Tasakulmainen monikulmio

Tasakulmainen monikulmio on geometriassa monikulmio, joka kaikki kulmat ovat yhtä suuret.[1] Jos vielä sivutkin ovat yhtä pitkät, on kyseessä säännöllinen monikulmio.[2][3]

Tasakulmaiset monikulmiot perivät kaikki yleisen monikulmion ominaisuudet, mutta tasakulmaisuudesta seuraa esimerkiksi seuraava ominaisuus. Konveksin monikulmion kulmien summa saadaan määritettyä jakamalla monikulmio osakolmioihin. Niitä saadaan n-kulmiolle, jossa on n kappaletta kulmaa, aina n - 2 kappaletta. Jokaisen kolmion kulmien summa on 180°, joten n-kulmion kulmien summa on

Koska tasakulmaisessa n-kulmiossa kaikki kulmat ovat samoja, antaa tämä yhdelle sisäkulmalle

Esimerkkejä

Seuraavat esimerkit ovat konvekseja monikulmioita. Sallimalla sellaisia kulmia, jotka "kääntyvät sisäalueen ulkopuolelle", kasvaa variaatioiden lukumäärä suuresti.

Kolmio

Kolmiossa sisäkulmien summa on 180°. Jokaiselle kulmalle riittää siitä 60°. Johtuen kolmion yksinkertaisesta rakenteesta, on tämän muotoisia kolmioita vain yksi. Tasasivuinen kolmio on tasakulmaisena myös säännöllinen kolmio.[4]

  • Tasasivuinen kolmio
    Tasasivuinen kolmio
  • Suorakulmio
    Suorakulmio
  • Neliö
    Neliö

Nelikulmio

Konveksissa nelikulmiossa sisäkulmien summa on 360° ja se jaettuna neljälle kulmalle antaa sisäkulmaksi 90°. Näitä kutsutaan suorakulmaisiksi nelikulmioiksi eli suorakulmioiksi, koska niillä on vain suoria kulmia. Sellainen suorakulmio, jonka sivut ovat saman pituisia, kutsutaan neliöksi ja se on siten säännöllinen nelikulmio.

Mielenkiintoinen poikkeus syntyy ajatuksesta, että yksi kulma olisi 270°. Silloin muidenkin kulmien olisi oltava sama 270° ja kuvioksi syntyy "nurinkurinen" suorakulmio.

Viisikulmio

Konveksissa viisikulmiossa sisäkulmien summa on 540°, joka antaa kulmille 108°.

  • Säännöllinen viisikulmio
    Säännöllinen viisikulmio
  • Tasakulmainen viisikulmio
    Tasakulmainen viisikulmio

Kuusikulmio

Konveksissa kuusikulmiossa sisäkulmien summa on 720°, joka antaa kulmille 120°.

  • Säännöllinen kuusikulmio
    Säännöllinen kuusikulmio
  • Itseään leikkaava tasakulmainen kuusikulmio.
    Itseään leikkaava tasakulmainen kuusikulmio.

Lähteet

Viitteet

  1. ↑ Weisstein, Eric W.: Equiangular Polygon (Math World – A Wolfram Web Resource) Wolfram Research. (englanniksi)
  2. ↑ Weisstein, Eric W.: Equilateral Polygon (Math World – A Wolfram Web Resource) Wolfram Research. (englanniksi)
  3. ↑ Weisstein, Eric W.: Regular Polygon (Math World – A Wolfram Web Resource) Wolfram Research. (englanniksi)
  4. ↑ Weisstein, Eric W.: Equilateral Triangle (Math World – A Wolfram Web Resource) Wolfram Research. (englanniksi)

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