Zostrojte rez kocky rovinou KLM: K∈AD, L∈FG, M∈GH

Metóda rovnobežnosti

1.rovnobežku r (K ∈ r ∧ r ∥ ML) 

Zostrojme:

1

2

3

2. priesečníky 1, 2 a 3 rovnobežky s hranami podstavy ABCD

4

5

3. body L a 2 ležia v bočnej stene ⇒ existujú body 4, 5

6

4. body M a 3 ležia v zadnej stene ⇒ existuje bod 6

Rezom je n-uholník určený bodmi K,1, 4, L, ...

A = (-4, -4, 0)
B = (1.0767553765951243, -3.464995019585716, 0)
C = Point(Circle[B, Distance[A, B], Segment[A, B]])
a, D, E, F, G, H, stenaABCD, stenaADHE, stenaABFE, stenaBCGF, stenaCDHG, stenaEFGH, hranaAD, hranaAB, hranaBC, hranaCD, hranaAE, hranaDH, hranaEH, hranaEF, hranaBF, hranaFG, hranaCG, hranaGH = Cube(A, B, C)
K = Point(hranaAD)
L = Point(hranaFG)
M = Point(hranaGH)
f = Line(M, L)
r = Line(K, f)
g = Line(A, B)
h = Line(B, C)
i = Line(C, D)
j = Line(D, A)
I = Intersect(r, g)
J = Intersect(h, r)
N = Intersect(r, i)
k = Line(G, C)
l = Line(J, L)
m = Line(F, B)
O = Intersect(m, l)
P = Intersect(k, l)
Q = Point(j)
n = Line(D, H)
p = Line(N, M)
R = Intersect(n, p)
mnohouholník1, k_1, i_1, o, l_1, m_1, r_1 = Polygon(K, I, O, L, M, R)
b = Plane(K, L, M)
mnohouholník2, S, T, U, V, W, Z, q, s, t, c, d, e = IntersectPath(b, a)