Dit is een bestand van Wikimedia Commons. Onderstaande beschrijving komt van de beschrijving van het bestand daar. Commons is een vrij-gelicenceerde database voor afbeeldingen, geluid, video en andere bestanden.
The main reason for this diagram is to emphasise that the Fermat point is NOT the same as the first isogonic center which is (unfortunately) a very widespread misconception. The source is licensed under the same license as the image. Feel free to edit, fix, or improve it!
fermat_point_scope.euk
% Combination of 3 figures in 1.
box(0,0,10,24)
draw(segment(point(0,9),point(10,9)))
draw(segment(point(0,16),point(10,16)))
% Proof that the Fermat point lies within the triangle
A = point(7,21)
B = point(1,18)
C = point(9,18)
D = point(4,17)
E = point(7.5,23)
thickness(2)
draw(line(B,C))
draw(line(A,B))
draw(line(A,C))
thickness(0.5)
draw(segment(D,A))
draw(segment(D,B))
draw(segment(D,C))
draw(segment(E,A))
draw(segment(E,B))
draw(segment(E,C))
label(A,0.2,170:)
label(B,0.2,110:)
label(C,0.2,45:)
draw($P'$,intersection(line(A,D),line(B,C)),0.1,280:)
draw($P$,D,0.1,270:)
draw("\textbf{A-zone only}",D,2,350:)
draw($P'$,A,0.2,355:)
draw($P$,E,0.2,0:)
draw("\textbf{B-zone and C-zone}",E,0.4,90:)
draw("\textbf{C-zone only}",segment(A,B),2,120:)
% Case 1 - an angle at least 120 degrees
H = point(6,11.5)
I = point(1,10)
J = point(9,10)
K = point(4.8,10.5)
I H F equilateral
K H G equilateral
thickness(2)
draw(H,I,J)
thickness(0.5)
draw(H,K,G)
draw(segment(F,H))
draw(segment(F,I))
draw(segment(F,G))
draw(segment(K,I))
draw(segment(K,J))
draw($A$,H,0.2,20:)
draw($B$,I,0.2,180:)
draw($C$,J,0.2,0:)
draw($P$,K,0.1,270:)
draw($Q$,G,0.1,210:)
draw($F$,F,0.2,180:)
draw("\textbf{\Huge Case 1}",F,4.5,0:)
mark(segment(K,I),simple,0.7)
mark(segment(G,F),simple,0.7)
mark(segment(H,K),double,0.7)
mark(segment(K,G),double,0.7)
mark(segment(G,H),double,0.7)
mark(segment(H,I),triple,0.7)
mark(segment(I,F),triple,0.7)
mark(segment(F,H),triple,0.7)
% Case 2 - no angle greater than 120 degrees
L = point(4,8)
M = point(3.5,5)
N = point(9,5)
P = point(6.2,6.1)
M L O equilateral
N P Q equilateral
N M R equilateral
S = intersection(line(N,O),line(L,R))
N S T equilateral
thickness(2)
draw(L,M,N)
thickness(0.5)
draw(N,P,Q)
draw(segment(M,R))
draw(segment(N,R))
draw(segment(O,L))
draw(segment(O,M))
draw(segment(R,Q))
draw(segment(P,L))
draw(segment(P,N))
draw(segment(M,P))
draw(segment(S,M))
draw($A$,L,0.2,20:)
draw($B$,M,0.2,180:)
draw($C$,N,0.2,0:)
draw($P$,P,0.2,180:)
draw($Q$,Q,0.1,180:)
draw($F$,O,0.2,180:)
draw($D$,R,0.2,0:)
draw($P_0$,S,0.1,45:)
draw($Q_0$,T,0.1,0:)
draw("\textbf{\Huge Case 2}",L,2.5,0:)
draw(segment(L,R))
draw(segment(N,O))
draw(segment(N,T))
mark(segment(M,P),simple,0.7)
mark(segment(Q,R),simple,0.7)
mark(segment(N,P),triple,0.7)
mark(segment(N,Q),triple,0.7)
mark(segment(P,Q),triple,0.7)
mark(segment(M,N),double,0.7)
mark(segment(M,R),double,0.7)
mark(segment(N,R),double,0.7)
Licentie
Public domainPublic domainfalsefalse
Ik, de auteursrechthebbende van dit werk, geef dit werk vrij in het publieke domein. Dit is wereldwijd van toepassing. In sommige landen is dit wettelijk niet mogelijk; in die gevallen geldt: Ik sta iedereen toe dit werk voor eender welk doel te gebruiken, zonder enige voorwaarden, tenzij zulke voorwaarden door de wet worden voorgeschreven.
{{Information |Description={{en|1=Proof that the Fermat point cannot lie outside the triangle}} |Source=Own work by uploader |Author=MRFS |Date=31 August 2008 |Permission= |other_versions= }} <!--{{ImageUpload|full}}--> [[Category:Fermat po