Hulknurk \; ja \; tema \; sisenurkade \; summa

Kõige \; väiksem \; geomeetriline \; kujund \; on\punkt. \; Kui \; tasandil \; ühendada \; mitu\punkti \; lõikudega, \; siis \; tekib \; murdjoon.

Murdjooni \; on \; nii \; kinniseid \; kui  \; lahtiseid.\Meie \; vaatleme \; kinnist \; murdjoont.\Hulknurgaks \; nimetatakse \; lihtsat \; kinnist \; murdjoont \; \left( joonisel \; lilla  \right)  .

Kui \; saadud \; hulknurga \; külgi \; pikendada, \; siis \; näeme, \; et \;\külgede \; pikendused \; ei  \; lõika \; murdjoont.\Sellist \; hulknurka \; nimetatakse \; kumeraks \; hulknurgaks.

Tekkis \;ebakorrapärane\left(   küljed \; on \; kõik \; eripikkused\right) \7-nurkne \; kumer \; hulknurk.

Kui \; ühest \; hulknurga \; tipust \; tõmmata \; diagonaalid,\siis \; tekib  \; tema  \; sisse \; 5 \; kolmnurka.

Teades \; mitu \; kolmnurka \; on  \; hulknurga \; sees,\saame \; kasutades \; kolmnurga \; sisenurkade\reeglit,  \; arvutada \; kogu \; hulknurga \; sisenurkade \; summa.

Kogu  \; hulknurga \; sisenurkade \; summa \; on\5×180⁰=900⁰

Läbi  \; tippude \; arvu  \; n \; on  \; meil \; samuti\võimalus  \; leida \; iga \; kumera \; hulknurga \; sisenurkade\summa\s=\left( n-2  \right)×180⁰ \
n=tippude \; arv

A = (2.05, 0.3)
a = 1 (slider from 1 to 16, step 1)
B = (4.48, 2.16)
C = (8.71, 3.03)
D = (11.2, -0.81)
E = (9.46, -3.63)
f = Segment(A, B)
g = Segment(B, C)
h = Segment(C, D)
i = Segment(D, E)
F = (2.44, -3.21)
G = (6.64, -4.35)
j = Segment(A, F)
k = Segment(F, G)
l = Segment(G, E)
hulknurk1, a_1, b, c, d, e, g_1, f_1 = Polygon(A, B, C, D, E, G, F)
m = Line(C, D)
n = Line(A, B)
p = Line(F, G)
r = Line(A, F)
s = Line(G, E)
t = Line(B, C)
q = Segment(A, C)
h_1 = Segment(A, D)
i_1 = Segment(A, E)
j_1 = Segment(A, G)
t2, d_1, a_3, c_2 = Polygon(A, C, D)
t3, e_1, a_4, d_2 = Polygon(A, D, E)
t4, g_2, a_5, e_2 = Polygon(A, E, G)
t5, g_3, a_6, f_2 = Polygon(A, F, G)
t1, c_1, a_2, b_1 = Polygon(A, B, C)
kaugusFG = Distance(F, G)
TekstFG: Name[F] + (Name[G]) + " = " + kaugusFG
kaugusFA = Distance(F, A)
TekstFA: Name[F] + (Name[A]) + " = " + kaugusFA
kaugusAB = Distance(A, B)
TekstAB: Name[A] + (Name[B]) + " = " + kaugusAB
kaugusBC = Distance(B, C)
TekstBC: Name[B] + (Name[C]) + " = " + kaugusBC
kaugusCD = Distance(C, D)
TekstCD: Name[C] + (Name[D]) + " = " + kaugusCD
kaugusDE = Distance(D, E)
TekstDE: Name[D] + (Name[E]) + " = " + kaugusDE
kaugusEG = Distance(E, G)
TekstEG: Name[E] + (Name[G]) + " = " + kaugusEG
k_1 = Segment(A, C)
l_1 = Segment(A, D)
m_1 = Segment(A, E)
n_1 = Segment(A, G)
α = Angle(F, A, B)
β = Angle(A, B, C)
γ = Angle(B, C, D)
δ = Angle(C, D, E)
ε = Angle(D, E, G)
ζ = Angle(E, G, F)
η = Angle(G, F, A)
tekst10: "s=" + (LaTeX[α]) + "+" + (LaTeX[β]) + "+" + (LaTeX[γ]) + "+" + (LaTeX[δ]) + "+" + (LaTeX[ε]) + "+" + (LaTeX[ζ]) + "+" + (LaTeX[η]) + "=900⁰"
p_1 = Line(E, D)