Elements of the triangle ::
about ::
The interior angle bisectors of a triangle
Circumscribed circle - Wikipedia
Mollweide's formula - Wikipedia
...
def ::
{a2=b2+c2−2bc·Cos αb2=c2+a2−2ca·Cos ßc2=a2+b2−2ab·Cos γ
2·p=P=a+b+c
abc4R=pr=S=√p(p−a)(p−b)(p−c)
2R2 Sin α Sin ß Sin γ=S=p2 Tan α2 Tan ß2 Tan γ2
{ha=2a·Shb=2b·Shc=2c·S
1r=1ha+1hb+1hc
r2=(p−a)(p−b)(p−c)p
2·R=aSin α=bSin ß=aSin γ
R=abc√(a+b−c)(b+c−a)(c+a−b)(a+b+c)
S={a·ha2b·hb2c·hc2={bc·Sin α2ca·Sin ß2ab·Sin γ2={a2 Sin ß Sin γ2 Sin αb2 Sin γ Sin α2 Sin ßc2 Sin α Sin ß2 Sin γ
some x-ref formulas to verify the above figure and formulas ::
Some basics ::
The intersection of two lines ::
{y=a0·x+b0y=a1·x+b1 → [Δs=s1−s0] →
from: y=ax+b0=x·Δa+Δbthus:x=− ΔbΔa=− b1−b0a1−a0from: ya=x+bay·Δ1a=0+Δbathus:y=ΔbaΔ1a=b1a1−b0a01a1−1a0=a0b1−a1b0a0−a1
The intersection of an arbitrary line and the perpendicular line crossing it drawn through an arbitrary point ::
! note : the slope for the perpendicular line in the below tutor is
my notation : a⊥=− 1a (about : Parallel and perpendicular symbol from Mathematica to $\LaTeX$ - Mathematica Stack Exchange)
the notation in the video tutor : m⊥=− 1m
The intersection of two Circles ::
... write out general , analytical solution for the system :
{(x−a0)2+(y−b0)2=R0(x−a1)2+(y−b1)2=R1
etc. ...
[Eop]
No comments:
Post a Comment