center {pt:B} through {pt:A}',
'Mark where the circles cross',
'Draw a line from {pt:C} to {pt:A}',
'Draw a line from {pt:C} to {pt:B}',
],
standard: [
'Draw a circle centered at {pt:A} through {pt:B}',
'Draw a circle centered at {pt:B} through {pt:A}',
'Mark the point where the circles meet',
'Draw a line from {pt:C} to {pt:A}',
'Draw a line from {pt:C} to {pt:B}',
],
classical: [
'Describe a circle with center {pt:A} and radius {seg:AB}',
'Describe a circle with center {pt:B} and radius {seg:BA}',
'Mark where the circles cut one another',
'Join {pt:C} to {pt:A}',
'Join {pt:C} to {pt:B}',
],
}
function getProp1Tutorial(isTouch: boolean, options?: EuclidNarrationOptions): TutorialSubStep[][] {
const style = options?.languageStyle ?? DEFAULT_LANGUAGE_STYLE
const tapHold = isTouch ? 'Tap and hold' : 'Click and hold'
const drag = isTouch ? 'Drag' : 'Drag'
const sweep = isTouch ? 'Sweep your finger' : 'Move your mouse'
const tap = isTouch ? 'Tap' : 'Click'
const byStyle = (copy: Record<KidLanguageStyle, string>) => copy[style] ?? copy.standard
return [
// ── Step 0: Circle centered at A through B ──
[
{
instruction: `${tapHold} point {pt:A}`,
speech: isTouch
? byStyle({
simple:
'Postulate 3 lets us draw a circle from any center with any radius. Press and hold on A to choose the center.',
standard:
'Postulate 3 says we may describe a circle with any center and radius. Press and hold on A to set the center.',
classical:
'By Postulate 3, describe a circle with any center and radius. Take A as the center.',
})
: byStyle({
simple:
'Postulate 3 lets us draw a circle from any center with any radius. Click and hold on A to choose the center.',
standard:
'Postulate 3 says we may describe a circle with any center and radius. Click and hold on A to set the center.',
classical:
'By Postulate 3, describe a circle with any center and radius. Take A as the center.',
}),
hint: { type: 'point', pointId: 'pt-A' },
advanceOn: { kind: 'compass-phase', phase: 'center-set' },
},
{
instruction: `${drag} to point {pt:B}`,
speech: byStyle({
simple: 'Drag to B to set the radius. Every point on this circle is AB away from A.',
standard:
'Drag to B to set the radius. Every point on this circle will be exactly AB away from A.',
classical:
'Drag to B to set the radius AB. Every point on the circle is at a distance AB from A.',
}),
hint: { type: 'arrow', fromId: 'pt-A', toId: 'pt-B' },
advanceOn: { kind: 'compass-phase', phase: 'radius-set' },
},
{
instruction: `${sweep} all the way around`,
speech: isTouch
? byStyle({
simple: 'Sweep around to draw the circle centered at A.',
standard: 'Sweep all the way around to draw the circle centered at A with radius AB.',
classical: 'Carry the circle around until it is complete.',
})
: byStyle({
simple: 'Move around to draw the circle centered at A.',
standard: 'Move all the way around to draw the circle centered at A with radius AB.',
classical: 'Carry the circle around until it is complete.',
}),
hint: { type: 'sweep', centerId: 'pt-A', radiusPointId: 'pt-B' },
advanceOn: null,
},
],
// ── Step 1: Circle centered at B through A ──
[
{
instruction: `${tapHold} point {pt:B}`,
speech: isTouch
? byStyle({
simple: 'Now do the same with center B. Press and hold on B.',
standard: 'Now do the same with center B. Press and hold on B.',
classical: 'Again, take B as the center.',
})
: byStyle({
simple: 'Now do the same with center B. Click and hold on B.',
standard: 'Now do the same with center B. Click and hold on B.',
classical: 'Again, take B as the center.',
}),
hint: { type: 'point', pointId: 'pt-B' },
advanceOn: { kind: 'compass-phase', phase: 'center-set' },
},
{
instruction: `${drag} to point {pt:A}`,
speech: byStyle({
simple: 'Drag to A to set the radius BA. Every point on this circle is BA away from B.',
standard:
'Drag to A to make the radius BA. Every point on this circle is BA away from B.',
classical:
'Drag to A so the radius is BA. Every point on this circle is at distance BA from B.',
}),
hint: { type: 'arrow', fromId: 'pt-B', toId: 'pt-A' },
advanceOn: { kind: 'compass-phase', phase: 'radius-set' },
},
{
instruction: `${sweep} around again`,
speech: isTouch
? byStyle({
simple: 'Sweep around to draw the second circle.',
standard: 'Sweep all the way around to draw the second circle.',
classical: 'Carry the circle around again.',
})
: byStyle({
simple: 'Move around to draw the second circle.',
standard: 'Move all the way around to draw the second circle.',
classical: 'Carry the circle around again.',
}),
hint: { type: 'sweep', centerId: 'pt-B', radiusPointId: 'pt-A' },
advanceOn: null,
},
],
// ── Step 2: Mark intersection ──
[
{
instruction: `${tap} where the circles cross`,
speech: byStyle({
simple: 'Tap where the circles cross. That point is the same distance from A and from B.',
standard:
'Mark a point where the circles meet. That point is on both circles, so it is the same distance from A as from B.',
classical:
'Mark one of the points where the circles cut one another; it lies on both circles and is equidistant from A and B.',
}),
hint: { type: 'candidates' },
advanceOn: null,
},
],
// ── Step 3: Segment C → A ──
[
{
instruction: `${drag} from {pt:C} to {pt:A}`,
speech: byStyle({
simple:
'Postulate 1 lets us draw a straight line from any point to any point. Draw the line from C to A.',
standard:
'Postulate 1 lets us draw a straight line from any point to any point. Draw the line from C to A.',
classical: 'By Postulate 1, join C to A.',
}),
hint: { type: 'arrow', fromId: 'pt-C', toId: 'pt-A' },
advanceOn: null,
},
],
// ── Step 4: Segment C → B ──
[
{
instruction: `${drag} from {pt:C} to {pt:B}`,
speech: byStyle({
simple:
'Draw the line from C to B. Now CA = AB and CB = AB, so all three sides are equal.',
standard:
'Draw the line from C to B. Now CA = AB and CB = AB, so the triangle is equilateral.',
classical:
'Join C to B. Since CA equals AB and CB equals AB, the triangle is equilateral.',
}),
hint: { type: 'arrow', fromId: 'pt-C', toId: 'pt-B' },
advanceOn: null,
},
],
]
}
/**
* Proposition I.1: On a given finite straight line to construct
* an equilateral triangle.
*/
export const PROP_1: PropositionDef = {
id: 1,
title: 'Construct an equilateral triangle on a given line',
draggablePointIds: ['pt-A', 'pt-B'],
givenElements: [
{
kind: 'point',
id: 'pt-A',
x: -2,
y: 0,
label: 'A',
color: BYRNE.given,
origin: 'given',
},
{
kind: 'point',
id: 'pt-B',
x: 2,
y: 0,
label: 'B',
color: BYRNE.given,
origin: 'given',
},
{
kind: 'segment',
id: 'seg-AB',
fromId: 'pt-A',
toId: 'pt-B',
color: BYRNE.given,
origin: 'given',
},
] as ConstructionElement[],
steps: deriveSteps(RECIPE_PROP_1, PROP_1_ANNOTATIONS),
stepInstructionsByStyle: PROP_1_STEP_INSTRUCTIONS,
// completionMessage derived from proof engine at runtime
resultSegments: [
{ fromId: 'pt-A', toId: 'pt-C' },
{ fromId: 'pt-C', toId: 'pt-B' },
{ fromId: 'pt-A', toId: 'pt-B' },
],
getTutorial: getProp1Tutorial,
explorationNarration: {
introSpeech:
'You built an equilateral triangle by definition: C lies on both circles, so CA = AB and CB = AB. Drag A or B to see the logic still forces those equalities.',
pointTips: [
{
pointId: 'pt-A',
speech: 'No matter where A moves, C stays on both circles, so CA and AB remain equal.',
},
{
pointId: 'pt-B',
speech:
'C stays the same distance from B as A is from B, so the triangle stays equilateral.',
},
],
},
explorationNarrationByStyle: {
simple: {
introSpeech:
'C is on both circles, so CA = AB and CB = AB. Drag A or B and watch the equal sides stay equal.',
pointTips: [
{
pointId: 'pt-A',
speech: 'C stays on both circles, so CA always matches AB.',
},
{
pointId: 'pt-B',
speech: 'C stays the same distance from B as A does, so the triangle stays equal.',
},
],
},
standard: {
introSpeech:
'You built an equilateral triangle by definition: C lies on both circles, so CA = AB and CB = AB. Drag A or B to see the logic still forces those equalities.',
pointTips: [
{
pointId: 'pt-A',
speech: 'No matter where A moves, C stays on both circles, so CA and AB remain equal.',
},
{
pointId: 'pt-B',
speech:
'C stays the same distance from B as A is from B, so the triangle stays equilateral.',
},
],
},
classical: {
introSpeech:
'C lies on both circles, so CA = AB and CB = AB. Hence the triangle is equilateral. Drag A or B to see the equalities persist.',
pointTips: [
{
pointId: 'pt-A',
speech: 'Because C remains on the circle with center A, CA is always equal to AB.',
},
{
pointId: 'pt-B',
speech: 'Because C remains on the circle with center B, CB is always equal to AB.',
},
],
},
},
}
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