### Complete construction protocol for the mirascope project

For a step-by-step demonstration of the protocol, please open a dynamic worksheet (link), go to View and then Construction Protocols. No. Name Definition Value
1 Number a   a = 0.15
2 Number c   c = 1.67
3 Function pu pu(x) = a x² pu(x) = 0.15 x²
4 Function pd pd(x) = -(a) x² + c pd(x) = -(0.15) x² + 1.67
5 Point P   P = (0.36, 0.22)
6 Point G Point on pd G = (1.19, 1.46)
7 Line j Tangent to pd at x = x(G) j: y = -0.36x + 1.88
8 Line k Line through G perpendicular to j k: -x + 0.36y = -0.67
9 Segment i Segment [P, G] i = 1.49
10 Point P' P mirrored at k P' = (1.05, -0.03)
11 Point G'1 G mirrored at k G'1 = (1.19, 1.46)
12 Segment i' Segment [P', G'1] i' = 1.49
13 Ray l Ray through G, P' l: 1.49x - 0.14y = 1.57
14 Point E Intersection point of pu, l E = (1.07, 0.17)
15 Segment m Segment [G, E] m = 1.29
16 Line n Tangent to pu at x = x(E) n: y = 0.32x - 0.17
17 Line p Line through E perpendicular to n p: -x - 0.32y = -1.12
18 Point G' G mirrored at p G' = (0.22, 1.14)
19 Point E' E mirrored at p E' = (1.07, 0.17)
20 Segment m' Segment [G', E'] m' = 1.29
21 Ray q Ray through E', G' q: -0.97x - 0.85y = -1.19
22 Point H Point on pd H = (-1.61, 1.28)
23 Segment b MiraReflection[P, H, a, c] b = 2.24
23 Segment d MiraReflection[P, H, a, c] d = 0.84
23 Point I MiraReflection[P, H, a, c] I = (-1.75, 0.46)
23 Ray e MiraReflection[P, H, a, c] e: -0.59x + 0.6y = 1.3
24 Point J Intersection point of q, e J = (-0.37, 1.82)
25 Text text1   text1 = "Drag P to draw a small picture;
Right click on P or J to toggle Trace On.

Drag c to change vertical alignment of the two parabolas;
Drag a to change the curvature of the parabolas."
26 Point A   A = (-2, 3)
27 Point B   B = (2, 3)
28 Line f Line through A parallel to yAxis f: x = -2
29 Line g Line through B parallel to yAxis g: x = 2
30 Point C Intersection point of pu, f C = (-2, 0.6)
31 Point D Intersection point of pu, g D = (2, 0.6)
32 Line h Tangent to pu at x = x(C) h: y = -0.6x - 0.6
33 Line r Tangent to pu at x = x(D) r: y = 0.6x - 0.6
34 Line s Line through C perpendicular to h s: -x + 0.6y = 2.36
35 Line t Line through D perpendicular to r t: -x - 0.6y = -2.36
36 Line g' g mirrored at t g': -0.47x - 0.88y = -1.47
37 Line f' f mirrored at s f': -0.47x + 0.88y = 1.47
38 Point F Intersection point of f', g' F = (0, 1.67)
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