TXM728: Area in Distance Geometry
1
. Note
TXM728 is the author’s formula code
TXM728 is the author’s formula code
2
.Caption
LetA,B,C,D,E,Fbesixarbitrarypoints.Thenwehave:16=++++++++---------Where=areaΔABC=areaΔDEF
S
ABC
S
DEF
2
DA
2
EB
2
DB
2
EC
2
DC
2
EA
2
EA
2
FB
2
EB
2
FC
2
EC
2
FA
2
FA
2
DB
2
FB
2
DC
2
FC
2
DA
2
DB
2
EA
2
DC
2
EB
2
DA
2
EC
2
EB
2
FA
2
EC
2
FB
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EA
2
FC
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FB
2
DA
2
FC
2
DB
2
FA
2
DC
S
ABC
S
DEF
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.Code
In[]:=
ManipulateModule{AA,BB,CC,DD,EE,FF,ABC,DEF,DA,DB,DC,EA,EB,EC,FA,FB,FC},AA={z^2+x^2,0};BB={((-x^2)*y^2+x^2*z^2+y^2*z^2+z^4)/(x^2+z^2),(2*Sqrt[x^2*y^2*z^2*(x^2+y^2+z^2)])/(x^2+z^2)};CC={0,0};DD={m,n};EE={p,q};FF={r,s};ABC=Area[Triangle[{AA,BB,CC}]];DEF=Area[Triangle[{DD,EE,FF}]];DA=EuclideanDistance[DD,AA];DB=EuclideanDistance[DD,BB];DC=EuclideanDistance[DD,CC];EA=EuclideanDistance[EE,AA];EB=EuclideanDistance[EE,BB];EC=EuclideanDistance[EE,CC];FA=EuclideanDistance[FF,AA];FB=EuclideanDistance[FF,BB];FC=EuclideanDistance[FF,CC];ColumnText@Grid","++++++++---------",
"16S
ABC
S
DEF
2
DA
2
EB
2
DB
2
EC
2
DC
2
EA
2
EA
2
FB
2
EB
2
FC
2
EC
2
FA
2
FA
2
DB
2
FB
2
DC
2
FC
2
DA
2
DB
2
EA
2
DC
2
EB
2
DA
2
EC
2
EB
2
FA
2
EC
2
FB
2
EA
2
FC
2
FB
2
DA
2
FC
2
DB
2
FA
2
DC
{16×ABC×DEF,FullSimplify[Abs[(-EB^2)*FA^2+EC^2*FA^2+EA^2*FB^2-EC^2*FB^2+DC^2*(EA^2-EB^2-FA^2+FB^2)+(-EA+EB)*(EA+EB)*FC^2+DB^2*(-EA^2+EC^2+FA^2-FC^2)+DA^2*(EB^2-EC^2-FB^2+FC^2)]]},Frame->All,FrameStyle->Hue[.6,.4,.8],Background->{None,{{None,GrayLevel[.9]}},{{1,1}->Hue[.6,.2,1],{1,2}->Hue[.6,.2,1]}},BaseStyle->{FontFamily->Times,FontSize->20},{Graphics[{Style[Point/@{AA,BB,CC,DD,EE,FF}],Text[Style["A",20,"Label"],AA+{0,.15}],Text[Style["B",20,"Label"],BB+{0,.15}],Text[Style["C",20,"Label"],CC+{0,.15}],Text[Style["D",20,"Label"],DD+{0,.15}],Text[Style["E",20,"Label"],EE+{0,.15}],Text[Style["F",20,"Label"],FF+{0,.15}],Style[{Line[{DD,AA}],Line[{DD,BB}],Line[{DD,CC}],Line[{EE,AA}],Line[{EE,BB}],Line[{EE,CC}],Line[{FF,AA}],Line[{FF,BB}],Line[{FF,CC}]},Gray,DotDashed,Thick],Style[Triangle[{AA,BB,CC}],Opacity[.2`],RGBColor[x,y,z],EdgeForm[{Thick,Blue}]],Style[Triangle[{DD,EE,FF}],Opacity[.2`],RGBColor[m,q,r],EdgeForm[{Thick,Red}]]},ImageSize{450,375}]},Alignment{Center,Top},Style["TXM728",30,FontFamily->"Times",Bold],Column[{Row[{Control@{{x,5/6,Style["x",15]},-5,5,1/6,Appearance->"Labeled"},Control@{{m,-5/6,Style["m",15]},-5,5,1/6,Appearance->"Labeled"},Control@{{n,5/2,Style["n",15]},-5,5,1/6,Appearance->"Labeled"}}],Row[{Control@{{y,2,Style["y",15]},-5,5,1/7,Appearance->"Labeled"},Control@{{p,4/3,Style["p",15]},-5,5,1/7,Appearance->"Labeled"},Control@{{q,1/2,Style["q",15]},-5,5,1/7,Appearance->"Labeled"}}],Row[{Control@{{z,5/3,Style["z",15]},-5,5,1/6,Appearance->"Labeled"},Control@{{r,-1/3,Style["r",15]},-5,5,1/6,Appearance->"Labeled"},Control@{{s,7/2,Style["s",15]},-5,5,1/6,Appearance->"Labeled"}}]}],SaveDefinitions->True
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.Author information