Kohtisuoruus

Euklidisessa geometriassa suorat ovat kohtisuorassa, jos niiden leikkauskulma on 90 astetta.[1] Yleisemmin kohtisuoruus on määritelty kaikissa sisätuloavaruuksissa siten, että kaksi vektoria on keskenään kohtisuorassa, jos niiden sisätulo on nolla.

Kohtisuoran suoran piirtäminen

Euklidisessa geometriassa suoralle voi piirtää sitä kohtisuoraan leikkaavan suoran (joita on äärettömästi) seuraavasti:

  1. Valitaan suoralta mielivaltainen piste p1.
  2. Käytetään pistettä p1 mielivaltaisen kokoisen ympyrän y1 keskipisteenä.
  3. Käytetään ympyrän y1 kehän ja suoran leikkauspisteitä kahden uuden, samankokoisen, mutta säteeltään ympyrää y1 suuremman ympyrän keskipisteinä.
  4. Piirretään kahden uuden ympyrän kehän leikkauspisteiden läpi uusi suora, joka kulkee myös pisteen p1 läpi.
  5. Näin syntynyt suora on kohtisuora alkuperäistä suoraa vastaan.

Kahden uuden ympyrän leikkauspisteet ovat siis pisteet, jotka kaikista yhtä kaukana pisteestä p1 olevista pisteistä ovat kauimpana myös muista suoran pisteistä.

Yllä kuvatun esimerkin pitäisi (?) toimia myös muussa kuin euklidisessa geometriassa (sillä varauksella, että geometriset muodot vaihdetaan kyseisen tapauksen vastaaviksi).

Katso myös

Lähteet

  1. ↑ Kivelä, Simo K.: Algebra ja geometria, s. 101. Helsinki: Otatieto, 1989. ISBN 951-672-103-6


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