regular pentagon (Q7812): Difference between revisions

@@ Property / has quality @@
+area of plane shape
@@ Property / has quality: area of plane shape / rank @@
+Normal rank
@@ Property / has quality: area of plane shape / qualifier @@
+defining formula:  $A={\frac {5}{4}}t^{2}\mathop {\mathrm {ctg} } \,{\frac {\pi }{5}}={\frac {{\sqrt {5}}{\sqrt {5+2{\sqrt {5}}}}}{4}}t^{2}={\frac {5}{12}}Rd$ 
A=\frac{5}{4} t^2 \mathop{\mathrm{ctg}}\, \frac{\pi}{5} = \frac{\sqrt 5 \sqrt{5 + 2 \sqrt{5}}}{4} t^2 = \frac{5}{12}Rd
@@ Property / has quality @@
+inradius
@@ Property / has quality: inradius / rank @@
+Normal rank
@@ Property / has quality: inradius / qualifier @@
+defining formula:  $r={\frac {t}{2\tan(\pi /5)}}={\frac {t}{2{\sqrt {5-{\sqrt {20}}}}}}$ 
r=\frac{t}{2\tan ( \pi /5)}=\frac{t}{2\sqrt{5-\sqrt{20}}}
@@ Property / has quality @@
+circumradius
@@ Property / has quality: circumradius / rank @@
+Normal rank
@@ Property / has quality: circumradius / qualifier @@
+defining formula:  $R={\frac {a}{2}}\csc {\frac {\pi }{5}}$ 
R = \frac{a}{2}\csc\frac\pi{5}

Latest revision as of 22:25, 30 April 2023