a2+b2=c2⇒c=a2+b2{\displaystyle a^{2}+b^{2}=c^{2}\Rightarrow c={\sqrt {a^{2}+b^{2}}}} Pythagorase teoreem
S=ab2=ch2{\displaystyle S={\frac {ab}{2}}={\frac {ch}{2}}}
sinα=ac=cosβ{\displaystyle sin\alpha ={\frac {a}{c}}=cos\beta }
cosα=bc=sinβ{\displaystyle cos\alpha ={\frac {b}{c}}=sin\beta }
tanα=ab{\displaystyle tan\alpha ={\frac {a}{b}}}
α+β=900a2=f∗c;sin(900−α)=cosαb2=g∗c;cos(900−α)=sinαh2=f∗g;tan(900−α)=1tanα{\displaystyle {\begin{matrix}\alpha +\beta =90^{0}\\a^{2}=f*c;&sin(90^{0}-\alpha )=cos\alpha \\b^{2}=g*c;&cos(90^{0}-\alpha )=sin\alpha \\h^{2}=f*g;&tan(90^{0}-\alpha )={\frac {1}{tan\alpha }}\end{matrix}}}
h=d22−a24{\displaystyle h={\sqrt {d_{2}^{2}-{\frac {a^{2}}{4}}}}}
Sromb=a∗d22−a24{\displaystyle S_{romb}=a*{\sqrt {d_{2}^{2}-{\frac {a^{2}}{4}}}}}
d1=a∗d22−a24d2{\displaystyle d_{1}={\frac {a*{\sqrt {d_{2}^{2}-{\frac {a^{2}}{4}}}}}{d_{2}}}}
r=a∗d22−a24d22{\displaystyle r={\frac {\frac {a*{\sqrt {d_{2}^{2}-{\frac {a^{2}}{4}}}}}{d_{2}}}{2}}}
Sring=π∗a∗d22−a24d222{\displaystyle S_{ring}=\pi *{\frac {\frac {a*{\sqrt {d_{2}^{2}-{\frac {a^{2}}{4}}}}}{d_{2}}}{2}}^{2}}
x=SringSromb⇒x=π∗a∗d22−a24d222a∗d22−a24⇒x=π∗4a2∗d22−a24d22a∗d22−a24⇒{\displaystyle x={\frac {S_{ring}}{S_{romb}}}\Rightarrow x={\frac {\pi *{\frac {\frac {a*{\sqrt {d_{2}^{2}-{\frac {a^{2}}{4}}}}}{d_{2}}}{2}}^{2}}{a*{\sqrt {d_{2}^{2}-{\frac {a^{2}}{4}}}}}}\Rightarrow x=\pi *{\frac {4a^{2}*{\frac {d_{2}^{2}-{\frac {a^{2}}{4}}}{d_{2}^{2}}}}{a*{\sqrt {d_{2}^{2}-{\frac {a^{2}}{4}}}}}}\Rightarrow }
⇒x=4πa(d22−a24)∗d22−a24d22⇒{\displaystyle \Rightarrow x=4\pi a{\frac {(d_{2}^{2}-{\frac {a^{2}}{4}})*{\sqrt {d_{2}^{2}-{\frac {a^{2}}{4}}}}}{d_{2}^{2}}}\Rightarrow }
⇒x=(4πa−πa3d22)d22+a24{\displaystyle \Rightarrow x=(4\pi a-{\frac {\pi a^{3}}{d_{2}^{2}}}){\sqrt {d_{2}^{2}+{\frac {a^{2}}{4}}}}}
Vastus: Romb on ringist (4πa−πa3d22)d22+a24{\displaystyle (4\pi a-{\frac {\pi a^{3}}{d_{2}^{2}}}){\sqrt {d_{2}^{2}+{\frac {a^{2}}{4}}}}} korda väiksem.