Matematik for lærerstuderende
Geometri 4.-10. klasse
Kapitel 1 - Undersøgelse 1

A = (2.37, 1.47)
B = (13.87, 1.47)
C = (5.947933884297528, 9.568429752066114)
D = (6.328099173553726, 8.18)
E = (6.030578512396701, 7.171735537190081)
F = (5.6008264462809985, 6.213057851239668)
G = (5.022314049586782, 6.08082644628099)
H = (5.0388429752066175, 6.791570247933882)
I = (4.790909090909096, 7.3535537190082625)
J = (4.807438016528931, 8.427933884297518)
K = (4.989256198347113, 8.940330578512395)
L = (5.352892561983477, 9.370082644628097)
polygon1, c, d, e, f, g, h, i, j, k, l = Polygon(C, D, E, F, G, H, I, J, K, L)
M = (7.782644628099182, 9.188264462809915)
N = (6.559504132231412, 9.502314049586776)
O = (6.245454545454552, 9.584958677685949)
P = (5.385950413223147, 5.568429752066114)
Q = (6.080165289256206, 5.221322314049585)
R = (6.443801652892569, 4.890743801652891)
S = (7.022314049586785, 6.1469421487603295)
T = (6.757851239669429, 7.700661157024792)
polygon2, m, n, o, c_1, d_1, e_1, f_1, g_1, p, q, r, s, t = Polygon(M, N, O, C, D, E, F, G, P, Q, R, S, T)
U = (8.642148760330588, 9.17173553719008)
V = (9.881818181818193, 8.741983471074379)
W = (9.518181818181828, 8.39487603305785)
Z = (9.10495867768596, 7.039504132231404)
polygon3, m_1, u, v, w, z_1, t_1 = Polygon(M, U, V, W, Z, T)
A_1 = (6.606702542986458, 4.655922770678466)
B_1 = (6.54273645710537, 4.442702484408174)
C_1 = (8.525685119419089, 3.653787425208094)
D_1 = (9.026752792154275, 4.29344828401897)
E_1 = (8.472380047851516, 5.146329429100137)
polygon4, r_1, a_1, b_1, c_2, d_2, e_2, z_2, t_2, s_1 = Polygon(R, A_1, B_1, C_1, D_1, E_1, Z, T, S)
F_1 = (8.323125847462311, 3.280651924235083)
G_1 = (7.704787017278463, 2.5876859938566343)
H_1 = (6.382821242402651, 2.5237199079755466)
I_1 = (5.935058641235037, 2.6409910654242075)
J_1 = (5.732499369278259, 2.9288384518891015)
K_1 = (6.169600956132358, 3.888329740105415)
polygon5, c_3, f_2, g_2, h_1, i_1, j_1, k_1, b_2 = Polygon(C_1, F_1, G_1, H_1, I_1, J_1, K_1, B_1)
L_1 = Point(w)
M_1 = (10.863645558372843, 7.438447506505779)
N_1 = (12.868982350744943, 7.332903464801984)
O_1 = (12.693075614571951, 8.05998464098368)
P_1 = (12.646167151592488, 8.329708303115599)
Q_1 = (12.294353679246505, 8.869155627379438)
R_1 = (11.930813091155656, 8.998153900572964)
S_1 = (11.227186146463692, 8.951245437593501)
T_1 = (10.464923623047397, 8.728430238441046)
polygon6, l_1, m_2, n_1, o_1, p_1, q_1, r_2, s_2, t_3, v_1, w_1 = Polygon(L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, V, W)
U_1 = (10.69946593794472, 4.999207431573638)
V_1 = (10.3945609285782, 5.116478589022299)
W_1 = (10.136564382191146, 5.081297241787701)
Z_1 = (9.902022067293824, 5.257203977960692)
A_2 = (9.561935710692708, 4.858482042635246)
polygon7, l_2, m_3, u_1, v_2, w_2, z_3, a_2, d_3, e_3, z_4 = Polygon(L_1, M_1, U_1, V_1, W_1, Z_1, A_2, D_1, E_1, Z)
B_2 = (12.552350225633559, 6.488551131171628)
C_2 = (12.51716887839896, 6.312644394998637)
D_2 = (12.376443489460568, 6.12501054308078)
E_2 = (12.036357132859452, 4.78811934816605)
F_2 = (11.754906354982666, 4.354216065606005)
G_2 = (11.109914989015031, 4.389397412840603)
polygon8, m_4, n_2, b_3, c_4, d_4, e_4, f_3, g_3, u_2 = Polygon(M_1, N_1, B_2, C_2, D_2, E_2, F_2, G_2, U_1)

Tool: Opdel linje (command Opdellinje)
Tryk startpunkt og slutpunkt for linjen. Derefter skrives antal opdelinger.
Input: A, B, n
Output: a, list1

a = Segment(A, B)
list1 = Sequence(((k * B) + ((n - k) * A)) / n, k, 1, n)

Tool: Toppunkt & Rødder for funktion. (command Toppunktogrod)
Tryk på en funktion.
Input: f
Output: A, B, C

f(x) = (2 * x^(2)) + (2 * x) - 4
A = Extremum(f)
B, C = Root(f)

Tool: Cirkelbue på x-aksen ud fra 2 punkter (command Cirkelbuepåx)
Afsæt 2 punkter på tegneblokken
Input: A, B
Output: c

b = LineBisector(A, B)
C = Intersect(b, xAxis)
c_1 = Circle(C, A)
D = Intersect(c_1, xAxis, 1)
E = Intersect(c_1, xAxis, 2)
c = CircumcircleArc(D, A, E)

Tool: Parabel gennem 3 punkter (command Parabelgennem3punkter)
Afsæt 3 punkter på tegneblokken.
Input: A, B, C
Output: f

Liste: {A, B, C}
f = FitPoly(Liste, 2)

Tool: Dannebrog
Afsæt 2 punkter
Input: A, B
Output: polygon1, polygon2, polygon3, polygon4, polygon5

f = Segment(A, B)
c = Circle(A, (f / 37 * 12))
d = Circle(A, (f / 28 * 12))
C = Intersect(c, f, 1)
D = Intersect(d, f, 1)
g = OrthogonalLine(A, f)
E = Intersect(c, g, 2)
F = Intersect(d, g, 2)
h = Circle(A, (f / 37 * 28))
G = Intersect(h, g, 2)
i = OrthogonalLine(C, f)
j = OrthogonalLine(D, f)
k = OrthogonalLine(E, g)
l = OrthogonalLine(F, g)
m = OrthogonalLine(G, g)
n = OrthogonalLine(B, f)
H = Intersect(j, m)
I = Intersect(i, m)
J = Intersect(i, l)
K = Intersect(j, l)
L = Intersect(j, k)
M = Intersect(i, k)
N = Intersect(m, n)
polygon1, g_1, i_1, j_1, f_1 = Polygon(G, I, J, F)
polygon2, e_1, m_1, c_1, a = Polygon(E, M, C, A)
O = Intersect(l, n)
P = Intersect(k, n)
polygon3, h_1, n_1, o, k_1 = Polygon(H, N, O, K)
polygon4, l_1, p, b, d_1 = Polygon(L, P, B, D)
polygon5, g_2, n_2, b_1, a_1 = Polygon(G, N, B, A)