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." |
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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) |