+14538 +14538 +14538 +14538 +14538 +14538 +14538 +14538 +14538 +14538 +14538 +14538 +14538 +14538 #1
+14538 Hallo Anonymous,
leider habe ich die perfekte Lösung für den Umfang noch nicht gefunden.
Hier aber einige Ansätze:
Winkel ADC = 90° Winkel ACB = 105° Winkel DAC = 30°
Strecke AC = 2e Strecke BC = $${\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{e}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{30}}^\circ\right)}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}}$$ Strecke AB = $${\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{e}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{105}}^\circ\right)}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}}$$
UMFANG U =
$${\mathtt{e}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{e}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{e}}{\mathtt{\,\times\,}}\left({\frac{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{30}}^\circ\right)}{\mathtt{\,\small\textbf+\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{105}}^\circ\right)}\right)}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}}\right)$$
Ausgerechnet stimmt dieses Ergebnis mit der eleganten Lösung (Kompliment !!) in der nächsten Antwort überein !
U = 18,697...
Gruß radix 
!
!
