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→Achteck
Ralph (Diskussion | Beiträge) |
Ralph (Diskussion | Beiträge) |
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| Zeile 1: | Zeile 1: | ||
== Achteck == | == Achteck == | ||
Inkreisradius | === Inkreisradius === | ||
<math> r_i = a \ \frac{1}{2} (1+ \sqrt{2}) </math> | <math> r_i = a \ \frac{1}{2} (1+ \sqrt{2}) </math> | ||
| Zeile 7: | Zeile 7: | ||
<math> a = 2 r_i \ (\sqrt{2}-1) </math> | <math> a = 2 r_i \ (\sqrt{2}-1) </math> | ||
Umkreisradius | === Umkreisradius === | ||
<math> r_u = a \ \frac{1}{2} \sqrt{4 + 2\sqrt{2}} </math> | <math> r_u = a \ \frac{1}{2} \sqrt{4 + 2\sqrt{2}} </math> | ||
| Zeile 14: | Zeile 14: | ||
<math> a = r_u \ \sqrt{2 - \sqrt{2}} </math> | <math> a = r_u \ \sqrt{2 - \sqrt{2}} </math> | ||
=== Große Diagonale === | |||
<math> d_1 = a \ \sqrt{4 + 2\sqrt{2}} \ = \ 2 r_u </math> | |||
=== Mittlere Diagonale === | |||
<math> d_2 = a \ (1 + \sqrt{2}) \ = \ 2 r_i</math> | |||
=== Kleine Diagonale === | |||
<math> d_3 = a \ \sqrt{2 + \sqrt{2}} \ = \ r_u \, \sqrt{2} </math> | |||
=== Zentriwinkel === | |||
<math> \alpha = \frac{360^\circ}{8} = 45^\circ </math> | |||
=== Innenwinkel === | |||
|<math> \delta = 180^\circ - \alpha = 135^\circ </math> | |||
<math> \cos \delta = \frac{-1}{\sqrt{2}} </math> | |||
=== Flächeninhalt === | |||
<math> A = a^2 \ (2+ 2 \sqrt{2})</math> | |||
<math> A = r_u^2 \ 2 \sqrt{2}</math> | |||