Řez pětibokého jehlanu rovinou
Author: Radka Hamříková
Date: 2. leden 2012

Sestrojte řez pětibokého jehlanu rovinou α (5,8,5).

Podstava jehlanu A [2;1,5;0], B [-1;1;0], C [-3;3;0], D [-1,5;5;0], E [1;4,5;0], hlavní vrchol V [5,8,8].

A_1(0)

B_1

C_1

D_1

E_1

V_1(8)

p_1^α

h_1^α(5)

p_1^β

h_1^β(8)

4

6

5

h_1^β(5)

D'_1

E'_1

I

A'_1

II

B'_1

III

C'_1

A = (-1, -1)
B = (-3, -3)
C = (-1.5, -5)
D = (1, -4.5)
E = (2, -1.5)
F = (5, -8)
a = Segment(F, C)
b = Segment(F, D)
c = Segment(F, E)
d = Segment(E, D)
e = Segment(D, C)
f = Segment(C, B)
g = Segment(B, A)
h = Segment(A, E)
i = Segment(A, F)
j = Segment(B, F)
G = Point(xAxis)
H = (0, -8)
I = Point(xAxis)
k = Line(G, H)
l = Line(I, k)
m = Line(C, D)
n = Line(F, m)
J = Midpoint(C, F)
K = Midpoint(J, F)
L = Midpoint(J, K)
p = Line(L, m)
M = Intersect(k, m)
N = Intersect(l, p)
q = Line(N, M)
O = Intersect(q, a)
P = Intersect(q, b)
r = Segment(O, P)
s = Line(E, D)
Q = Intersect(k, s)
t = Line(Q, P)
R = Intersect(t, c)
a_1 = Segment(P, R)
b_1 = Line(A, E)
S = Intersect(k, b_1)
c_1 = Line(S, R)
T = Intersect(c_1, i)
d_1 = Segment(R, T)
e_1 = Line(B, C)
U = Intersect(k, e_1)
f_1 = Line(U, O)
V = Intersect(f_1, j)
g_1 = Segment(O, V)
h_1 = Segment(V, T)
mnohoúhelník1, o, p_1, r_1, t_1, v = Polygon(O, P, R, T, V)